Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: √32 simplified
Before any working — hunt first
Given
Numbers and units already in the sentence: 32 simplified. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: √32 simplified. Circle that word — that is the missing variable.
Find
We are required to find: √32 simplified. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: √(16×2)=4√2. Then substitute the given, one line at a time, to get √32 simplified.
In other words — as if you have never seen this before
If you have never seen this before: √(16×2)=4√2. We will name a method in words, write the formula with no numbers, then substitute one line at a time.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 32 simplified. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
√16×2=4√2.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 32 simplified. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: √32 simplified. Circle that word — that is the missing variable.
Find: We are required to find: √32 simplified. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: √(16×2)=4√2. Then substitute the given, one line at a time, to get √32 simplified.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 32 simplified. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
√16×2=4√2.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Reason
√16×2=4√2.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
4√2
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
4√2
Copy onto your answer sheet — in this order
Answer: 4√2
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
1.2 · 10 Marks · Quadratic equations & nature of roots
Nature of roots of x² + 4x + 4 = 0
Formulas
Δ=b²−4ac
Discriminant
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Nature of roots of x² + 4x + 4 = 0
Before any working — hunt first
Given
Numbers and units already in the sentence: 4x · 4 · 0. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Nature of roots of x² + 4x + 4 = 0. Circle that word — that is the missing variable.
Find
We are required to find: Nature of roots of x² + 4x + 4 = 0. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Δ=0, perfect square. Then substitute the given, one line at a time, to get Nature of roots of x² + 4x + 4 = 0.
In other words — as if you have never seen this before
If you have never seen this before: Δ=0, perfect square. We will name a method in words, write the formula with no numbers, then substitute one line at a time.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 4x · 4 · 0. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Δ=0, perfect square.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 4x · 4 · 0. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Nature of roots of x² + 4x + 4 = 0. Circle that word — that is the missing variable.
Find: We are required to find: Nature of roots of x² + 4x + 4 = 0. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Δ=0, perfect square. Then substitute the given, one line at a time, to get Nature of roots of x² + 4x + 4 = 0.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 4x · 4 · 0. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Δ=0, perfect square.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Reason
Δ=0, perfect square.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
real, rational, equal
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
real, rational, equal
Copy onto your answer sheet — in this order
Answer: real, rational, equal
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
2.1 · 12 Marks · Identities, reduction & equations
sin θ = √32 in [0°; 180°]
Identities, reduction & equations
Formulas
sin²θ+cos²θ=1
Pythagorean identity
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: sin θ = √32 in [0°; 180°]
Before any working — hunt first
Given
Numbers and units already in the sentence: 3/ · 2 in · 0° · 180°. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: sin θ = √32 in [0°; 180°]. Circle that word — that is the missing variable.
Find
We are required to find: sin θ = √32 in [0°; 180°]. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Q1 and Q2. Then substitute the given, one line at a time, to get sin θ = √32 in [0°; 180°].
In other words — as if you have never seen this before
If you have never seen this before: Q1 and Q2. We will name a method in words, write the formula with no numbers, then substitute one line at a time.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 3/ · 2 in · 0° · 180°. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Q1 and Q2.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 3/ · 2 in · 0° · 180°. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: sin θ = √32 in [0°; 180°]. Circle that word — that is the missing variable.
Find: We are required to find: sin θ = √32 in [0°; 180°]. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Q1 and Q2. Then substitute the given, one line at a time, to get sin θ = √32 in [0°; 180°].
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 3/ · 2 in · 0° · 180°. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Q1 and Q2.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Reason
Q1 and Q2.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
60° and 120°
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
60° and 120°
Copy onto your answer sheet — in this order
Answer: 60° and 120°
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
2.2 · 12 Marks · Parabola, hyperbola & exponential
TP of y = −(x+3)² + 1
Parabola, hyperbola & exponential
Formulas
y=a(x + p)²+q
Shifted parabola
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: TP of y = −(x+3)² + 1
Before any working — hunt first
Given
Numbers and units already in the sentence: 3 · 1. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: TP of y = −(x+3)² + 1. Circle that word — that is the missing variable.
Find
We are required to find: TP of y = −(x+3)² + 1. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: a(x−(−3))²+1. Then substitute the given, one line at a time, to get TP of y = −(x+3)² + 1.
In other words — as if you have never seen this before
If you have never seen this before: a(x−(−3))²+1. We will name a method in words, write the formula with no numbers, then substitute one line at a time.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 3 · 1. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
a(x−(−3))²+1.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 3 · 1. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: TP of y = −(x+3)² + 1. Circle that word — that is the missing variable.
Find: We are required to find: TP of y = −(x+3)² + 1. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: a(x−(−3))²+1. Then substitute the given, one line at a time, to get TP of y = −(x+3)² + 1.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 3 · 1. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
a(x−(−3))²+1.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Reason
a(x−(−3))²+1.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
(−3; 1)
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
(−3; 1)
Copy onto your answer sheet — in this order
Answer: (−3; 1)
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
3.1 · 14 Marks · Nominal vs effective interest
12% p.a. compounded monthly. Periods per year m =
Nominal vs effective interest
Formulas
1+ieff=(1 + inom/m)m
Effective rate
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: 12% p.a. compounded monthly. Periods per year m =
Before any working — hunt first
Given
Numbers and units already in the sentence: 12%. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Periods per year m =. Circle that word — that is the missing variable.
Find
We are required to find: Periods per year m =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Monthly. Then substitute the given, one line at a time, to get Periods per year m =.
In other words — as if you have never seen this before
If you have never seen this before: Monthly → 12. We will name a method in words, write the formula with no numbers, then substitute one line at a time.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 12%. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Monthly → 12.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 12%. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Periods per year m =. Circle that word — that is the missing variable.
Find: We are required to find: Periods per year m =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Monthly. Then substitute the given, one line at a time, to get Periods per year m =.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 12%. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Monthly → 12.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Reason
Monthly → 12.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
12
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
12
Copy onto your answer sheet — in this order
Answer: 12
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
3.2 · 14 Marks · Proportion & midpoint theorem
Angle at circumference is 36°. Angle at centre on same arc
Proportion & midpoint theorem
Formulas
DE ∥ BC, AD=DB⇒AE=EC
Midpoint theorem
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Angle at circumference is 36°. Angle at centre on same arc
Before any working — hunt first
Given
Numbers and units already in the sentence: 36°. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Angle at centre on same arc. Circle that word — that is the missing variable.
Find
We are required to find: Angle at centre on same arc. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Double. Then substitute the given, one line at a time, to get Angle at centre on same arc.
In other words — as if you have never seen this before
If you have never seen this before: Double. We will name a method in words, write the formula with no numbers, then substitute one line at a time.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 36°. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Double.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 36°. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Angle at centre on same arc. Circle that word — that is the missing variable.
Find: We are required to find: Angle at centre on same arc. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Double. Then substitute the given, one line at a time, to get Angle at centre on same arc.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 36°. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Double.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Reason
Double.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
72°
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
72°
Copy onto your answer sheet — in this order
Answer: 72°
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
7 · 2 Marks · Quadratic equations & nature of roots
If second differences are constant, the pattern is
Formulas
Δ=b²−4ac
Discriminant
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: If second differences are constant, the pattern is
In other words — as if you have never seen this before
Constant second difference ⇒ quadratic.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Constant second difference ⇒ quadratic.
4. Step-by-step working
01 / 07
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 07
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
03 / 07
Step C — Name the method in words
Constant second difference ⇒ quadratic.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
04 / 07
Working
Constant second difference ⇒ quadratic.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
05 / 07
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
06 / 07
Step F — Box the answer with its unit
quadratic
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
07 / 07
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
quadratic
Copy onto your answer sheet — in this order
Answer: quadratic
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
8 · 2 Marks · Exponents & surds
√18 simplified
Exponents & surds
Formulas
am/ⁿ=ⁿ√aᵐ
Rational exponent
√a·√b=√ab
Product of surds
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: √18 simplified
Before any working — hunt first
Given
Numbers and units already in the sentence: 18 simplified. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: √18 simplified. Circle that word — that is the missing variable.
Find
We are required to find: √18 simplified. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: √(9×2)=3√2. Then substitute the given, one line at a time, to get √18 simplified.
In other words — as if you have never seen this before
√9×2=3√2.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 18 simplified. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
√9×2=3√2.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 18 simplified. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: √18 simplified. Circle that word — that is the missing variable.
Find: We are required to find: √18 simplified. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: √(9×2)=3√2. Then substitute the given, one line at a time, to get √18 simplified.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 18 simplified. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
√9×2=3√2.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
√9×2=3√2.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
3√2
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
3√2
Copy onto your answer sheet — in this order
Answer: 3√2
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
9 · 4 Marks · Variance, ogives & five-number summary
Outlier fence: values below Q1 − 1.5 IQR
Variance, ogives & five-number summary
Formulas
x̄=Σxn
Mean
σ²=Σ(x − x̄)²n
Population variance (CAPS uses n)
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Outlier fence: values below Q1 − 1.5 IQR
Before any working — hunt first
Given
Numbers and units already in the sentence: 1 · 1.5 IQR. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: 5 IQR. Circle that word — that is the missing variable.
Find
We are required to find: 5 IQR. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 1. Then substitute the given, one line at a time, to get 5 IQR.
In other words — as if you have never seen this before
1.5×IQR rule.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1 · 1.5 IQR. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
1.5×IQR rule.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 1 · 1.5 IQR. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: 5 IQR. Circle that word — that is the missing variable.
Find: We are required to find: 5 IQR. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 1. Then substitute the given, one line at a time, to get 5 IQR.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 1 · 1.5 IQR. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
1.5×IQR rule.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
1.5×IQR rule.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
are outliers
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
are outliers
Copy onto your answer sheet — in this order
Answer: are outliers
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
10 · 3 Marks · Sine, cosine & area rules
In △ABC, A = 30°, a = 5, B = 45°. b =
Formulas
asin A=bsin B=csin C=2R
Sine rule
c²=a²+b²−2ab cos C
Cosine rule
Area=½ ab sin C
Area rule
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: In △ABC, A = 30°, a = 5, B = 45°. b =
Before any working — hunt first
Given
Numbers and units already in the sentence: 30° · 5 · 45°. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: b =. Circle that word — that is the missing variable.
Find
We are required to find: b =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: bsin45=5sin30. Then substitute the given, one line at a time, to get b =.
In other words — as if you have never seen this before
bsin45=5sin30→b=5×(√2/2)(1/2)=5√2.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 30° · 5 · 45°. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
bsin45=5sin30→b=5×(√2/2)(1/2)=5√2.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 30° · 5 · 45°. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: b =. Circle that word — that is the missing variable.
Find: We are required to find: b =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: bsin45=5sin30. Then substitute the given, one line at a time, to get b =.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 30° · 5 · 45°. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
bsin45=5sin30→b=5×(√2/2)(1/2)=5√2.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
bsin45=5sin30→b=5×(√2/2)(1/2)=5√2.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
5√2
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
5√2
Copy onto your answer sheet — in this order
Answer: 5√2
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
11 · 3 Marks · Proportion & midpoint theorem
Midpoints of two sides of a triangle are joined. The third side is 10 cm. The join is
Proportion & midpoint theorem
Formulas
DE ∥ BC, AD=DB⇒AE=EC
Midpoint theorem
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Midpoints of two sides of a triangle are joined. The third side is 10 cm. The join is
Before any working — hunt first
Given
Numbers and units already in the sentence: 10 cm. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: The join is. Circle that word — that is the missing variable.
Find
We are required to find: The join is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Midpoint theorem: half the third side. Then substitute the given, one line at a time, to get The join is.
In other words — as if you have never seen this before
Midpoint theorem: half the third side.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 10 cm. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Midpoint theorem: half the third side.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 10 cm. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: The join is. Circle that word — that is the missing variable.
Find: We are required to find: The join is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Midpoint theorem: half the third side. Then substitute the given, one line at a time, to get The join is.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 10 cm. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Midpoint theorem: half the third side.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Midpoint theorem: half the third side.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
5 cm
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
5 cm
Copy onto your answer sheet — in this order
Answer: 5 cm
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
12 · 3 Marks · Nominal vs effective interest
12% p.a. compounded monthly. Monthly interest rate i =
Nominal vs effective interest
Formulas
1+ieff=(1 + inom/m)m
Effective rate
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: 12% p.a. compounded monthly. Monthly interest rate i =
Before any working — hunt first
Given
Numbers and units already in the sentence: 12%. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Monthly interest rate i =. Circle that word — that is the missing variable.
Find
We are required to find: Monthly interest rate i =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: i = 0. Then substitute the given, one line at a time, to get Monthly interest rate i =.
In other words — as if you have never seen this before
i=0.1212=0.01.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 12%. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
i=0.1212=0.01.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 12%. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Monthly interest rate i =. Circle that word — that is the missing variable.
Find: We are required to find: Monthly interest rate i =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: i = 0. Then substitute the given, one line at a time, to get Monthly interest rate i =.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 12%. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
i=0.1212=0.01.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
i=0.1212=0.01.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
0.01
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
0.01
Copy onto your answer sheet — in this order
Answer: 0.01
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
13 · 3 Marks · Proportion & midpoint theorem
Angle at the centre is 80°. Angle at the circumference on the same arc is
Proportion & midpoint theorem
Formulas
DE ∥ BC, AD=DB⇒AE=EC
Midpoint theorem
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Angle at the centre is 80°. Angle at the circumference on the same arc is
In other words — as if you have never seen this before
Angle at circumference is half the angle at the centre.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 80°. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Angle at circumference is half the angle at the centre.
4. Step-by-step working
01 / 07
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 07
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 80°. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
03 / 07
Step C — Name the method in words
Angle at circumference is half the angle at the centre.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
04 / 07
Working
Angle at circumference is half the angle at the centre.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
05 / 07
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
06 / 07
Step F — Box the answer with its unit
40°
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
07 / 07
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
40°
Copy onto your answer sheet — in this order
Answer: 40°
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
14 · 3 Marks · Identities, reduction & equations
sin(180°−θ)=
Identities, reduction & equations
Formulas
sin²θ+cos²θ=1
Pythagorean identity
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: sin(180°−θ) =
Before any working — hunt first
Given
Numbers and units already in the sentence: 180°. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: sin(180°−θ) =. Circle that word — that is the missing variable.
Find
We are required to find: sin(180°−θ) =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Reduction: Q2 sine is positive. Then substitute the given, one line at a time, to get sin(180°−θ) =.
In other words — as if you have never seen this before
Reduction: Q2 sine is positive.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 180°. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Reduction: Q2 sine is positive.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 180°. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: sin(180°−θ) =. Circle that word — that is the missing variable.
Find: We are required to find: sin(180°−θ) =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Reduction: Q2 sine is positive. Then substitute the given, one line at a time, to get sin(180°−θ) =.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 180°. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Reduction: Q2 sine is positive.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Reduction: Q2 sine is positive.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
sin θ
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
sin θ
Copy onto your answer sheet — in this order
Answer: sin θ
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
15 · 2 Marks · Sine, cosine & area rules
cos θ = 12 in [0°; 360°]. Solutions:
Formulas
asin A=bsin B=csin C=2R
Sine rule
c²=a²+b²−2ab cos C
Cosine rule
Area=½ ab sin C
Area rule
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: cos θ = 12 in [0°; 360°]. Solutions:
Before any working — hunt first
Given
Numbers and units already in the sentence: 1/ · 2 in · 0° · 360°. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Solutions:. Circle that word — that is the missing variable.
Find
We are required to find: Solutions:. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: CAST: cosine positive in Q1 and Q4. Then substitute the given, one line at a time, to get Solutions:.
In other words — as if you have never seen this before
CAST: cosine positive in Q1 and Q4.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1/ · 2 in · 0° · 360°. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
CAST: cosine positive in Q1 and Q4.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 1/ · 2 in · 0° · 360°. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Solutions:. Circle that word — that is the missing variable.
Find: We are required to find: Solutions:. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: CAST: cosine positive in Q1 and Q4. Then substitute the given, one line at a time, to get Solutions:.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 1/ · 2 in · 0° · 360°. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
CAST: cosine positive in Q1 and Q4.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
CAST: cosine positive in Q1 and Q4.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
60° and 300°
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
60° and 300°
Copy onto your answer sheet — in this order
Answer: 60° and 300°
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
16 · 3 Marks · Identities, reduction & equations
tan 45°=
Identities, reduction & equations
Formulas
sin²θ+cos²θ=1
Pythagorean identity
Notes: Special angle 45°.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: tan 45° =
Before any working — hunt first
Given
Numbers and units already in the sentence: 45°. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: tan 45° =. Circle that word — that is the missing variable.
Find
We are required to find: tan 45° =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write 1 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives tan 45° =.
In other words — as if you have never seen this before
At 45°, opposite = adjacent, so tan = 1.
2. What do we already know?
Special angle 45°.
3. Which method — and why this one?
At 45°, opposite = adjacent, so tan = 1.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 45°. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: tan 45° =. Circle that word — that is the missing variable.
Find: We are required to find: tan 45° =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: Write 1 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives tan 45° =.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Special angle 45°.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
At 45°, opposite = adjacent, so tan = 1.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Isosceles right triangle
oppadj=11=1.
1
Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
1
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
1
Copy onto your answer sheet — in this order
Formula: 1
Answer: 1
6. Check it like a marker
sin 45 = cos 45, so their ratio is 1.
7. A trap first-timers fall into
undefined is tan 90°. 45° is safe.
17 · 3 Marks · Nominal vs effective interest
12% p.a. compounded quarterly. i per period =
Nominal vs effective interest
Formulas
1+ieff=(1 + inom/m)m
Effective rate
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: 12% p.a. compounded quarterly. i per period =
Before any working — hunt first
Given
Numbers and units already in the sentence: 12%. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: i per period =. Circle that word — that is the missing variable.
Find
We are required to find: i per period =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 0. Then substitute the given, one line at a time, to get i per period =.
In other words — as if you have never seen this before
0.03
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 12%. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
0.03
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 12%. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: i per period =. Circle that word — that is the missing variable.
Find: We are required to find: i per period =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 0. Then substitute the given, one line at a time, to get i per period =.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 12%. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
0.03
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Reason
m=4. 0.124=0.03.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
0.03
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
0.03
Copy onto your answer sheet — in this order
Answer: 0.03
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
18 · 2 Marks · Quadratic equations & nature of roots
Nature of roots of x² + 6x + 9 = 0
Formulas
Δ=b²−4ac
Discriminant
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Nature of roots of x² + 6x + 9 = 0
Before any working — hunt first
Given
Numbers and units already in the sentence: 6x · 9 · 0. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Nature of roots of x² + 6x + 9 = 0. Circle that word — that is the missing variable.
Find
We are required to find: Nature of roots of x² + 6x + 9 = 0. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: real, rational, equal. Then substitute the given, one line at a time, to get Nature of roots of x² + 6x + 9 = 0.
In other words — as if you have never seen this before
real, rational, equal
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 6x · 9 · 0. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
real, rational, equal
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 6x · 9 · 0. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Nature of roots of x² + 6x + 9 = 0. Circle that word — that is the missing variable.
Find: We are required to find: Nature of roots of x² + 6x + 9 = 0. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: real, rational, equal. Then substitute the given, one line at a time, to get Nature of roots of x² + 6x + 9 = 0.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 6x · 9 · 0. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
real, rational, equal
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Δ = 36 − 36 = 0. Equal real rational roots; it is a perfect square (x+3)².
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
real, rational, equal
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
real, rational, equal
Copy onto your answer sheet — in this order
Answer: real, rational, equal
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
19 · 2 Marks · Parabola, hyperbola & exponential
y = 2^x. y when x = 3
Parabola, hyperbola & exponential
Formulas
y=a(x + p)²+q
Shifted parabola
Notes: Exponential base 2. x=3.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: y = 2^x. y when x = 3
Before any working — hunt first
Given
Numbers and units already in the sentence: 2 · 3. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: y when x = 3. Circle that word — that is the missing variable.
Find
We are required to find: y when x = 3. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write 8 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives y when x = 3.
In other words — as if you have never seen this before
2x means multiply 2, x times. 2³=8, not 2×3.
2. What do we already know?
Exponential base 2. x=3.
3. Which method — and why this one?
2x means multiply 2, x times. 2³=8, not 2×3.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 2 · 3. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: y when x = 3. Circle that word — that is the missing variable.
Find: We are required to find: y when x = 3. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: Write 8 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives y when x = 3.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Exponential base 2. x=3.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
2x means multiply 2, x times. 2³=8, not 2×3.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Expand
2×2×2=8.
8
Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
8
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
8
Copy onto your answer sheet — in this order
Formula: 8
Answer: 8
6. Check it like a marker
Table: x=0 →1, x=1 →2, x=2 →4, x=3 →8.
7. A trap first-timers fall into
6 is 2×3. Exponents are not multiplication.
20 · 3 Marks · Inclination & circles
TP of y = 2(x − 4)² + 1
Formulas
tan θ=m
Inclination
(x − a)²+(y − b)²=r²
Circle centre (a;b)
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: TP of y = 2(x − 4)² + 1
Before any working — hunt first
Given
Numbers and units already in the sentence: 2 · 4 · 1. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: TP of y = 2(x − 4)² + 1. Circle that word — that is the missing variable.
Find
We are required to find: TP of y = 2(x − 4)² + 1. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: (4; 1). Then substitute the given, one line at a time, to get TP of y = 2(x − 4)² + 1.
In other words — as if you have never seen this before
(4; 1)
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2 · 4 · 1. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
(4; 1)
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 2 · 4 · 1. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: TP of y = 2(x − 4)² + 1. Circle that word — that is the missing variable.
Find: We are required to find: TP of y = 2(x − 4)² + 1. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: (4; 1). Then substitute the given, one line at a time, to get TP of y = 2(x − 4)² + 1.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 2 · 4 · 1. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
(4; 1)
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Form a(x − p)² + q has turning point (p; q) = (4; 1). The 2 stretches, it does not move the point.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
(4; 1)
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
(4; 1)
Copy onto your answer sheet — in this order
Answer: (4; 1)
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
21 · 3 Marks · Proportion & midpoint theorem
Angle at centre 120°. Angle at circumference on same arc
Proportion & midpoint theorem
Formulas
DE ∥ BC, AD=DB⇒AE=EC
Midpoint theorem
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Angle at centre 120°. Angle at circumference on same arc
Before any working — hunt first
Given
Numbers and units already in the sentence: 120°. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Angle at circumference on same arc. Circle that word — that is the missing variable.
Find
We are required to find: Angle at circumference on same arc. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 60°. Then substitute the given, one line at a time, to get Angle at circumference on same arc.
In other words — as if you have never seen this before
60°
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 120°. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
60°
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 120°. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Angle at circumference on same arc. Circle that word — that is the missing variable.
Find: We are required to find: Angle at circumference on same arc. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 60°. Then substitute the given, one line at a time, to get Angle at circumference on same arc.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 120°. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
60°
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Theorem: angle at the circumference is half the angle at the centre, standing on the same arc.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
60°
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
60°
Copy onto your answer sheet — in this order
Answer: 60°
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
22 · 2 Marks · Parabola, hyperbola & exponential
x² − 5x + 6 < 0. Solution is
Parabola, hyperbola & exponential
Formulas
y=a(x + p)²+q
Shifted parabola
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: x² − 5x + 6 < 0. Solution is
Before any working — hunt first
Given
Numbers and units already in the sentence: 5x · 6 · 0. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Solution is. Circle that word — that is the missing variable.
Find
We are required to find: Solution is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Smile-parabola negative between roots 2 and 3. Then substitute the given, one line at a time, to get Solution is.
In other words — as if you have never seen this before
Smile-parabola negative between roots 2 and 3.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 5x · 6 · 0. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Smile-parabola negative between roots 2 and 3.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 5x · 6 · 0. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Solution is. Circle that word — that is the missing variable.
Find: We are required to find: Solution is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Smile-parabola negative between roots 2 and 3. Then substitute the given, one line at a time, to get Solution is.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 5x · 6 · 0. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Smile-parabola negative between roots 2 and 3.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Smile-parabola negative between roots 2 and 3.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
(2; 3)
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
(2; 3)
Copy onto your answer sheet — in this order
Answer: (2; 3)
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
23 · 2 Marks
2⁴=
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: 2⁴ =
Before any working — hunt first
Given
Numbers and units already in the sentence: 2. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: 2⁴ =. Circle that word — that is the missing variable.
Find
We are required to find: 2⁴ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 2×2×2×2 = 16. Then substitute the given, one line at a time, to get 2⁴ =.
In other words — as if you have never seen this before
2×2×2×2=16.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
2×2×2×2=16.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 2. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: 2⁴ =. Circle that word — that is the missing variable.
Find: We are required to find: 2⁴ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 2×2×2×2 = 16. Then substitute the given, one line at a time, to get 2⁴ =.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 2. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
2×2×2×2=16.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
2×2×2×2=16.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
16
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
16
Copy onto your answer sheet — in this order
Answer: 16
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
24 · 4 Marks · Dependent events & Venn
P(A)=0.3, P(B)=0.4, independent. P(A and B) =
Formulas
P(A ∪ B)=P(A)+P(B)−P(A ∩ B)
Addition rule
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: P(A)=0.3, P(B)=0.4, independent. P(A and B) =
Before any working — hunt first
Given
Numbers and units already in the sentence: 0.3 · 0.4. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: P(A and B) =. Circle that word — that is the missing variable.
Find
We are required to find: P(A and B) =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Independent: P(A∩B)=P(A)P(B)=0. Then substitute the given, one line at a time, to get P(A and B) =.
In other words — as if you have never seen this before
Independent: P(A∩B)=P(A)P(B)=0.12.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 0.3 · 0.4. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Independent: P(A∩B)=P(A)P(B)=0.12.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 0.3 · 0.4. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: P(A and B) =. Circle that word — that is the missing variable.
Find: We are required to find: P(A and B) =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Independent: P(A∩B)=P(A)P(B)=0. Then substitute the given, one line at a time, to get P(A and B) =.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 0.3 · 0.4. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Independent: P(A∩B)=P(A)P(B)=0.12.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Independent: P(A∩B)=P(A)P(B)=0.12.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
0.12
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
0.12
Copy onto your answer sheet — in this order
Answer: 0.12
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
25 · 3 Marks · Parabola, hyperbola & exponential
Turning point of y = (x − 3)² + 2
Parabola, hyperbola & exponential
Formulas
y=a(x + p)²+q
Shifted parabola
Notes: y = (x − 3)² + 2. Completed-squareturning-point form a(x − p)² + q.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Turning point of y = (x − 3)² + 2
Before any working — hunt first
Given
Numbers and units already in the sentence: 3 · 2. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Turning point of y = (x − 3)² + 2. Circle that word — that is the missing variable.
Find
We are required to find: Turning point of y = (x − 3)² + 2. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write TP = (p; q) = (3; 2) with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Turning point of y = (x − 3)² + 2.
In other words — as if you have never seen this before
The turning point is (p; q). Here p = 3 (opposite of the sign inside), q = 2.
2. What do we already know?
y = (x − 3)² + 2. Completed-squareturning-point form a(x − p)² + q.
3. Which method — and why this one?
The turning point is (p; q). Here p = 3 (opposite of the sign inside), q = 2.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 3 · 2. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Turning point of y = (x − 3)² + 2. Circle that word — that is the missing variable.
Find: We are required to find: Turning point of y = (x − 3)² + 2. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: Write TP = (p; q) = (3; 2) with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Turning point of y = (x − 3)² + 2.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
y = (x − 3)² + 2. Completed-squareturning-point form a(x − p)² + q.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
The turning point is (p; q). Here p = 3 (opposite of the sign inside), q = 2.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Read (p; q)
a(x − p)²+q has TP (p; q). We have (x − 3)²+2, so p=3, q=2. TP=(3; 2).
TP=(p; q)=(3; 2)
Why this step: The minus inside the bracket is already “x minus p”. Do not flip 3 into −3 — that is the (x + 3)² story.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
(3; 2)
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
(3; 2)
Copy onto your answer sheet — in this order
Formula: TP=(p; q)=(3; 2)
Answer: (3; 2)
6. Check it like a marker
At x = 3, y = 0 + 2 = 2. Neighbours: x = 2 or 4 give y = 1 + 2 = 3, which is higher, so (3; 2) is a minimum. Good.
7. A trap first-timers fall into
Writing (−3; 2) because “the sign flips”. It already flipped in the form (x − p).
26 · 2 Marks · Inclination & circles
Distance between (0;0) and (3;4)
Formulas
tan θ=m
Inclination
(x − a)²+(y − b)²=r²
Circle centre (a;b)
Notes: A(0;0), B(3;4). Unknown: AB.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Distance between (0;0) and (3;4)
Before any working — hunt first
Given
Numbers and units already in the sentence: 0 · 0 · 3 · 4. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Distance between (0;0) and (3;4). Circle that word — that is the missing variable.
Find
We are required to find: Distance between (0;0) and (3;4). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write 5 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Distance between (0;0) and (3;4).
In other words — as if you have never seen this before
Distance formula is Pythagoras. 3-4-5 triangle.
2. What do we already know?
A(0;0), B(3;4). Unknown: AB.
3. Which method — and why this one?
Distance formula is Pythagoras. 3-4-5 triangle.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 0 · 0 · 3 · 4. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Distance between (0;0) and (3;4). Circle that word — that is the missing variable.
Find: We are required to find: Distance between (0;0) and (3;4). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: Write 5 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Distance between (0;0) and (3;4).
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
A(0;0), B(3;4). Unknown: AB.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Distance formula is Pythagoras. 3-4-5 triangle.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
√(3²+4²)
√9+16=√25=5.
5
Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
5
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
5
Copy onto your answer sheet — in this order
Formula: 5
Answer: 5
6. Check it like a marker
A famous triple. Sketch it.
7. A trap first-timers fall into
3+4=7 adds the legs instead of squaring.
27 · 2 Marks · Quadratic equations & nature of roots
x² − 1 < 0 has solution
Formulas
Δ=b²−4ac
Discriminant
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: x² − 1 < 0 has solution
Before any working — hunt first
Given
Numbers and units already in the sentence: 1 · 0 has. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: x² − 1 < 0 has solution. Circle that word — that is the missing variable.
Find
We are required to find: x² − 1 < 0 has solution. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Negative between the roots of (x−1)(x+1). Then substitute the given, one line at a time, to get x² − 1 < 0 has solution.
In other words — as if you have never seen this before
Negative between the roots of (x−1)(x+1).
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1 · 0 has. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Negative between the roots of (x−1)(x+1).
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 1 · 0 has. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: x² − 1 < 0 has solution. Circle that word — that is the missing variable.
Find: We are required to find: x² − 1 < 0 has solution. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Negative between the roots of (x−1)(x+1). Then substitute the given, one line at a time, to get x² − 1 < 0 has solution.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 1 · 0 has. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Negative between the roots of (x−1)(x+1).
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Negative between the roots of (x−1)(x+1).
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
−1 < x < 1
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
−1 < x < 1
Copy onto your answer sheet — in this order
Answer: −1 < x < 1
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
28 · 2 Marks · Identities, reduction & equations
sin θ = 12 in [0°; 360°]
Identities, reduction & equations
Formulas
sin²θ+cos²θ=1
Pythagorean identity
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: sin θ = 12 in [0°; 360°]
Before any working — hunt first
Given
Numbers and units already in the sentence: 1/ · 2 in · 0° · 360°. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: sin θ = 12 in [0°; 360°]. Circle that word — that is the missing variable.
Find
We are required to find: sin θ = 12 in [0°; 360°]. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 30° and 150°. Then substitute the given, one line at a time, to get sin θ = 12 in [0°; 360°].
In other words — as if you have never seen this before
30° and 150°
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1/ · 2 in · 0° · 360°. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
30° and 150°
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 1/ · 2 in · 0° · 360°. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: sin θ = 12 in [0°; 360°]. Circle that word — that is the missing variable.
Find: We are required to find: sin θ = 12 in [0°; 360°]. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 30° and 150°. Then substitute the given, one line at a time, to get sin θ = 12 in [0°; 360°].
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 1/ · 2 in · 0° · 360°. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
30° and 150°
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Reason
Sine positive Q1 and Q2.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
30° and 150°
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
30° and 150°
Copy onto your answer sheet — in this order
Answer: 30° and 150°
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
29 · 2 Marks · Exponents & surds
√48 simplified
Exponents & surds
Formulas
am/ⁿ=ⁿ√aᵐ
Rational exponent
√a·√b=√ab
Product of surds
Notes: √48. Unknown: simplest surd form (no square factor left under the radical).
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: √48 simplified
Before any working — hunt first
Given
Numbers and units already in the sentence: 48 simplified. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: √48 simplified. Circle that word — that is the missing variable.
Find
We are required to find: √48 simplified. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write 48 = 16 × 3 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives √48 simplified.
In other words — as if you have never seen this before
Pull out the biggest square factor. 48 = 16 × 3, and 16 is 4².
2. What do we already know?
√48. Unknown: simplest surd form (no square factor left under the radical).
3. Which method — and why this one?
Pull out the biggest square factor. 48 = 16 × 3, and 16 is 4².
4. Step-by-step working
01 / 05
Factor 48
48 = 16 × 3, and 16 is a perfect square. (You could use 4 × 12, but then you would simplify again.)
48=16×3
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
02 / 05
Take the square out
√48=√16×3=√16×√3=4√3.
√48=4√3
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
03 / 05
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
04 / 05
Step F — Box the answer with its unit
4√3
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
05 / 05
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
4√3
Copy onto your answer sheet — in this order
Formula: 48=16×3
Answer: 4√3
6. Check it like a marker
4√3 squared: 16 × 3 = 48. Lands back. 16√3 would square to a much bigger number.
7. A trap first-timers fall into
Stopping at √16 × √3 without taking √16. Or writing 3√4, which is not simplified (√4 is still 2).
30 · 2 Marks · Identities, reduction & equations
sin θ = 12 in [0°; 180°]
Identities, reduction & equations
Formulas
sin²θ+cos²θ=1
Pythagorean identity
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: sin θ = 12 in [0°; 180°]
Before any working — hunt first
Given
Numbers and units already in the sentence: 1/ · 2 in · 0° · 180°. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: sin θ = 12 in [0°; 180°]. Circle that word — that is the missing variable.
Find
We are required to find: sin θ = 12 in [0°; 180°]. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 30° and 150°. Then substitute the given, one line at a time, to get sin θ = 12 in [0°; 180°].
In other words — as if you have never seen this before
30° and 150°
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1/ · 2 in · 0° · 180°. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
30° and 150°
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 1/ · 2 in · 0° · 180°. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: sin θ = 12 in [0°; 180°]. Circle that word — that is the missing variable.
Find: We are required to find: sin θ = 12 in [0°; 180°]. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 30° and 150°. Then substitute the given, one line at a time, to get sin θ = 12 in [0°; 180°].
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 1/ · 2 in · 0° · 180°. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
30° and 150°
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Sine is positive in Q1 and Q2. Reference 30°. Q2: 180° − 30° = 150°.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
30° and 150°
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
30° and 150°
Copy onto your answer sheet — in this order
Answer: 30° and 150°
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”