Notes: Surd √50. Simplify by taking out square factors.
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: √50 simplified is
Before any working — hunt first
Given
Numbers and units already in the sentence: 50 simplified. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: √50 simplified is. Circle that word — that is the missing variable.
Find
We are required to find: √50 simplified is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write √50 = √(25×2) with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives √50 simplified is.
In other words — as if you have never seen this before
√50=√25×2=5√2.
2. What do we already know?
Surd √50. Simplify by taking out square factors.
3. Which method — and why this one?
√50=√25×2=5√2.
4. Step-by-step working
01 / 05
Factor the largest square
50=25×2. √25=5.
√50=√25×2
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
Take it out
√50=5√2.
5√2
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
5√2
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
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.
25√2 would be if you forgot to square-root the 25. 2√5 is √20.
1.2 · 10 Marks · Quadratic equations & nature of roots
Roots of (x−3)(x+5)=0 are
Formulas
Δ=b²−4ac
Discriminant
Notes: Already factorised. Zero product.
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: Roots of (x−3)(x+5)=0 are
Before any working — hunt first
Given
Numbers and units already in the sentence: 3 · 5 · 0 are. 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: Roots of (x−3)(x+5)=0 are. Circle that word — that is the missing variable.
Find
We are required to find: Roots of (x−3)(x+5)=0 are. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write x=3 or x=−5 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Roots of (x−3)(x+5)=0 are.
In other words — as if you have never seen this before
A product is zero if a factor is zero. x−3=0 or x+5=0.
2. What do we already know?
Already factorised. Zero product.
3. Which method — and why this one?
A product is zero if a factor is zero. x−3=0 or x+5=0.
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 · 5 · 0 are. 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: Roots of (x−3)(x+5)=0 are. Circle that word — that is the missing variable.
Find: We are required to find: Roots of (x−3)(x+5)=0 are. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: Write x=3 or x=−5 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Roots of (x−3)(x+5)=0 are.
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
Already factorised. Zero product.
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 product is zero if a factor is zero. x−3=0 or x+5=0.
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
Zero product
x−3=0→x=3. x+5=0→x=−5.
x=3 or x=−5
Why this step: Write the formula before numbers. The memo awards a method mark for the law 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
3 and −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
3 and −5
Copy onto your answer sheet — in this order
Formula: x=3 or x=−5
Answer: 3 and −5
6. Check it like a marker
(3−3)(3+5)=0×8=0. (−5−3)(−5+5)=−8×0=0.
7. A trap first-timers fall into
The roots are the opposites of the numbers you see with the signs: minus 3 becomes +3, plus 5 becomes −5.
2.1 · 10 Marks · Sine, cosine & area rules
cos θ = 12 in [0°; 360°]. Solutions:
Formulas
asin A=bsin B=csin C=2R
Sine rule
c²=a²+b²−2ab cos C
Cosine rule
Area=½ ab sin C
Area rule
Notes: cos θ=+12. Full revolution.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: cos θ = 12 in [0°; 360°]. Solutions:
Before any working — hunt first
Given
Numbers and units already in the sentence: 1/ · 2 in · 0° · 360°. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Solutions:. Circle that word — that is the missing variable.
Find
We are required to find: Solutions:. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write α = 60° with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Solutions:.
In other words — as if you have never seen this before
CAST: cosine positive in Q1 and Q4. Reference angle 60°.
2. What do we already know?
cos θ=+12. Full revolution.
3. Which method — and why this one?
CAST: cosine positive in Q1 and Q4. Reference angle 60°.
4. Step-by-step working
01 / 05
Reference angle
cos⁻¹(1/2)=60°.
α=60°
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
CAST
Q1: 60°. Q4: 360°−60°=300°.
60° and 300°
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
60° and 300°
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
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
60° and 300°
Copy onto your answer sheet — in this order
Formula: α=60°
Answer: 60° and 300°
6. Check it like a marker
cos 120° = −12, not +12. That is the sine-positive quadrant mix-up.
7. A trap first-timers fall into
60° and 120° is the sine pair for sin=12. Cosine in Q2 is negative.
2.2 · 12 Marks · Parabola, hyperbola & exponential
Turning point of y = (x+1)² − 4 is
Parabola, hyperbola & exponential
Formulas
y=a(x + p)²+q
Shifted parabola
Notes: Completed square: a(x+p)² + q with a=1, p=1, q=−4.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Turning point of y = (x+1)² − 4 is
Before any working — hunt first
Given
Numbers and units already in the sentence: 1 · 4 is. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Turning point of y = (x+1)² − 4 is. Circle that word — that is the missing variable.
Find
We are required to find: Turning point of y = (x+1)² − 4 is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write TP = (−p; q) with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Turning point of y = (x+1)² − 4 is.
In other words — as if you have never seen this before
Turning point is (−p; q) = (−1; −4). Opens up so it is a minimum.
2. What do we already know?
Completed square: a(x+p)² + q with a=1, p=1, q=−4.
3. Which method — and why this one?
Turning point is (−p; q) = (−1; −4). Opens up so it is a minimum.
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 · 4 is. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Turning point of y = (x+1)² − 4 is. Circle that word — that is the missing variable.
Find: We are required to find: Turning point of y = (x+1)² − 4 is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: Write TP = (−p; q) with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Turning point of y = (x+1)² − 4 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
Completed square: a(x+p)² + q with a=1, p=1, q=−4.
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
Turning point is (−p; q) = (−1; −4). Opens up so it is a minimum.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Read p and q
y=(x − (−1))²+(−4). TP (−1; −4).
TP=(−p; q)
Why this step: Write the formula before numbers. The memo awards a method mark for the law even if a digit slips later.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
(−1; −4)
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
(−1; −4)
Copy onto your answer sheet — in this order
Formula: TP=(−p; q)
Answer: (−1; −4)
6. Check it like a marker
At x=−1, y=0−4=−4. Either side, (x+1)² is positive so y > −4. Minimum.
7. A trap first-timers fall into
The sign inside the bracket flips. (x+1) is (x−(−1)), so x=−1, not +1.
5 · 3 Marks · Sine, cosine & area rules
cos θ = 12 in [0°; 360°]
Formulas
asin A=bsin B=csin C=2R
Sine rule
c²=a²+b²−2ab cos C
Cosine rule
Area=½ ab sin C
Area rule
Notes: cos θ = +12. Interval a full revolution.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: cos θ = 12 in [0°; 360°]
Before any working — hunt first
Given
Numbers and units already in the sentence: 1/ · 2 in · 0° · 360°. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: cos θ = 12 in [0°; 360°]. Circle that word — that is the missing variable.
Find
We are required to find: cos θ = 12 in [0°; 360°]. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write α = 60° with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives cos θ = 12 in [0°; 360°].
In other words — as if you have never seen this before
CAST: cosine is positive in Q1 and Q4. Reference angle 60°.
2. What do we already know?
cos θ = +12. Interval a full revolution.
3. Which method — and why this one?
CAST: cosine is positive in Q1 and Q4. Reference angle 60°.
4. Step-by-step working
01 / 05
Reference
cos⁻¹(1/2)=60°.
α=60°
Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
02 / 05
Quadrants
Q1: 60°. Q4: 360°−60°=300°.
60° and 300°
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
60° and 300°
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
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
60° and 300°
Copy onto your answer sheet — in this order
Formula: α=60°
Answer: 60° and 300°
6. Check it like a marker
cos 120° = −12, the other sign. Sketch the CAST diagram.
7. A trap first-timers fall into
60° and 120° is the sine pair. Cosine does not live in Q2 when it is positive.
6 · 2 Marks · Variance, ogives & five-number summary
Mean of 5, 7, 9, 11 is
Variance, ogives & five-number summary
Formulas
x̄=Σxn
Mean
σ²=Σ(x − x̄)²n
Population variance (CAPS uses n)
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Mean of 5, 7, 9, 11 is
Before any working — hunt first
Given
Numbers and units already in the sentence: 5 · 7 · 9 · 11 is. 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: Mean of 5, 7, 9, 11 is. Circle that word — that is the missing variable.
Find
We are required to find: Mean of 5, 7, 9, 11 is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: (5+7+9+11)4=8. Then substitute the given, one line at a time, to get Mean of 5, 7, 9, 11 is.
In other words — as if you have never seen this before
(5+7+9+11)4=8.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 5 · 7 · 9 · 11 is. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
(5+7+9+11)4=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: 5 · 7 · 9 · 11 is. 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: Mean of 5, 7, 9, 11 is. Circle that word — that is the missing variable.
Find: We are required to find: Mean of 5, 7, 9, 11 is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: (5+7+9+11)4=8. Then substitute the given, one line at a time, to get Mean of 5, 7, 9, 11 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: 5 · 7 · 9 · 11 is. 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+7+9+11)4=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
Working
(5+7+9+11)4=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…”
7 · 2 Marks
Δ for x² − 5x + 6 = 0
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: Δ for x² − 5x + 6 = 0
Before any working — hunt first
Given
Numbers and units already in the sentence: 5x · 6 · 0. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Δ for x² − 5x + 6 = 0. Circle that word — that is the missing variable.
Find
We are required to find: Δ for x² − 5x + 6 = 0. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 1. Then substitute the given, one line at a time, to get Δ for x² − 5x + 6 = 0.
In other words — as if you have never seen this before
1
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 5x · 6 · 0. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
1
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 5x · 6 · 0. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Δ for x² − 5x + 6 = 0. Circle that word — that is the missing variable.
Find: We are required to find: Δ for x² − 5x + 6 = 0. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 1. Then substitute the given, one line at a time, to get Δ for x² − 5x + 6 = 0.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 5x · 6 · 0. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
1
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Δ = b² − 4ac = 25 − 24 = 1. Positive perfect square → two real rational unequal roots.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
1
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
1
Copy onto your answer sheet — in this order
Answer: 1
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
8 · 2 Marks · Identities, reduction & equations
sin θ = 12 in [0°; 180°]
Identities, reduction & equations
Formulas
sin²θ+cos²θ=1
Pythagorean identity
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: sin θ = 12 in [0°; 180°]
Before any working — hunt first
Given
Numbers and units already in the sentence: 1/ · 2 in · 0° · 180°. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: sin θ = 12 in [0°; 180°]. Circle that word — that is the missing variable.
Find
We are required to find: sin θ = 12 in [0°; 180°]. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 30° and 150°. Then substitute the given, one line at a time, to get sin θ = 12 in [0°; 180°].
In other words — as if you have never seen this before
30° and 150°
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1/ · 2 in · 0° · 180°. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
30° and 150°
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 1/ · 2 in · 0° · 180°. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: sin θ = 12 in [0°; 180°]. Circle that word — that is the missing variable.
Find: We are required to find: sin θ = 12 in [0°; 180°]. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 30° and 150°. Then substitute the given, one line at a time, to get sin θ = 12 in [0°; 180°].
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 1/ · 2 in · 0° · 180°. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
30° and 150°
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Sine is positive in Q1 and Q2. Reference 30°. Q2: 180° − 30° = 150°.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
30° and 150°
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
30° and 150°
Copy onto your answer sheet — in this order
Answer: 30° and 150°
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
9 · 2 Marks · Parabola, hyperbola & exponential
y=−x²+4. Maximum y=
Parabola, hyperbola & exponential
Formulas
y=a(x + p)²+q
Shifted parabola
Notes: A downward parabola. Vertex on the y-axis.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: y = −x² + 4. Maximum y =
Before any working — hunt first
Given
Numbers and units already in the sentence: 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: Maximum y =. Circle that word — that is the missing variable.
Find
We are required to find: Maximum y =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write y = 4 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Maximum y =.
In other words — as if you have never seen this before
Coefficient of x² is negative, so a maximum. It is the +4.
2. What do we already know?
A downward parabola. Vertex on the y-axis.
3. Which method — and why this one?
Coefficient of x² is negative, so a maximum. It is the +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. 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: Maximum y =. Circle that word — that is the missing variable.
Find: We are required to find: Maximum y =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: Write y = 4 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Maximum y =.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
A downward parabola. Vertex on the y-axis.
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
Coefficient of x² is negative, so a maximum. It is the +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
Read q
Completed square already: max = 4 at x = 0.
y=4
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
4
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
Copy onto your answer sheet — in this order
Formula: y=4
Answer: 4
6. Check it like a marker
At x=0, y=4. At x=1, y=3, lower.
7. A trap first-timers fall into
−4 would be if the square were added with a plus in front of x².
10 · 2 Marks · Inclination & circles
Distance between (0;0) and (3;4)
Formulas
tan θ=m
Inclination
(x − a)²+(y − b)²=r²
Circle centre (a;b)
Notes: A(0;0), B(3;4). Unknown: AB.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Distance between (0;0) and (3;4)
Before any working — hunt first
Given
Numbers and units already in the sentence: 0 · 0 · 3 · 4. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Distance between (0;0) and (3;4). Circle that word — that is the missing variable.
Find
We are required to find: Distance between (0;0) and (3;4). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write 5 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Distance between (0;0) and (3;4).
In other words — as if you have never seen this before
Distance formula is Pythagoras. 3-4-5 triangle.
2. What do we already know?
A(0;0), B(3;4). Unknown: AB.
3. Which method — and why this one?
Distance formula is Pythagoras. 3-4-5 triangle.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 0 · 0 · 3 · 4. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Distance between (0;0) and (3;4). Circle that word — that is the missing variable.
Find: We are required to find: Distance between (0;0) and (3;4). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: Write 5 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Distance between (0;0) and (3;4).
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
A(0;0), B(3;4). Unknown: AB.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Distance formula is Pythagoras. 3-4-5 triangle.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
√(3²+4²)
√9+16=√25=5.
5
Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
5
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
5
Copy onto your answer sheet — in this order
Formula: 5
Answer: 5
6. Check it like a marker
A famous triple. Sketch it.
7. A trap first-timers fall into
3+4=7 adds the legs instead of squaring.
11 · 2 Marks · Quadratic equations & nature of roots
For ax²+bx+c=0, if Δ>0 and not a square, roots are
Formulas
Δ=b²−4ac
Discriminant
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: For ax²+bx+c=0, if Δ>0 and not a square, roots are
In other words — as if you have never seen this before
Positive non-square discriminant.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 0 · 0 and. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Positive non-square discriminant.
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: 0 · 0 and. 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
Positive non-square discriminant.
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
Positive non-square discriminant.
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
real irrational unequal
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
real irrational unequal
Copy onto your answer sheet — in this order
Answer: real irrational unequal
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 · Exponents & surds
√72 simplified=
Exponents & surds
Formulas
am/ⁿ=ⁿ√aᵐ
Rational exponent
√a·√b=√ab
Product of surds
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: √72 simplified =
Before any working — hunt first
Given
Numbers and units already in the sentence: 72 simplified. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: √72 simplified =. Circle that word — that is the missing variable.
Find
We are required to find: √72 simplified =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 6√2. Then substitute the given, one line at a time, to get √72 simplified =.
In other words — as if you have never seen this before
6√2
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 72 simplified. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
6√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: 72 simplified. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: √72 simplified =. Circle that word — that is the missing variable.
Find: We are required to find: √72 simplified =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 6√2. Then substitute the given, one line at a time, to get √72 simplified =.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 72 simplified. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
6√2
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Reason
√72=√36×2=6√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
6√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
6√2
Copy onto your answer sheet — in this order
Answer: 6√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…”
13 · 2 Marks · Inclination & circles
Equation of a circle centre (0;0), r=5
Formulas
tan θ=m
Inclination
(x − a)²+(y − b)²=r²
Circle centre (a;b)
Notes: Centre origin. r = 5 so r² = 25.
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: Equation of a circle centre (0;0), r=5
Before any working — hunt first
Given
Numbers and units already in the sentence: 0 · 0 · 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: Equation of a circle centre (0;0), r=5. Circle that word — that is the missing variable.
Find
We are required to find: Equation of a circle centre (0;0), r=5. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write x²+y²=25 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Equation of a circle centre (0;0), r=5.
In other words — as if you have never seen this before
x²+y²=r².
2. What do we already know?
Centre origin. r = 5 so r² = 25.
3. Which method — and why this one?
x²+y²=r².
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 0 · 0 · 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: Equation of a circle centre (0;0), r=5. Circle that word — that is the missing variable.
Find: We are required to find: Equation of a circle centre (0;0), r=5. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: Write x²+y²=25 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Equation of a circle centre (0;0), r=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
Centre origin. r = 5 so r² = 25.
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
x²+y²=r².
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
Square the radius
r²=25. Write x²+y²=25.
x²+y²=25
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
x²+y²=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
x²+y²=25
Copy onto your answer sheet — in this order
Formula: x²+y²=25
Answer: x²+y²=25
6. Check it like a marker
Point (3;4): 9+16=25, on the circle. A 3-4-5 radius.
7. A trap first-timers fall into
= 5 forgets to square r. The formula uses r².
14 · 2 Marks · Quadratic equations & nature of roots
Δ for x² − 4x + 4 = 0
Formulas
Δ=b²−4ac
Discriminant
Notes: a = 1, b = −4, c = 4. Unknown: discriminant Δ = b² − 4ac.
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: Δ for x² − 4x + 4 = 0
Before any working — hunt first
Given
Numbers and units already in the sentence: 4x · 4 · 0. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Δ for x² − 4x + 4 = 0. Circle that word — that is the missing variable.
Find
We are required to find: Δ for x² − 4x + 4 = 0. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write Δ = b² − 4ac with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Δ for x² − 4x + 4 = 0.
In other words — as if you have never seen this before
Δ tells the nature of roots. Zero means one real rational root (a repeated root) — a perfect square.
2. What do we already know?
a = 1, b = −4, c = 4. Unknown: discriminant Δ = b² − 4ac.
3. Which method — and why this one?
Δ tells the nature of roots. Zero means one real rational root (a repeated root) — a perfect square.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 4x · 4 · 0. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Δ for x² − 4x + 4 = 0. Circle that word — that is the missing variable.
Find: We are required to find: Δ for x² − 4x + 4 = 0. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: Write Δ = b² − 4ac with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Δ for x² − 4x + 4 = 0.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
a = 1, b = −4, c = 4. Unknown: discriminant Δ = b² − 4ac.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Δ tells the nature of roots. Zero means one real rational root (a repeated root) — a perfect square.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Write Δ
Δ=b²−4ac=(−4)²−4(1)(4)=16−16=0.
Δ=b²−4ac
Why this step: The minus on b is squared away. (−4)² is +16, not −16.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
0
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
0
Copy onto your answer sheet — in this order
Formula: Δ=b²−4ac
Answer: 0
6. Check it like a marker
x² − 4x + 4 = (x − 2)². A repeated root x = 2, which is what Δ = 0 promised.
7. A trap first-timers fall into
Writing 16 (that is b², you forgot to subtract 4ac) or −16 (you squared −4 into −16).
15 · 4 Marks · Dependent events & Venn
P(A)=0.3, P(B)=0.4, independent. P(A and B) =
Formulas
P(A ∪ B)=P(A)+P(B)−P(A ∩ B)
Addition rule
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: P(A)=0.3, P(B)=0.4, independent. P(A and B) =
Before any working — hunt first
Given
Numbers and units already in the sentence: 0.3 · 0.4. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: P(A and B) =. Circle that word — that is the missing variable.
Find
We are required to find: P(A and B) =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Independent: P(A∩B)=P(A)P(B)=0. Then substitute the given, one line at a time, to get P(A and B) =.
In other words — as if you have never seen this before
Independent: P(A∩B)=P(A)P(B)=0.12.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 0.3 · 0.4. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Independent: P(A∩B)=P(A)P(B)=0.12.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 0.3 · 0.4. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: P(A and B) =. Circle that word — that is the missing variable.
Find: We are required to find: P(A and B) =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Independent: P(A∩B)=P(A)P(B)=0. Then substitute the given, one line at a time, to get P(A and B) =.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 0.3 · 0.4. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Independent: P(A∩B)=P(A)P(B)=0.12.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Independent: P(A∩B)=P(A)P(B)=0.12.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
0.12
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
0.12
Copy onto your answer sheet — in this order
Answer: 0.12
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
16 · 2 Marks · Parabola, hyperbola & exponential
Asymptotes of y = 1(x−2) + 3
Parabola, hyperbola & exponential
Formulas
y=a(x + p)²+q
Shifted parabola
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Asymptotes of y = 1(x−2) + 3
Before any working — hunt first
Given
Numbers and units already in the sentence: 1/ · 2 · 3. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Asymptotes of y = 1(x−2) + 3. Circle that word — that is the missing variable.
Find
We are required to find: Asymptotes of y = 1(x−2) + 3. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Vertical x=−p=2, horizontal y=q=3. Then substitute the given, one line at a time, to get Asymptotes of y = 1(x−2) + 3.
In other words — as if you have never seen this before
Vertical x=−p=2, horizontal y=q=3.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1/ · 2 · 3. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Vertical x=−p=2, horizontal y=q=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: 1/ · 2 · 3. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Asymptotes of y = 1(x−2) + 3. Circle that word — that is the missing variable.
Find: We are required to find: Asymptotes of y = 1(x−2) + 3. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Vertical x=−p=2, horizontal y=q=3. Then substitute the given, one line at a time, to get Asymptotes of y = 1(x−2) + 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: 1/ · 2 · 3. 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
Vertical x=−p=2, horizontal y=q=3.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Vertical x=−p=2, horizontal y=q=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
x=2 and y=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
x=2 and y=3
Copy onto your answer sheet — in this order
Answer: x=2 and y=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…”
17 · 2 Marks · Proportion & midpoint theorem
Angle in a semicircle is
Proportion & midpoint theorem
Formulas
DE ∥ BC, AD=DB⇒AE=EC
Midpoint theorem
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Angle in a semicircle 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: Angle in a semicircle is. Circle that word — that is the missing variable.
Find
We are required to find: Angle in a semicircle is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Theorem: angle in a semicircle is a right angle. Then substitute the given, one line at a time, to get Angle in a semicircle is.
In other words — as if you have never seen this before
Theorem: angle in a semicircle is a right angle.
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?
Theorem: angle in a semicircle is a right angle.
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: Angle in a semicircle is. Circle that word — that is the missing variable.
Find: We are required to find: Angle in a semicircle is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Theorem: angle in a semicircle is a right angle. Then substitute the given, one line at a time, to get Angle in a semicircle 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
Theorem: angle in a semicircle is a right angle.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Theorem: angle in a semicircle is a right angle.
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
90°
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
90°
Copy onto your answer sheet — in this order
Answer: 90°
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
18 · 2 Marks · Quadratic equations & nature of roots
Quadratic pattern. Second difference constantly 6. a =
Formulas
Δ=b²−4ac
Discriminant
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Quadratic pattern. Second difference constantly 6. a =
Before any working — hunt first
Given
Numbers and units already in the sentence: 6. 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: a =. Circle that word — that is the missing variable.
Find
We are required to find: a =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 2a = second difference, a = 3. Then substitute the given, one line at a time, to get a =.
In other words — as if you have never seen this before
2a = second difference, a = 3.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 6. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
2a = second difference, a = 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: 6. 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: a =. Circle that word — that is the missing variable.
Find: We are required to find: a =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 2a = second difference, a = 3. Then substitute the given, one line at a time, to get a =.
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: 6. 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
2a = second difference, a = 3.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
2a = second difference, a = 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…”
19 · 3 Marks · Nominal vs effective interest
12% p.a. compounded monthly. Monthly interest rate i =
Nominal vs effective interest
Formulas
1+ieff=(1 + inom/m)m
Effective rate
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: 12% p.a. compounded monthly. Monthly interest rate i =
Before any working — hunt first
Given
Numbers and units already in the sentence: 12%. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Monthly interest rate i =. Circle that word — that is the missing variable.
Find
We are required to find: Monthly interest rate i =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: i = 0. Then substitute the given, one line at a time, to get Monthly interest rate i =.
In other words — as if you have never seen this before
i=0.1212=0.01.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 12%. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
i=0.1212=0.01.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 12%. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Monthly interest rate i =. Circle that word — that is the missing variable.
Find: We are required to find: Monthly interest rate i =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: i = 0. Then substitute the given, one line at a time, to get Monthly interest rate i =.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 12%. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
i=0.1212=0.01.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
i=0.1212=0.01.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
0.01
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
0.01
Copy onto your answer sheet — in this order
Answer: 0.01
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
20 · 2 Marks · Quadratic equations & nature of roots
Nature of roots of x² + 4x + 4 = 0
Formulas
Δ=b²−4ac
Discriminant
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Nature of roots of x² + 4x + 4 = 0
Before any working — hunt first
Given
Numbers and units already in the sentence: 4x · 4 · 0. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Nature of roots of x² + 4x + 4 = 0. Circle that word — that is the missing variable.
Find
We are required to find: Nature of roots of x² + 4x + 4 = 0. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: real, rational, equal. Then substitute the given, one line at a time, to get Nature of roots of x² + 4x + 4 = 0.
In other words — as if you have never seen this before
real, rational, equal
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 4x · 4 · 0. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
real, rational, equal
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 4x · 4 · 0. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Nature of roots of x² + 4x + 4 = 0. Circle that word — that is the missing variable.
Find: We are required to find: Nature of roots of x² + 4x + 4 = 0. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: real, rational, equal. Then substitute the given, one line at a time, to get Nature of roots of x² + 4x + 4 = 0.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 4x · 4 · 0. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
real, rational, equal
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Reason
Δ=0, perfect square.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
real, rational, equal
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
real, rational, equal
Copy onto your answer sheet — in this order
Answer: real, rational, equal
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
21 · 2 Marks · Dependent events & Venn
P(A or B) for mutually exclusive events
Formulas
P(A ∪ B)=P(A)+P(B)−P(A ∩ B)
Addition rule
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: P(A or B) for mutually exclusive events
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(A or B) for mutually exclusive events. Circle that word — that is the missing variable.
Find
We are required to find: P(A or B) for mutually exclusive events. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: No overlap, so add. Then substitute the given, one line at a time, to get P(A or B) for mutually exclusive events.
In other words — as if you have never seen this before
No overlap, so add.
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?
No overlap, so add.
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(A or B) for mutually exclusive events. Circle that word — that is the missing variable.
Find: We are required to find: P(A or B) for mutually exclusive events. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: No overlap, so add. Then substitute the given, one line at a time, to get P(A or B) for mutually exclusive events.
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
No overlap, so add.
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
No overlap, so add.
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
P(A)+P(B)
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
P(A)+P(B)
Copy onto your answer sheet — in this order
Answer: P(A)+P(B)
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 · 3 Marks · Quadratic equations & nature of roots
First differences of a quadratic with a=2. Second difference =
Formulas
Δ=b²−4ac
Discriminant
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: First differences of a quadratic with a=2. Second difference =
Before any working — hunt first
Given
Numbers and units already in the sentence: 2. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Second difference =. Circle that word — that is the missing variable.
Find
We are required to find: Second difference =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 2a = second difference = 4. Then substitute the given, one line at a time, to get Second difference =.
In other words — as if you have never seen this before
2a = second difference = 4.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
2a = second difference = 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: 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: Second difference =. Circle that word — that is the missing variable.
Find: We are required to find: Second difference =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 2a = second difference = 4. Then substitute the given, one line at a time, to get Second difference =.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 2. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
2a = second difference = 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
Working
2a = second difference = 4.
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
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
Copy onto your answer sheet — in this order
Answer: 4
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 · 4 Marks · Parabola, hyperbola & exponential
Range of y = (x−1)² + 4
Parabola, hyperbola & exponential
Formulas
y=a(x + p)²+q
Shifted parabola
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Range of y = (x−1)² + 4
Before any working — hunt first
Given
Numbers and units already in the sentence: 1 · 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: Range of y = (x−1)² + 4. Circle that word — that is the missing variable.
Find
We are required to find: Range of y = (x−1)² + 4. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Parabola opens up, minimum 4. Then substitute the given, one line at a time, to get Range of y = (x−1)² + 4.
In other words — as if you have never seen this before
Parabola opens up, minimum 4.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1 · 4. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Parabola opens up, minimum 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: 1 · 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: Range of y = (x−1)² + 4. Circle that word — that is the missing variable.
Find: We are required to find: Range of y = (x−1)² + 4. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Parabola opens up, minimum 4. Then substitute the given, one line at a time, to get Range of y = (x−1)² + 4.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 1 · 4. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Parabola opens up, minimum 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
Working
Parabola opens up, minimum 4.
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
y ≥ 4
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
y ≥ 4
Copy onto your answer sheet — in this order
Answer: y ≥ 4
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
24 · 4 Marks · Quadratic equations & nature of roots
x² − 2x + 5 = 0. Nature of roots?
Formulas
Δ=b²−4ac
Discriminant
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: x² − 2x + 5 = 0. Nature of roots?
Before any working — hunt first
Given
Numbers and units already in the sentence: 2x · 5 · 0. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Nature of roots. Circle that word — that is the missing variable.
Find
We are required to find: Nature of roots. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Δ=4−20=−16<0. Then substitute the given, one line at a time, to get Nature of roots.
In other words — as if you have never seen this before
Δ=4−20=−16<0.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2x · 5 · 0. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Δ=4−20=−16<0.
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: 2x · 5 · 0. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Nature of roots. Circle that word — that is the missing variable.
Find: We are required to find: Nature of roots. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Δ=4−20=−16<0. Then substitute the given, one line at a time, to get Nature of roots.
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: 2x · 5 · 0. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Δ=4−20=−16<0.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Δ=4−20=−16<0.
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
non-real
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
non-real
Copy onto your answer sheet — in this order
Answer: non-real
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 · 2 Marks
Δ for x² − 6x + 9 = 0 is
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: Δ for x² − 6x + 9 = 0 is
Before any working — hunt first
Given
Numbers and units already in the sentence: 6x · 9 · 0 is. 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: Δ for x² − 6x + 9 = 0 is. Circle that word — that is the missing variable.
Find
We are required to find: Δ for x² − 6x + 9 = 0 is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 0. Then substitute the given, one line at a time, to get Δ for x² − 6x + 9 = 0 is.
In other words — as if you have never seen this before
0
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 6x · 9 · 0 is. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
0
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 6x · 9 · 0 is. 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: Δ for x² − 6x + 9 = 0 is. Circle that word — that is the missing variable.
Find: We are required to find: Δ for x² − 6x + 9 = 0 is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 0. Then substitute the given, one line at a time, to get Δ for x² − 6x + 9 = 0 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: 6x · 9 · 0 is. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
0
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
36−36=0. Equal real rational roots.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
0
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
0
Copy onto your answer sheet — in this order
Answer: 0
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 · 3 Marks · Proportion & midpoint theorem
Midpoints of two sides of a triangle are joined. The third side is 10 cm. The join is
Proportion & midpoint theorem
Formulas
DE ∥ BC, AD=DB⇒AE=EC
Midpoint theorem
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Midpoints of two sides of a triangle are joined. The third side is 10 cm. The join is
Before any working — hunt first
Given
Numbers and units already in the sentence: 10 cm. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: The join is. Circle that word — that is the missing variable.
Find
We are required to find: The join is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Midpoint theorem: half the third side. Then substitute the given, one line at a time, to get The join is.
In other words — as if you have never seen this before
Midpoint theorem: half the third side.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 10 cm. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Midpoint theorem: half the third side.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 10 cm. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: The join is. Circle that word — that is the missing variable.
Find: We are required to find: The join is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Midpoint theorem: half the third side. Then substitute the given, one line at a time, to get The join is.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 10 cm. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Midpoint theorem: half the third side.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Midpoint theorem: half the third side.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
5 cm
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
5 cm
Copy onto your answer sheet — in this order
Answer: 5 cm
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
27 · 3 Marks · Inclination & circles
y=(x−1)²+2. Turning point?
Formulas
tan θ=m
Inclination
(x − a)²+(y − b)²=r²
Circle centre (a;b)
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: y = (x−1)² + 2. Turning point?
Before any working — hunt first
Given
Numbers and units already in the sentence: 1 · 2. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Turning point. Circle that word — that is the missing variable.
Find
We are required to find: Turning point. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: (1; 2). Then substitute the given, one line at a time, to get Turning point.
In other words — as if you have never seen this before
(1; 2)
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1 · 2. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
(1; 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. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Turning point. Circle that word — that is the missing variable.
Find: We are required to find: Turning point. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: (1; 2). Then substitute the given, one line at a time, to get Turning point.
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. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
(1; 2)
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Reason
TP (p; q) with opposite sign on p.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
(1; 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
(1; 2)
Copy onto your answer sheet — in this order
Answer: (1; 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…”
28 · 3 Marks · Dependent events & Venn
Independent: P(A)=0.4, P(B)=0.5. P(A and B)=
Formulas
P(A ∪ B)=P(A)+P(B)−P(A ∩ B)
Addition rule
Notes: Independent events. P(A)=0.4, P(B)=0.5.
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: Independent: P(A)=0.4, P(B)=0.5. P(A and B)=
Before any working — hunt first
Given
Numbers and units already in the sentence: 0.4 · 0.5. 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: P(A and B)=. Circle that word — that is the missing variable.
Find
We are required to find: P(A and B)=. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write 0.20 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives P(A and B)=.
In other words — as if you have never seen this before
Independent ⇒ P(A and B) = P(A)P(B).
2. What do we already know?
Independent events. P(A)=0.4, P(B)=0.5.
3. Which method — and why this one?
Independent ⇒ P(A and B) = P(A)P(B).
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: 0.4 · 0.5. 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: P(A and B)=. Circle that word — that is the missing variable.
Find: We are required to find: P(A and B)=. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: Write 0.20 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives P(A and B)=.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Independent events. P(A)=0.4, P(B)=0.5.
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
Independent ⇒ P(A and B) = P(A)P(B).
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
Product
0.4×0.5=0.20.
0.20
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
0.20
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
0.20
Copy onto your answer sheet — in this order
Formula: 0.20
Answer: 0.20
6. Check it like a marker
0.90 would be A or B if they were exclusive, which they are not.
7. A trap first-timers fall into
Adding 0.4+0.5 is the exclusive-or shortcut, wrong for “and”.
29 · 3 Marks · Identities, reduction & equations
cos θ = 0 in [0°; 360°]
Identities, reduction & equations
Formulas
sin²θ+cos²θ=1
Pythagorean identity
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: cos θ = 0 in [0°; 360°]
Before any working — hunt first
Given
Numbers and units already in the sentence: 0 in · 0° · 360°. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: cos θ = 0 in [0°; 360°]. Circle that word — that is the missing variable.
Find
We are required to find: cos θ = 0 in [0°; 360°]. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 90° and 270°. Then substitute the given, one line at a time, to get cos θ = 0 in [0°; 360°].
In other words — as if you have never seen this before
90° and 270°
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 0 in · 0° · 360°. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
90° and 270°
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 in · 0° · 360°. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: cos θ = 0 in [0°; 360°]. Circle that word — that is the missing variable.
Find: We are required to find: cos θ = 0 in [0°; 360°]. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 90° and 270°. Then substitute the given, one line at a time, to get cos θ = 0 in [0°; 360°].
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 0 in · 0° · 360°. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
90° and 270°
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
Cosine is the x-coordinate on the unit circle. x = 0 at the top (90°) and the bottom (270°).
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
90° and 270°
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
90° and 270°
Copy onto your answer sheet — in this order
Answer: 90° and 270°
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 · 3 Marks · Identities, reduction & equations
Inclination of a line with m = 1 is
Identities, reduction & equations
Formulas
sin²θ+cos²θ=1
Pythagorean identity
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Inclination of a line with m = 1 is
Before any working — hunt first
Given
Numbers and units already in the sentence: 1 is. 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: Inclination of a line with m = 1 is. Circle that word — that is the missing variable.
Find
We are required to find: Inclination of a line with m = 1 is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: tan θ = m = 1. Then substitute the given, one line at a time, to get Inclination of a line with m = 1 is.
In other words — as if you have never seen this before
tan θ=m=1→θ=45°.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1 is. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
tan θ=m=1→θ=45°.
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 is. 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: Inclination of a line with m = 1 is. Circle that word — that is the missing variable.
Find: We are required to find: Inclination of a line with m = 1 is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: tan θ = m = 1. Then substitute the given, one line at a time, to get Inclination of a line with m = 1 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 is. 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
tan θ=m=1→θ=45°.
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
tan θ=m=1→θ=45°.
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
45°
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
45°
Copy onto your answer sheet — in this order
Answer: 45°
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…”