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: Expand (x + 5)(x − 2).
Before any working — hunt first
Given
Numbers and units already in the sentence: 5 · 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: Expand (x + 5)(x − 2). Circle that word — that is the missing variable.
Find
We are required to find: Expand (x + 5)(x − 2). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write x² + 3x − 10 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Expand (x + 5)(x − 2).
In other words — as if you have never seen this before
If you have never seen this before: FOIL: x² − 2x + 5x − 10 = x² + 3x − 10. The middle terms add, they do not cancel. 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: 5 · 2. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
FOIL: x² − 2x + 5x − 10 = x² + 3x − 10. The middle terms add, they do not cancel.
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: 5 · 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: Expand (x + 5)(x − 2). Circle that word — that is the missing variable.
Find: We are required to find: Expand (x + 5)(x − 2). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: Write x² + 3x − 10 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Expand (x + 5)(x − 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
Copy these onto the left of your page, one per line, with units: 5 · 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
FOIL: x² − 2x + 5x − 10 = x² + 3x − 10. The middle terms add, they do not cancel.
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
FOIL: x² − 2x + 5x − 10 = x² + 3x − 10. The middle terms add, they do not cancel.
x²+3x−10
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
x² + 3x − 10
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
x² + 3x − 10
Copy onto your answer sheet — in this order
Formula: x² + 3x − 10
Answer: x² + 3x − 10
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 · 8 Marks
A taxi from Gqeberha to Mthatha is 480 km at 80 kmh. Time?
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: A taxi from Gqeberha to Mthatha is 480 km at 80 kmh. Time?
Before any working — hunt first
Given
Numbers and units already in the sentence: 480 km · 80 kmh. 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: Time. Circle that word — that is the missing variable.
Find
We are required to find: Time. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: t = distancespeed=480 ÷ 80 = 6 hours. Then substitute the given, one line at a time, to get Time.
In other words — as if you have never seen this before
If you have never seen this before: t = distancespeed=480 ÷ 80 = 6 hours. Write units: km(km/h) leaves hours. 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: 480 km · 80 kmh. Mixing cm with m, or minutes with seconds, loses a method mark.
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: 480 km · 80 kmh. 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: Time. Circle that word — that is the missing variable.
Find: We are required to find: Time. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: t = distancespeed=480 ÷ 80 = 6 hours. Then substitute the given, one line at a time, to get Time.
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: 480 km · 80 kmh. 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.
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.
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
6 h
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
6 h
Copy onto your answer sheet — in this order
Answer: 6 h
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 · 8 Marks · Probability
P(heart) from a 52-card pack
Formulas
P(A)=n(A)n(S)
Classical probability
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(heart) from a 52-card pack
Before any working — hunt first
Given
Numbers and units already in the sentence: 52. 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(heart) from a 52-card pack. Circle that word — that is the missing variable.
Find
We are required to find: P(heart) from a 52-card pack. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 13 hearts out of 52 cards. Then substitute the given, one line at a time, to get P(heart) from a 52-card pack.
In other words — as if you have never seen this before
If you have never seen this before: 13 hearts out of 52 cards. Simplify later to 14 if the paper asks. Favourabletotal. 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: 52. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
13 hearts out of 52 cards. Simplify later to 14 if the paper asks. Favourabletotal.
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: 52. 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(heart) from a 52-card pack. Circle that word — that is the missing variable.
Find: We are required to find: P(heart) from a 52-card pack. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 13 hearts out of 52 cards. Then substitute the given, one line at a time, to get P(heart) from a 52-card pack.
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: 52. 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
13 hearts out of 52 cards. Simplify later to 14 if the paper asks. Favourabletotal.
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
13 hearts out of 52 cards. Simplify later to 14 if the paper asks. Favourabletotal.
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
1352
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
1352
Copy onto your answer sheet — in this order
Answer: 1352
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 · 10 Marks · Analytical geometry
Gradient of the line through (2; 3) and (6; 11)
Analytical geometry
Formulas
d=√[(x₂−x₁)² + (y₂−y₁)²]
Distance
M=((x₁+x₂)/2 ; (y₁+y₂)/2)
Midpoint
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: Gradient of the line through (2; 3) and (6; 11)
In other words — as if you have never seen this before
If you have never seen this before: m = (11 − 3)/(6 − 2) = 84=2. Rise over run, top minus bottom in the same order. 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: 2 · 3 · 6 · 11. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
m = (11 − 3)/(6 − 2) = 84=2. Rise over run, top minus bottom in the same order.
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: 2 · 3 · 6 · 11. 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
m = (11 − 3)/(6 − 2) = 84=2. Rise over run, top minus bottom in the same order.
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
m = (11 − 3)/(6 − 2) = 84=2. Rise over run, top minus bottom in the same order.
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
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.
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
2
Copy onto your answer sheet — in this order
Answer: 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…”
3.1 · 9 Marks · Surface area & volume
Area of a rectangle 12 m by 5 m
Formulas
Vcyl=πr²h
Cylinder volume
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: Area of a rectangle 12 m by 5 m
Before any working — hunt first
Given
Numbers and units already in the sentence: 12 m · 5 m. 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: Area of a rectangle 12 m by 5 m. Circle that word — that is the missing variable.
Find
We are required to find: Area of a rectangle 12 m by 5 m. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: A = l × b = 12 × 5 = 60 m². Then substitute the given, one line at a time, to get Area of a rectangle 12 m by 5 m.
In other words — as if you have never seen this before
If you have never seen this before: A = l × b = 12 × 5 = 60 m². Length times breadth, units squared. 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 m · 5 m. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
A = l × b = 12 × 5 = 60 m². Length times breadth, units squared.
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 m · 5 m. 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: Area of a rectangle 12 m by 5 m. Circle that word — that is the missing variable.
Find: We are required to find: Area of a rectangle 12 m by 5 m. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: A = l × b = 12 × 5 = 60 m². Then substitute the given, one line at a time, to get Area of a rectangle 12 m by 5 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 m · 5 m. 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 = l × b = 12 × 5 = 60 m². Length times breadth, units squared.
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
A = l × b = 12 × 5 = 60 m². Length times breadth, units squared.
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 m²
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 m²
Copy onto your answer sheet — in this order
Answer: 60 m²
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 · 9 Marks
3²×3³=
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: 3² × 3³ =
Before any working — hunt first
Given
Numbers and units already in the sentence: 3² · 3³. 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 × 3³ =. Circle that word — that is the missing variable.
Find
We are required to find: 3² × 3³ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Same base: add the indices. Then substitute the given, one line at a time, to get 3² × 3³ =.
In other words — as if you have never seen this before
If you have never seen this before: Same base: add the indices. 2 + 3 = 5, so 3⁵. Do not multiply the bases. 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 · 3³. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Same base: add the indices. 2 + 3 = 5, so 3⁵. Do not multiply the bases.
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 · 3³. 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 × 3³ =. Circle that word — that is the missing variable.
Find: We are required to find: 3² × 3³ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Same base: add the indices. Then substitute the given, one line at a time, to get 3² × 3³ =.
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 · 3³. 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
Same base: add the indices. 2 + 3 = 5, so 3⁵. Do not multiply the bases.
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
Same base: add the indices. 2 + 3 = 5, so 3⁵. Do not multiply the bases.
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
3⁵
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
3⁵
Copy onto your answer sheet — in this order
Answer: 3⁵
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 · Simple & compound interest
Simple interest formula is
Simple & compound interest
Formulas
A=P(1 + in)
Simple interest
A=P(1 + i)ⁿ
Compound interest
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: Simple interest formula is
Before any working — hunt first
Given
Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. 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: Simple interest formula is. Circle that word — that is the missing variable.
Find
We are required to find: Simple interest formula is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: I = principal × rate × time. Then substitute the given, one line at a time, to get Simple interest formula is.
In other words — as if you have never seen this before
I=principal×rate×time.
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?
I=principal×rate×time.
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: no numbers yet — only a name, a diagram, or a worded unknown. 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: Simple interest formula is. Circle that word — that is the missing variable.
Find: We are required to find: Simple interest formula is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: I = principal × rate × time. Then substitute the given, one line at a time, to get Simple interest formula 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: 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.
04 / 08
Step C — Name the method in words
I=principal×rate×time.
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=principal×rate×time.
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
I=Pin
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
I=Pin
Copy onto your answer sheet — in this order
Answer: I=Pin
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 · Analytical geometry
Gradient of the line through (1; 2) and (5; 14).
Analytical geometry
Formulas
d=√[(x₂−x₁)² + (y₂−y₁)²]
Distance
M=((x₁+x₂)/2 ; (y₁+y₂)/2)
Midpoint
Notes: Point A (1; 2), point B (5; 14). Unknown: gradient m.
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: Gradient of the line through (1; 2) and (5; 14).
In other words — as if you have never seen this before
Gradient is rise over run: change in y divided by change in x, in the same order.
2. What do we already know?
Point A (1; 2), point B (5; 14). Unknown: gradient m.
3. Which method — and why this one?
Gradient is rise over run: change in y divided by change in x, in the same order.
4. Step-by-step working
01 / 06
Write the formula
m = (y₂ − y₁) / (x₂ − x₁). Call (1; 2) point 1 and (5; 14) point 2.
m=(y₂ − y₁)(x₂ − x₁)
Why this step: Order matters. If you subtract the x’s the other way, you must also flip the y’s, or the sign of m flips.
02 / 06
Substitute
m=(14 − 2)(5 − 1)=124.
m=124
Why this step: Rise 12, run 4. A 12-up-for-4-along line is steep, so m around 3 is sensible — not 12, not 1/3.
03 / 06
Simplify
124=3. So m = 3. From x = 1 to x = 5 we add 4; y must add 12, which is 3 × 4.
m=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.
04 / 06
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.
05 / 06
Step F — Box the answer with its unit
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.
06 / 06
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
Copy onto your answer sheet — in this order
Formula: m=(y₂ − y₁)(x₂ − x₁)
Answer: 3
6. Check it like a marker
Start at (1; 2), add 4 to x and 12 to y: (5; 14). Lands on the second point.
7. A trap first-timers fall into
Writing 412=13 — that is run over rise. Gradient is never “along over up”.
9 · 3 Marks · Surface area & volume
Volume of a cube of side 4 cm
Formulas
Vcyl=πr²h
Cylinder volume
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: Volume of a cube of side 4 cm
Before any working — hunt first
Given
Numbers and units already in the sentence: 4 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: Volume of a cube of side 4 cm. Circle that word — that is the missing variable.
Find
We are required to find: Volume of a cube of side 4 cm. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 64 cm³. Then substitute the given, one line at a time, to get Volume of a cube of side 4 cm.
In other words — as if you have never seen this before
64 cm³
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 4 cm. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
64 cm³
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: 4 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: Volume of a cube of side 4 cm. Circle that word — that is the missing variable.
Find: We are required to find: Volume of a cube of side 4 cm. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 64 cm³. Then substitute the given, one line at a time, to get Volume of a cube of side 4 cm.
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: 4 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
64 cm³
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
s³=64.
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
64 cm³
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
64 cm³
Copy onto your answer sheet — in this order
Answer: 64 cm³
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 · 2 Marks
Solve x4=5
Notes: x divided by 4 equals 5.
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: Solve x4=5
Before any working — hunt first
Given
Numbers and units already in the sentence: 4 · 5. 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: Solve x4=5. Circle that word — that is the missing variable.
Find
We are required to find: Solve x4=5. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write x = 20 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Solve x4=5.
In other words — as if you have never seen this before
Undo division by multiplying both sides by 4.
2. What do we already know?
x divided by 4 equals 5.
3. Which method — and why this one?
Undo division by multiplying both sides by 4.
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: 4 · 5. 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: Solve x4=5. Circle that word — that is the missing variable.
Find: We are required to find: Solve x4=5. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: Write x = 20 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Solve x4=5.
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
x divided by 4 equals 5.
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
Undo division by multiplying both sides by 4.
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
Multiply by 4
x=20.
x=20
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
x=20
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
x=20
Copy onto your answer sheet — in this order
Formula: x=20
Answer: x=20
6. Check it like a marker
204=5. Matches.
7. A trap first-timers fall into
Adding 4 gives 9. Reverse BODMAS: × andbefore +.
11 · 2 Marks · Exponents
2³×2²=
Formulas
aᵐ·aⁿ=aᵐ⁺ⁿ
Same base, add
a⁻ⁿ=1aⁿ
Negative exponent
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: 2³ × 2² =
Before any working — hunt first
Given
Numbers and units already in the sentence: 2³ · 2². 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: 2³ × 2² =. Circle that word — that is the missing variable.
Find
We are required to find: 2³ × 2² =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Same base: add exponents. Then substitute the given, one line at a time, to get 2³ × 2² =.
In other words — as if you have never seen this before
Same base: add exponents. 3+2=5.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2³ · 2². Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Same base: add exponents. 3+2=5.
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: 2³ · 2². 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: 2³ × 2² =. Circle that word — that is the missing variable.
Find: We are required to find: 2³ × 2² =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Same base: add exponents. Then substitute the given, one line at a time, to get 2³ × 2² =.
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: 2³ · 2². 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
Same base: add exponents. 3+2=5.
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
Same base: add exponents. 3+2=5.
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
2⁵
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
2⁵
Copy onto your answer sheet — in this order
Answer: 2⁵
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 · 2 Marks
2⁻²=
Notes: Negative exponent on 2.
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: 2⁻² =
Before any working — hunt first
Given
Numbers and units already in the sentence: 2⁻². 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: 2⁻² =. Circle that word — that is the missing variable.
Find
We are required to find: 2⁻² =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write a⁻ⁿ = 1aⁿ with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives 2⁻² =.
In other words — as if you have never seen this before
a⁻ⁿ=1aⁿ. 2⁻²=12²=14.
2. What do we already know?
Negative exponent on 2.
3. Which method — and why this one?
a⁻ⁿ=1aⁿ. 2⁻²=12²=14.
4. Step-by-step working
01 / 05
Write the law
A negative index means reciprocal.
a⁻ⁿ=1aⁿ
Why this step: Write the formula before numbers. The memo awards a method mark for the law even if a digit slips later.
02 / 05
Evaluate
14=14.
14
Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
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
14
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
14
Copy onto your answer sheet — in this order
Formula: a⁻ⁿ=1aⁿ
Answer: 14
6. Check it like a marker
2²=4, so 2⁻² is the reciprocal 14. Not negative 4.
7. A trap first-timers fall into
The minus is on the exponent, not on the 2. 2⁻² is not −4.
13 · 2 Marks
Solve 3x−7=11.
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: Solve 3x − 7 = 11.
Before any working — hunt first
Given
Numbers and units already in the sentence: 3x · 7 · 11. 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: Solve 3x − 7 = 11. Circle that word — that is the missing variable.
Find
We are required to find: Solve 3x − 7 = 11. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 3x = 18, x = 6. Then substitute the given, one line at a time, to get Solve 3x − 7 = 11.
In other words — as if you have never seen this before
3x=18, x=6.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 3x · 7 · 11. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
3x=18, x=6.
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: 3x · 7 · 11. 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: Solve 3x − 7 = 11. Circle that word — that is the missing variable.
Find: We are required to find: Solve 3x − 7 = 11. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 3x = 18, x = 6. Then substitute the given, one line at a time, to get Solve 3x − 7 = 11.
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: 3x · 7 · 11. 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
3x=18, x=6.
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
3x=18, x=6.
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
x=6
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
x=6
Copy onto your answer sheet — in this order
Answer: x=6
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 · 2 Marks · Simple & compound interest
R5 000 at 8% p.a. simple interest for 3 years. Interest earned?
Simple & compound interest
Formulas
A=P(1 + in)
Simple interest
A=P(1 + i)ⁿ
Compound interest
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: R5 000 at 8% p.a. simple interest for 3 years. Interest earned?
Before any working — hunt first
Given
Numbers and units already in the sentence: R5 · 000 at · 8% · 3 years. 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: Interest earned. Circle that word — that is the missing variable.
Find
We are required to find: Interest earned. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: R1 200. Then substitute the given, one line at a time, to get Interest earned.
In other words — as if you have never seen this before
R1 200
2. What do we already know?
Copy these onto the left of your page, one per line, with units: R5 · 000 at · 8% · 3 years. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
R1 200
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: R5 · 000 at · 8% · 3 years. 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: Interest earned. Circle that word — that is the missing variable.
Find: We are required to find: Interest earned. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: R1 200. Then substitute the given, one line at a time, to get Interest earned.
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: R5 · 000 at · 8% · 3 years. 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
R1 200
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
I=Pin=5000×0.08×3=1200.
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
R1 200
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
R1 200
Copy onto your answer sheet — in this order
Answer: R1 200
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 · Number patterns
Solve x + 4 > 10.
Number patterns
Formulas
Tₙ=a+(n − 1)d
nth term
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: Solve x + 4 > 10.
Before any working — hunt first
Given
Numbers and units already in the sentence: 4 · 10. 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: Solve x + 4 > 10. Circle that word — that is the missing variable.
Find
We are required to find: Solve x + 4 > 10. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Subtract 4: x > 6. Then substitute the given, one line at a time, to get Solve x + 4 > 10.
In other words — as if you have never seen this before
Subtract 4: x > 6. Open circle on the number line.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 4 · 10. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Subtract 4: x > 6. Open circle on the number line.
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: 4 · 10. 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: Solve x + 4 > 10. Circle that word — that is the missing variable.
Find: We are required to find: Solve x + 4 > 10. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Subtract 4: x > 6. Then substitute the given, one line at a time, to get Solve x + 4 > 10.
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: 4 · 10. 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
Subtract 4: x > 6. Open circle on the number line.
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
Subtract 4: x > 6. Open circle on the number line.
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
x > 6
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
x > 6
Copy onto your answer sheet — in this order
Answer: x > 6
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 · 2 Marks
2⁵2²=
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: 2⁵2² =
Before any working — hunt first
Given
Numbers and units already in the sentence: 2 · 2². 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: 2⁵2²=. Circle that word — that is the missing variable.
Find
We are required to find: 2⁵2²=. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 8. Then substitute the given, one line at a time, to get 2⁵2²=.
In other words — as if you have never seen this before
8
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2 · 2². Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
8
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 · 2². 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: 2⁵2²=. Circle that word — that is the missing variable.
Find: We are required to find: 2⁵2²=. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 8. Then substitute the given, one line at a time, to get 2⁵2²=.
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 · 2². 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
8
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
2³=8.
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
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
Answer: 8
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…”
17 · 3 Marks · Simple & compound interest
Simple interest on R5 000 at 8% for 3 years
Simple & compound interest
Formulas
A=P(1 + in)
Simple interest
A=P(1 + i)ⁿ
Compound interest
Notes: P=5000, i=8%=0.08, n=3. Asked for interest I, not amount A.
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: Simple interest on R5 000 at 8% for 3 years
In other words — as if you have never seen this before
I=Pin.
2. What do we already know?
P=5000, i=8%=0.08, n=3. Asked for interest I, not amount A.
3. Which method — and why this one?
I=Pin.
4. Step-by-step working
01 / 05
Write I = Pin
Change 8% to 0.08.
I=Pin
Why this step: Write the formula before numbers. The memo awards a method mark for the law even if a digit slips later.
02 / 05
Substitute
I=5000×0.08×3=400×3=R1 200.
I=R1 200
Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
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
R1 200
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
R1 200
Copy onto your answer sheet — in this order
Formula: I=Pin
Answer: R1 200
6. Check it like a marker
8% of 5000 is R400 per year. Three years: R1 200.
7. A trap first-timers fall into
R6 200 is the amount P+I. The paper asked for interest.
18 · 3 Marks · Statistics
Data 1,2,2,3,12. The median is
Statistics
Formulas
x̄=Σxn
Mean
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: Data 1,2,2,3,12. The median is
Before any working — hunt first
Given
Numbers and units already in the sentence: 1,2 · 2,3 · 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: The median is. Circle that word — that is the missing variable.
Find
We are required to find: The median is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Middle of ordered list is 2. Then substitute the given, one line at a time, to get The median is.
In other words — as if you have never seen this before
Middle of ordered list is 2.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1,2 · 2,3 · 12. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Middle of ordered list is 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: 1,2 · 2,3 · 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: The median is. Circle that word — that is the missing variable.
Find: We are required to find: The median is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Middle of ordered list is 2. Then substitute the given, one line at a time, to get The median 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: 1,2 · 2,3 · 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
Middle of ordered list is 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
Middle of ordered list is 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
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
2
Copy onto your answer sheet — in this order
Answer: 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…”
19 · 2 Marks
Expand (x+3)(x+4)
Notes: Two binomials. Unknown: expanded trinomial.
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: Expand (x+3)(x+4)
Before any working — hunt first
Given
Numbers and units already in the sentence: 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: Expand (x+3)(x+4). Circle that word — that is the missing variable.
Find
We are required to find: Expand (x+3)(x+4). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write x²+4x+3x+12 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Expand (x+3)(x+4).
In other words — as if you have never seen this before
FOIL: First, Outer, Inner, Last. Then collect like terms.
2. What do we already know?
Two binomials. Unknown: expanded trinomial.
3. Which method — and why this one?
FOIL: First, Outer, Inner, Last. Then collect like terms.
4. Step-by-step working
01 / 05
FOIL
x² + 4x + 3x + 12.
x²+4x+3x+12
Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
02 / 05
Collect
x² + 7x + 12.
x²+7x+12
Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.
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
x²+7x+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.
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
x²+7x+12
Copy onto your answer sheet — in this order
Formula: x²+4x+3x+12
Answer: x²+7x+12
6. Check it like a marker
At x=1: (4)(5)=20 and 1+7+12=20. Matches.
7. A trap first-timers fall into
x²+12 forgets the middle terms. They do not cancel — both plus.
20 · 3 Marks · Probability
P(red) from 3 red and 7 blue marbles?
Formulas
P(A)=n(A)n(S)
Classical probability
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(red) from 3 red and 7 blue marbles?
Before any working — hunt first
Given
Numbers and units already in the sentence: 3 red · 7 blue. 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(red) from 3 red and 7 blue marbles. Circle that word — that is the missing variable.
Find
We are required to find: P(red) from 3 red and 7 blue marbles. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 310. Then substitute the given, one line at a time, to get P(red) from 3 red and 7 blue marbles.
In other words — as if you have never seen this before
310
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 3 red · 7 blue. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
310
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 red · 7 blue. 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(red) from 3 red and 7 blue marbles. Circle that word — that is the missing variable.
Find: We are required to find: P(red) from 3 red and 7 blue marbles. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 310. Then substitute the given, one line at a time, to get P(red) from 3 red and 7 blue marbles.
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 red · 7 blue. 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
310
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
3 favourable out of 10.
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
310
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
310
Copy onto your answer sheet — in this order
Answer: 310
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 · 2 Marks · Number patterns
Which number is irrational?
Number patterns
Formulas
Tₙ=a+(n − 1)d
nth term
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: Which number is irrational?
Before any working — hunt first
Given
Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. 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: Which number is irrational. Circle that word — that is the missing variable.
Find
We are required to find: Which number is irrational. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: √2 cannot be ab. Then substitute the given, one line at a time, to get Which number is irrational.
In other words — as if you have never seen this before
√2 cannot be ab. √9=3 is rational.
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?
√2 cannot be ab. √9=3 is rational.
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: no numbers yet — only a name, a diagram, or a worded unknown. 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: Which number is irrational. Circle that word — that is the missing variable.
Find: We are required to find: Which number is irrational. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: √2 cannot be ab. Then substitute the given, one line at a time, to get Which number is irrational.
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: 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.
04 / 08
Step C — Name the method in words
√2 cannot be ab. √9=3 is rational.
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 cannot be ab. √9=3 is rational.
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
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
Copy onto your answer sheet — in this order
Answer: √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…”
22 · 2 Marks
Tₙ=3n+1. T₁₂=
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: Tₙ = 3n + 1. T₁₂ =
Before any working — hunt first
Given
Numbers and units already in the sentence: 3n · 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: T₁₂ =. Circle that word — that is the missing variable.
Find
We are required to find: T₁₂ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 37. Then substitute the given, one line at a time, to get T₁₂ =.
In other words — as if you have never seen this before
37
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 3n · 1. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
37
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: 3n · 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: T₁₂ =. Circle that word — that is the missing variable.
Find: We are required to find: T₁₂ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 37. Then substitute the given, one line at a time, to get T₁₂ =.
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: 3n · 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
37
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
3(12)+1=37.
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
37
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
37
Copy onto your answer sheet — in this order
Answer: 37
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 · 3 Marks · Probability
P(even) on a fair die
Formulas
P(A)=n(A)n(S)
Classical probability
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(even) on a fair die
Before any working — hunt first
Given
Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. 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(even) on a fair die. Circle that word — that is the missing variable.
Find
We are required to find: P(even) on a fair die. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 12. Then substitute the given, one line at a time, to get P(even) on a fair die.
In other words — as if you have never seen this before
12
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?
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: no numbers yet — only a name, a diagram, or a worded unknown. 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(even) on a fair die. Circle that word — that is the missing variable.
Find: We are required to find: P(even) on a fair die. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 12. Then substitute the given, one line at a time, to get P(even) on a fair die.
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: 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.
04 / 08
Step C — Name the method in words
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
2,4,6 out of 6.
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…”
24 · 2 Marks · Factorisation
Factorise x² − 25.
Formulas
a²−b²=(a − b)(a + b)
Difference of squares
x²+(p+q)x+pq=(x+p)(x+q)
Trinomial
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: Factorise x² − 25.
Before any working — hunt first
Given
Numbers and units already in the sentence: 25. 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: Factorise x² − 25. Circle that word — that is the missing variable.
Find
We are required to find: Factorise x² − 25. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Difference of squares with a = x, b = 5. Then substitute the given, one line at a time, to get Factorise x² − 25.
In other words — as if you have never seen this before
Difference of squares with a = x, b = 5.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 25. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Difference of squares with a = x, b = 5.
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: 25. 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: Factorise x² − 25. Circle that word — that is the missing variable.
Find: We are required to find: Factorise x² − 25. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Difference of squares with a = x, b = 5. Then substitute the given, one line at a time, to get Factorise x² − 25.
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: 25. 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
Difference of squares with a = x, b = 5.
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
Difference of squares with a = x, b = 5.
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
(x−5)(x+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
(x−5)(x+5)
Copy onto your answer sheet — in this order
Answer: (x−5)(x+5)
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 · Analytical geometry
Midpoint of (2; 4) and (6; 10) is
Analytical geometry
Formulas
d=√[(x₂−x₁)² + (y₂−y₁)²]
Distance
M=((x₁+x₂)/2 ; (y₁+y₂)/2)
Midpoint
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: Midpoint of (2; 4) and (6; 10) is
Before any working — hunt first
Given
Numbers and units already in the sentence: 2 · 4 · 6 · 10. 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: Midpoint of (2; 4) and (6; 10) is. Circle that word — that is the missing variable.
Find
We are required to find: Midpoint of (2; 4) and (6; 10) is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Average the coordinates: ((2+6)/2;(4+10)2)=(4;7). Then substitute the given, one line at a time, to get Midpoint of (2; 4) and (6; 10) is.
In other words — as if you have never seen this before
Average the coordinates: ((2+6)/2;(4+10)2)=(4;7).
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2 · 4 · 6 · 10. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Average the coordinates: ((2+6)/2;(4+10)2)=(4;7).
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 · 6 · 10. 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: Midpoint of (2; 4) and (6; 10) is. Circle that word — that is the missing variable.
Find: We are required to find: Midpoint of (2; 4) and (6; 10) is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Average the coordinates: ((2+6)/2;(4+10)2)=(4;7). Then substitute the given, one line at a time, to get Midpoint of (2; 4) and (6; 10) 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: 2 · 4 · 6 · 10. 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
Average the coordinates: ((2+6)/2;(4+10)2)=(4;7).
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
Average the coordinates: ((2+6)/2;(4+10)2)=(4;7).
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; 7)
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; 7)
Copy onto your answer sheet — in this order
Answer: (4; 7)
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…”
26 · 2 Marks · Analytical geometry
The line through (0; 1) and (2; 7). Gradient?
Analytical geometry
Formulas
d=√[(x₂−x₁)² + (y₂−y₁)²]
Distance
M=((x₁+x₂)/2 ; (y₁+y₂)/2)
Midpoint
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: The line through (0; 1) and (2; 7). Gradient?
Before any working — hunt first
Given
Numbers and units already in the sentence: 0 · 1 · 2 · 7. 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: Gradient. Circle that word — that is the missing variable.
Find
We are required to find: Gradient. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 3. Then substitute the given, one line at a time, to get Gradient.
In other words — as if you have never seen this before
3
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 0 · 1 · 2 · 7. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
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: 0 · 1 · 2 · 7. 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: Gradient. Circle that word — that is the missing variable.
Find: We are required to find: Gradient. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 3. Then substitute the given, one line at a time, to get Gradient.
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 · 1 · 2 · 7. 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
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
Reason
m=(7−1)(2−0)=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
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
3
Copy onto your answer sheet — in this order
Answer: 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…”
27 · 2 Marks · Simple & compound interest
Simple interest on R3 000 at 5% for 4 years
Simple & compound interest
Formulas
A=P(1 + in)
Simple interest
A=P(1 + i)ⁿ
Compound interest
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: Simple interest on R3 000 at 5% for 4 years
In other words — as if you have never seen this before
R600
2. What do we already know?
Copy these onto the left of your page, one per line, with units: R3 · 000 at · 5% · 4 years. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
R600
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: R3 · 000 at · 5% · 4 years. 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
R600
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
I=Pin=3000×0.05×4=600.
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
R600
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
R600
Copy onto your answer sheet — in this order
Answer: R600
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 · 4 Marks
Co-interior angles between parallel lines sum to
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: Co-interior angles between parallel lines sum to
In other words — as if you have never seen this before
Co-interior supplementary.
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?
Co-interior supplementary.
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
Co-interior supplementary.
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
Co-interior supplementary.
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
180°
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
180°
Copy onto your answer sheet — in this order
Answer: 180°
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 · 3 Marks · Analytical geometry
Distance (1; 1) to (4; 5)
Analytical geometry
Formulas
d=√[(x₂−x₁)² + (y₂−y₁)²]
Distance
M=((x₁+x₂)/2 ; (y₁+y₂)/2)
Midpoint
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 (1; 1) to (4; 5)
Before any working — hunt first
Given
Numbers and units already in the sentence: 1 · 1 · 4 · 5. 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 (1; 1) to (4; 5). Circle that word — that is the missing variable.
Find
We are required to find: Distance (1; 1) to (4; 5). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 5. Then substitute the given, one line at a time, to get Distance (1; 1) to (4; 5).
In other words — as if you have never seen this before
5
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1 · 1 · 4 · 5. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
5
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 · 4 · 5. 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 (1; 1) to (4; 5). Circle that word — that is the missing variable.
Find: We are required to find: Distance (1; 1) to (4; 5). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 5. Then substitute the given, one line at a time, to get Distance (1; 1) to (4; 5).
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 · 4 · 5. 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
5
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
√9+16=5.
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
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
Answer: 5
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…”
30 · 4 Marks
(3²)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: (3²)³ =
Before any working — hunt first
Given
Numbers and units already in the sentence: 3². 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)³ =. Circle that word — that is the missing variable.
Find
We are required to find: (3²)³ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Power of a power: 3⁶ = 729. Then substitute the given, one line at a time, to get (3²)³ =.
In other words — as if you have never seen this before
Power of a power: 3⁶ = 729.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 3². Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Power of a power: 3⁶ = 729.
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. 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)³ =. Circle that word — that is the missing variable.
Find: We are required to find: (3²)³ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Power of a power: 3⁶ = 729. Then substitute the given, one line at a time, to get (3²)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
Copy these onto the left of your page, one per line, with units: 3². 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
Power of a power: 3⁶ = 729.
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
Power of a power: 3⁶ = 729.
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
729
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
729
Copy onto your answer sheet — in this order
Answer: 729
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…”