Notes: Four numbers: 4, 6, 8, 10. Unknown: arithmetic mean.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Mean of 4, 6, 8, 10
Before any working — hunt first
Given
Numbers and units already in the sentence: 4 · 6 · 8 · 10. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Mean of 4, 6, 8, 10. Circle that word — that is the missing variable.
Find
We are required to find: Mean of 4, 6, 8, 10. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write sum = 28 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Mean of 4, 6, 8, 10.
In other words — as if you have never seen this before
Mean=sumcount.
2. What do we already know?
Four numbers: 4, 6, 8, 10. Unknown: arithmetic mean.
3. Which method — and why this one?
Mean=sumcount.
4. Step-by-step working
01 / 05
Add
4+6+8+10=28.
sum=28
Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
02 / 05
Divide
284=7.
mean=7
Why this step: Write the formula before numbers. The memo awards a method mark for the law 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
7
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
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
7
Copy onto your answer sheet — in this order
Formula: sum=28
Answer: 7
6. Check it like a marker
The numbers sit equally around 7. 4 and 10, 6 and 8.
7. A trap first-timers fall into
28 is the sum, not the mean. Do not forget to divide.
1.2 · 10 Marks
A taxi from Cape Town to Stellenbosch is 50 km at 100 kmh. Time?
Notes: Δx=50 km, v=100 kmh.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: A taxi from Cape Town to Stellenbosch is 50 km at 100 kmh. Time?
Before any working — hunt first
Given
Numbers and units already in the sentence: 50 km · 100 kmh. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Time. Circle that word — that is the missing variable.
Find
We are required to find: Time. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write t = Δxv with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Time.
In other words — as if you have never seen this before
t=Δxv=50100=0.5 h=30 min.
2. What do we already know?
Δx=50 km, v=100 kmh.
3. Which method — and why this one?
t=Δxv=50100=0.5 h=30 min.
4. Step-by-step working
01 / 05
Write t = Δx/v
Hours, because km ÷ kmh.
t=Δxv
Why this step: Write the formula before numbers. The memo awards a method mark for the law even if a digit slips later.
02 / 05
Substitute
t=50100=0.5 h.
t=0.5 h
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
0.5 h
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
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
0.5 h
Copy onto your answer sheet — in this order
Formula: t=Δxv
Answer: 0.5 h
6. Check it like a marker
Half an hour at 100 kmh covers 50 km. Yes.
7. A trap first-timers fall into
Do not multiply 50×100. That is not time.
2.1 · 10 Marks
2⁻²=
Notes: Negative exponent on 2.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: 2⁻² =
Before any working — hunt first
Given
Numbers and units already in the sentence: 2⁻². Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: 2⁻² =. Circle that word — that is the missing variable.
Find
We are required to find: 2⁻² =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write a⁻ⁿ = 1aⁿ with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives 2⁻² =.
In other words — as if you have never seen this before
a⁻ⁿ=1aⁿ. 2⁻²=12²=14.
2. What do we already know?
Negative exponent on 2.
3. Which method — and why this one?
a⁻ⁿ=1aⁿ. 2⁻²=12²=14.
4. Step-by-step working
01 / 05
Write the law
A negative index means reciprocal.
a⁻ⁿ=1aⁿ
Why this step: Write the formula before numbers. The memo awards a method mark for the law even if a digit slips later.
02 / 05
Evaluate
14=14.
14
Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
03 / 05
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
04 / 05
Step F — Box the answer with its unit
14
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
05 / 05
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
14
Copy onto your answer sheet — in this order
Formula: a⁻ⁿ=1aⁿ
Answer: 14
6. Check it like a marker
2²=4, so 2⁻² is the reciprocal 14. Not negative 4.
7. A trap first-timers fall into
The minus is on the exponent, not on the 2. 2⁻² is not −4.
2.2 · 12 Marks · Surface area & volume
Area of a rectangle 9 m by 4 m
Formulas
Vcyl=πr²h
Cylinder volume
Notes: ℓ=9 m, b=4 m. Unknown: area.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Area of a rectangle 9 m by 4 m
Before any working — hunt first
Given
Numbers and units already in the sentence: 9 m · 4 m. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Area of a rectangle 9 m by 4 m. Circle that word — that is the missing variable.
Find
We are required to find: Area of a rectangle 9 m by 4 m. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write A = ℓb with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Area of a rectangle 9 m by 4 m.
In other words — as if you have never seen this before
A=ℓ×b. Units squared.
2. What do we already know?
ℓ=9 m, b=4 m. Unknown: area.
3. Which method — and why this one?
A=ℓ×b. Units squared.
4. Step-by-step working
01 / 05
Write A = ℓb
Length times breadth.
A=ℓb
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
Multiply
9×4=36 m².
A=36 m²
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
36 m²
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
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
36 m²
Copy onto your answer sheet — in this order
Formula: A=ℓb
Answer: 36 m²
6. Check it like a marker
Perimeter would be 26 m. Area is 36 m². Different quantity, different units.
7. A trap first-timers fall into
13 m is a half-perimeter mix-up. 26 m is the perimeter. The paper asked for area.
5 · 4 Marks
In parallelogram ABCD, angle A = 110°. Angle 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: In parallelogram ABCD, angle A = 110°. Angle B =
Before any working — hunt first
Given
Numbers and units already in the sentence: 110°. 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 B =. Circle that word — that is the missing variable.
Find
We are required to find: Angle B =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Consecutive angles of a parallelogram are supplementary. Then substitute the given, one line at a time, to get Angle B =.
In other words — as if you have never seen this before
Consecutive angles of a parallelogram are supplementary.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 110°. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Consecutive angles of a parallelogram are supplementary.
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: 110°. 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 B =. Circle that word — that is the missing variable.
Find: We are required to find: Angle B =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Consecutive angles of a parallelogram are supplementary. Then substitute the given, one line at a time, to get Angle 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: 110°. 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
Consecutive angles of a parallelogram are supplementary.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Consecutive angles of a parallelogram are supplementary.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
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
70°
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
70°
Copy onto your answer sheet — in this order
Answer: 70°
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…”
6 · 2 Marks
Sequence 2; 5; 8; 11. Common difference d?
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: Sequence 2; 5; 8; 11. Common difference d?
Before any working — hunt first
Given
Numbers and units already in the sentence: 2 · 5 · 8 · 11. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Common difference d. Circle that word — that is the missing variable.
Find
We are required to find: Common difference d. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 5−2=3. Then substitute the given, one line at a time, to get Common difference d.
In other words — as if you have never seen this before
5−2=3.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2 · 5 · 8 · 11. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
5−2=3.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 2 · 5 · 8 · 11. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Common difference d. Circle that word — that is the missing variable.
Find: We are required to find: Common difference d. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 5−2=3. Then substitute the given, one line at a time, to get Common difference d.
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 · 5 · 8 · 11. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
5−2=3.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
5−2=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…”
7 · 2 Marks · Surface area & volume
Area of a rectangle 8 m by 3 m
Formulas
Vcyl=πr²h
Cylinder volume
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Area of a rectangle 8 m by 3 m
Before any working — hunt first
Given
Numbers and units already in the sentence: 8 m · 3 m. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Area of a rectangle 8 m by 3 m. Circle that word — that is the missing variable.
Find
We are required to find: Area of a rectangle 8 m by 3 m. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: A = ℓ × b = 24. Then substitute the given, one line at a time, to get Area of a rectangle 8 m by 3 m.
In other words — as if you have never seen this before
A=ℓ×b=24.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 8 m · 3 m. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
A=ℓ×b=24.
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: 8 m · 3 m. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Area of a rectangle 8 m by 3 m. Circle that word — that is the missing variable.
Find: We are required to find: Area of a rectangle 8 m by 3 m. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: A = ℓ × b = 24. Then substitute the given, one line at a time, to get Area of a rectangle 8 m by 3 m.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 8 m · 3 m. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
A=ℓ×b=24.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
A=ℓ×b=24.
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
24 m²
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
24 m²
Copy onto your answer sheet — in this order
Answer: 24 m²
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
8 · 2 Marks · Analytical geometry
Gradient of the line through (2; 3) and (6; 11)
Analytical geometry
Formulas
d=√[(x₂−x₁)² + (y₂−y₁)²]
Distance
M=((x₁+x₂)/2 ; (y₁+y₂)/2)
Midpoint
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Gradient of the line through (2; 3) and (6; 11)
In other words — as if you have never seen this before
2
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2 · 3 · 6 · 11. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
2
4. Step-by-step working
01 / 07
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 07
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 2 · 3 · 6 · 11. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
03 / 07
Step C — Name the method in words
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.
04 / 07
Working
m = (11 − 3)/(6 − 2) = 84=2. Rise over run, top minus bottom in the same order.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
05 / 07
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
06 / 07
Step F — Box the answer with its unit
2
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
07 / 07
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
2
Copy onto your answer sheet — in this order
Answer: 2
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
9 · 2 Marks
Solve 3x−7=11.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Solve 3x − 7 = 11.
Before any working — hunt first
Given
Numbers and units already in the sentence: 3x · 7 · 11. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Solve 3x − 7 = 11. Circle that word — that is the missing variable.
Find
We are required to find: Solve 3x − 7 = 11. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 3x = 18, x = 6. Then substitute the given, one line at a time, to get Solve 3x − 7 = 11.
In other words — as if you have never seen this before
3x=18, x=6.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 3x · 7 · 11. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
3x=18, x=6.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 3x · 7 · 11. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Solve 3x − 7 = 11. Circle that word — that is the missing variable.
Find: We are required to find: Solve 3x − 7 = 11. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 3x = 18, x = 6. Then substitute the given, one line at a time, to get Solve 3x − 7 = 11.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 3x · 7 · 11. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
3x=18, x=6.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
3x=18, x=6.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
x=6
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
x=6
Copy onto your answer sheet — in this order
Answer: x=6
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
10 · 2 Marks
Solve 23 x=8.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Solve 23 x = 8.
Before any working — hunt first
Given
Numbers and units already in the sentence: 2/ · 3 x · 8. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Solve 23 x = 8. Circle that word — that is the missing variable.
Find
We are required to find: Solve 23 x = 8. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Multiply both sides by 32. Then substitute the given, one line at a time, to get Solve 23 x = 8.
In other words — as if you have never seen this before
Multiply both sides by 32. x = 8 × 32=12. The 23 is a stacked fraction times x — not 2 over 3x.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2/ · 3 x · 8. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Multiply both sides by 32. x = 8 × 32=12. The 23 is a stacked fraction times x — not 2 over 3x.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 2/ · 3 x · 8. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Solve 23 x = 8. Circle that word — that is the missing variable.
Find: We are required to find: Solve 23 x = 8. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Multiply both sides by 32. Then substitute the given, one line at a time, to get Solve 23 x = 8.
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/ · 3 x · 8. 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
Multiply both sides by 32. x = 8 × 32=12. The 23 is a stacked fraction times x — not 2 over 3x.
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
Multiply both sides by 32. x = 8 × 32=12. The 23 is a stacked fraction times x — not 2 over 3x.
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=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
x=12
Copy onto your answer sheet — in this order
Answer: x=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…”
11 · 2 Marks · Simple & compound interest
R5 000 at 8% p.a. simple interest for 3 years. Interest earned?
Simple & compound interest
Formulas
A=P(1 + in)
Simple interest
A=P(1 + i)ⁿ
Compound interest
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: R5 000 at 8% p.a. simple interest for 3 years. Interest earned?
Before any working — hunt first
Given
Numbers and units already in the sentence: R5 · 000 at · 8% · 3 years. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Interest earned. Circle that word — that is the missing variable.
Find
We are required to find: Interest earned. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: R1 200. Then substitute the given, one line at a time, to get Interest earned.
In other words — as if you have never seen this before
R1 200
2. What do we already know?
Copy these onto the left of your page, one per line, with units: R5 · 000 at · 8% · 3 years. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
R1 200
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: R5 · 000 at · 8% · 3 years. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Interest earned. Circle that word — that is the missing variable.
Find: We are required to find: Interest earned. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: R1 200. Then substitute the given, one line at a time, to get Interest earned.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: R5 · 000 at · 8% · 3 years. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
R1 200
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Reason
I=Pin=5000×0.08×3=1200.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
R1 200
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
R1 200
Copy onto your answer sheet — in this order
Answer: R1 200
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
12 · 2 Marks
Expand (x + 5)(x − 2).
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Expand (x + 5)(x − 2).
Before any working — hunt first
Given
Numbers and units already in the sentence: 5 · 2. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Expand (x + 5)(x − 2). Circle that word — that is the missing variable.
Find
We are required to find: Expand (x + 5)(x − 2). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write x² + 3x − 10 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Expand (x + 5)(x − 2).
In other words — as if you have never seen this before
x² + 3x − 10
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 5 · 2. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
x² + 3x − 10
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 5 · 2. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Expand (x + 5)(x − 2). Circle that word — that is the missing variable.
Find: We are required to find: Expand (x + 5)(x − 2). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: Write x² + 3x − 10 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Expand (x + 5)(x − 2).
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 5 · 2. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
x² + 3x − 10
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
FOIL: x² − 2x + 5x − 10 = x² + 3x − 10. The middle terms add, they do not cancel.
x²+3x−10
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
x² + 3x − 10
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
x² + 3x − 10
Copy onto your answer sheet — in this order
Formula: x² + 3x − 10
Answer: x² + 3x − 10
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
13 · 3 Marks
Sequence 4; 9; 14; 19; … T₂₅=
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: Sequence 4; 9; 14; 19; … T₂₅ =
Before any working — hunt first
Given
Numbers and units already in the sentence: 4 · 9 · 14 · 19. 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: Sequence 4; 9; 14; 19; … T₂₅ =. Circle that word — that is the missing variable.
Find
We are required to find: Sequence 4; 9; 14; 19; … T₂₅ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 124. Then substitute the given, one line at a time, to get Sequence 4; 9; 14; 19; … T₂₅ =.
In other words — as if you have never seen this before
124
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 4 · 9 · 14 · 19. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
124
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 · 9 · 14 · 19. 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: Sequence 4; 9; 14; 19; … T₂₅ =. Circle that word — that is the missing variable.
Find: We are required to find: Sequence 4; 9; 14; 19; … T₂₅ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 124. Then substitute the given, one line at a time, to get Sequence 4; 9; 14; 19; … T₂₅ =.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 4 · 9 · 14 · 19. 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
124
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Reason
a=4, d=5. T₂₅=4+24×5=124.
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
124
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
124
Copy onto your answer sheet — in this order
Answer: 124
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
14 · 3 Marks · Analytical geometry
Midpoint of (2; 4) and (6; 10) is
Analytical geometry
Formulas
d=√[(x₂−x₁)² + (y₂−y₁)²]
Distance
M=((x₁+x₂)/2 ; (y₁+y₂)/2)
Midpoint
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Midpoint of (2; 4) and (6; 10) is
Before any working — hunt first
Given
Numbers and units already in the sentence: 2 · 4 · 6 · 10. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Midpoint of (2; 4) and (6; 10) is. Circle that word — that is the missing variable.
Find
We are required to find: Midpoint of (2; 4) and (6; 10) is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Average the coordinates: ((2+6)/2;(4+10)2)=(4;7). Then substitute the given, one line at a time, to get Midpoint of (2; 4) and (6; 10) is.
In other words — as if you have never seen this before
Average the coordinates: ((2+6)/2;(4+10)2)=(4;7).
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2 · 4 · 6 · 10. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Average the coordinates: ((2+6)/2;(4+10)2)=(4;7).
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 2 · 4 · 6 · 10. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Midpoint of (2; 4) and (6; 10) is. Circle that word — that is the missing variable.
Find: We are required to find: Midpoint of (2; 4) and (6; 10) is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Average the coordinates: ((2+6)/2;(4+10)2)=(4;7). Then substitute the given, one line at a time, to get Midpoint of (2; 4) and (6; 10) is.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 2 · 4 · 6 · 10. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Average the coordinates: ((2+6)/2;(4+10)2)=(4;7).
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Average the coordinates: ((2+6)/2;(4+10)2)=(4;7).
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
(4; 7)
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
(4; 7)
Copy onto your answer sheet — in this order
Answer: (4; 7)
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
15 · 2 Marks · Factorisation
Factorise x² − 16.
Formulas
a²−b²=(a − b)(a + b)
Difference of squares
x²+(p+q)x+pq=(x+p)(x+q)
Trinomial
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Factorise x² − 16.
Before any working — hunt first
Given
Numbers and units already in the sentence: 16. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Factorise x² − 16. Circle that word — that is the missing variable.
Find
We are required to find: Factorise x² − 16. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Difference of squares: a² − b² = (a−b)(a+b). Then substitute the given, one line at a time, to get Factorise x² − 16.
In other words — as if you have never seen this before
Difference of squares: a² − b² = (a−b)(a+b).
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 16. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Difference of squares: a² − b² = (a−b)(a+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: 16. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Factorise x² − 16. Circle that word — that is the missing variable.
Find: We are required to find: Factorise x² − 16. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Difference of squares: a² − b² = (a−b)(a+b). Then substitute the given, one line at a time, to get Factorise x² − 16.
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: 16. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Difference of squares: a² − b² = (a−b)(a+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
Working
Difference of squares: a² − b² = (a−b)(a+b).
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−4)(x+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
(x−4)(x+4)
Copy onto your answer sheet — in this order
Answer: (x−4)(x+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…”
16 · 4 Marks · Probability
Two coins. P(two heads)=
Formulas
P(A)=n(A)n(S)
Classical probability
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Two coins. P(two heads) =
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(two heads) =. Circle that word — that is the missing variable.
Find
We are required to find: P(two heads) =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: HH, HT, TH, TT — one of four. Then substitute the given, one line at a time, to get P(two heads) =.
In other words — as if you have never seen this before
HH, HT, TH, TT — one of four.
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?
HH, HT, TH, TT — one of four.
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(two heads) =. Circle that word — that is the missing variable.
Find: We are required to find: P(two heads) =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: HH, HT, TH, TT — one of four. Then substitute the given, one line at a time, to get P(two heads) =.
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
HH, HT, TH, TT — one of four.
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
HH, HT, TH, TT — one of four.
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
14
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
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
14
Copy onto your answer sheet — in this order
Answer: 14
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
17 · 3 Marks · Statistics
Data 2; 5; 5; 8. Mean=
Statistics
Formulas
x̄=Σxn
Mean
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Data 2; 5; 5; 8. Mean =
Before any working — hunt first
Given
Numbers and units already in the sentence: 2 · 5 · 5 · 8. 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 =. Circle that word — that is the missing variable.
Find
We are required to find: Mean =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: (2+5+5+8)4=5. Then substitute the given, one line at a time, to get Mean =.
In other words — as if you have never seen this before
(2+5+5+8)4=5.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2 · 5 · 5 · 8. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
(2+5+5+8)4=5.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 2 · 5 · 5 · 8. 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 =. Circle that word — that is the missing variable.
Find: We are required to find: Mean =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: (2+5+5+8)4=5. Then substitute the given, one line at a time, to get Mean =.
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 · 5 · 5 · 8. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
(2+5+5+8)4=5.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
(2+5+5+8)4=5.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
5
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
5
Copy onto your answer sheet — in this order
Answer: 5
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
18 · 2 Marks · Simple & compound interest
Simple interest on R3 000 at 5% for 4 years
Simple & compound interest
Formulas
A=P(1 + in)
Simple interest
A=P(1 + i)ⁿ
Compound interest
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Simple interest on R3 000 at 5% for 4 years
In other words — as if you have never seen this before
R600
2. What do we already know?
Copy these onto the left of your page, one per line, with units: R3 · 000 at · 5% · 4 years. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
R600
4. Step-by-step working
01 / 07
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 07
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: R3 · 000 at · 5% · 4 years. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
03 / 07
Step C — Name the method in words
R600
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
04 / 07
Working
I=Pin=3000×0.05×4=600.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
05 / 07
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
06 / 07
Step F — Box the answer with its unit
R600
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
07 / 07
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
R600
Copy onto your answer sheet — in this order
Answer: R600
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
19 · 2 Marks · Exponents
2³×2²=
Formulas
aᵐ·aⁿ=aᵐ⁺ⁿ
Same base, add
a⁻ⁿ=1aⁿ
Negative exponent
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: 2³ × 2² =
Before any working — hunt first
Given
Numbers and units already in the sentence: 2³ · 2². Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: 2³ × 2² =. Circle that word — that is the missing variable.
Find
We are required to find: 2³ × 2² =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Same base: add exponents. Then substitute the given, one line at a time, to get 2³ × 2² =.
In other words — as if you have never seen this before
Same base: add exponents. 3+2=5.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2³ · 2². Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Same base: add exponents. 3+2=5.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 2³ · 2². Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: 2³ × 2² =. Circle that word — that is the missing variable.
Find: We are required to find: 2³ × 2² =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Same base: add exponents. Then substitute the given, one line at a time, to get 2³ × 2² =.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 2³ · 2². Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Same base: add exponents. 3+2=5.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Same base: add exponents. 3+2=5.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
2⁵
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
2⁵
Copy onto your answer sheet — in this order
Answer: 2⁵
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
20 · 3 Marks · Analytical geometry
Gradient of the line through (1; 2) and (5; 10)
Analytical geometry
Formulas
d=√[(x₂−x₁)² + (y₂−y₁)²]
Distance
M=((x₁+x₂)/2 ; (y₁+y₂)/2)
Midpoint
Notes: Point A(1; 2) and B(5; 10). Unknown: m.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Gradient of the line through (1; 2) and (5; 10)
In other words — as if you have never seen this before
m = (y₂ − y₁)/(x₂ − x₁). Rise over run, same order on top and bottom.
2. What do we already know?
Point A(1; 2) and B(5; 10). Unknown: m.
3. Which method — and why this one?
m = (y₂ − y₁)/(x₂ − x₁). Rise over run, same order on top and bottom.
4. Step-by-step working
01 / 05
Write the formula
m=(y₂ − y₁)(x₂ − x₁).
m=(y₂−y₁)(x₂−x₁)
Why this step: Write the formula before numbers. The memo awards a method mark for the law even if a digit slips later.
02 / 05
Substitute
m=(10 − 2)(5 − 1)=84=2.
m=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
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.
5. The answer
2
Copy onto your answer sheet — in this order
Formula: m=(y₂−y₁)(x₂−x₁)
Answer: 2
6. Check it like a marker
From x = 1 to 5 we add 4. From y = 2 to 10 we add 8. 84=2.
7. A trap first-timers fall into
Do not swap to (x₂−x₁)/(y₂−y₁). That is run over rise, the reciprocal.
21 · 2 Marks
Expand (x+3)(x+4)
Notes: Two binomials. Unknown: expanded trinomial.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Expand (x+3)(x+4)
Before any working — hunt first
Given
Numbers and units already in the sentence: 3 · 4. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Expand (x+3)(x+4). Circle that word — that is the missing variable.
Find
We are required to find: Expand (x+3)(x+4). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write x²+4x+3x+12 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Expand (x+3)(x+4).
In other words — as if you have never seen this before
FOIL: First, Outer, Inner, Last. Then collect like terms.
2. What do we already know?
Two binomials. Unknown: expanded trinomial.
3. Which method — and why this one?
FOIL: First, Outer, Inner, Last. Then collect like terms.
4. Step-by-step working
01 / 05
FOIL
x² + 4x + 3x + 12.
x²+4x+3x+12
Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
02 / 05
Collect
x² + 7x + 12.
x²+7x+12
Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.
03 / 05
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
04 / 05
Step F — Box the answer with its unit
x²+7x+12
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
05 / 05
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
x²+7x+12
Copy onto your answer sheet — in this order
Formula: x²+4x+3x+12
Answer: x²+7x+12
6. Check it like a marker
At x=1: (4)(5)=20 and 1+7+12=20. Matches.
7. A trap first-timers fall into
x²+12 forgets the middle terms. They do not cancel — both plus.
22 · 4 Marks
Co-interior angles between parallel lines sum to
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Co-interior angles between parallel lines sum to
In other words — as if you have never seen this before
Co-interior supplementary.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Co-interior supplementary.
4. Step-by-step working
01 / 07
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 07
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
03 / 07
Step C — Name the method in words
Co-interior supplementary.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
04 / 07
Working
Co-interior supplementary.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
05 / 07
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
06 / 07
Step F — Box the answer with its unit
180°
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
07 / 07
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
180°
Copy onto your answer sheet — in this order
Answer: 180°
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
23 · 4 Marks · Surface area & volume
A cylinder r = 3 cm, h = 10 cm. Volume in cm³ (use π = 3.14)
Formulas
Vcyl=πr²h
Cylinder volume
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: A cylinder r = 3 cm, h = 10 cm. Volume in cm³ (use π = 3.14)
Before any working — hunt first
Given
Numbers and units already in the sentence: 3 cm · 10 cm · 3.14. 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: 14). Circle that word — that is the missing variable.
Find
We are required to find: 14). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: V = πr²h = 3. Then substitute the given, one line at a time, to get 14).
In other words — as if you have never seen this before
V=πr²h=3.14×9×10=282.6 cm³.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 3 cm · 10 cm · 3.14. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
V=πr²h=3.14×9×10=282.6 cm³.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 3 cm · 10 cm · 3.14. 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: 14). Circle that word — that is the missing variable.
Find: We are required to find: 14). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: V = πr²h = 3. Then substitute the given, one line at a time, to get 14).
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 3 cm · 10 cm · 3.14. 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
V=πr²h=3.14×9×10=282.6 cm³.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
V=πr²h=3.14×9×10=282.6 cm³.
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
282.6
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
282.6
Copy onto your answer sheet — in this order
Answer: 282.6
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
24 · 2 Marks · Analytical geometry
The line through (0; 1) and (2; 7). Gradient?
Analytical geometry
Formulas
d=√[(x₂−x₁)² + (y₂−y₁)²]
Distance
M=((x₁+x₂)/2 ; (y₁+y₂)/2)
Midpoint
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: The line through (0; 1) and (2; 7). Gradient?
Before any working — hunt first
Given
Numbers and units already in the sentence: 0 · 1 · 2 · 7. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Gradient. Circle that word — that is the missing variable.
Find
We are required to find: Gradient. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 3. Then substitute the given, one line at a time, to get Gradient.
In other words — as if you have never seen this before
3
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 0 · 1 · 2 · 7. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
3
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 0 · 1 · 2 · 7. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Gradient. Circle that word — that is the missing variable.
Find: We are required to find: Gradient. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 3. Then substitute the given, one line at a time, to get Gradient.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 0 · 1 · 2 · 7. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
3
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Reason
m=(7−1)(2−0)=3.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
3
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
3
Copy onto your answer sheet — in this order
Answer: 3
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
25 · 2 Marks · Trigonometry
In a right triangle, opposite = 5, hypotenuse = 13. sin θ =
Trigonometry
Formulas
sin θ=opphyp
Sine
tan θ=oppadj
Tangent
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: In a right triangle, opposite = 5, hypotenuse = 13. sin θ =
Before any working — hunt first
Given
Numbers and units already in the sentence: 5 · 13. 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 =. Circle that word — that is the missing variable.
Find
We are required to find: sin θ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: sin = oppositehypotenuse=513. Then substitute the given, one line at a time, to get sin θ =.
In other words — as if you have never seen this before
sin = oppositehypotenuse=513.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 5 · 13. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
sin = oppositehypotenuse=513.
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 · 13. 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 =. Circle that word — that is the missing variable.
Find: We are required to find: sin θ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: sin = oppositehypotenuse=513. Then substitute the given, one line at a time, to get sin θ =.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 5 · 13. 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
sin = oppositehypotenuse=513.
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
sin = oppositehypotenuse=513.
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
513
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
513
Copy onto your answer sheet — in this order
Answer: 513
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
26 · 2 Marks · Functions
2x+y=11, x−y=1. y=
Functions
Formulas
y=mx+c
Straight line
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: 2x + y = 11, x − y = 1. y =
Before any working — hunt first
Given
Numbers and units already in the sentence: 2x · 11 · 1. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: y =. Circle that word — that is the missing variable.
Find
We are required to find: y =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: x = 4 from adding, then 4 − y = 1. Then substitute the given, one line at a time, to get y =.
In other words — as if you have never seen this before
x=4 from adding, then 4−y=1.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2x · 11 · 1. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
x=4 from adding, then 4−y=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: 2x · 11 · 1. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: y =. Circle that word — that is the missing variable.
Find: We are required to find: y =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: x = 4 from adding, then 4 − y = 1. Then substitute the given, one line at a time, to get 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
Copy these onto the left of your page, one per line, with units: 2x · 11 · 1. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
x=4 from adding, then 4−y=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
x=4 from adding, then 4−y=1.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
3
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
3
Copy onto your answer sheet — in this order
Answer: 3
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
27 · 3 Marks · Functions
A die is fair. P(rolling an even number)?
Functions
Formulas
y=mx+c
Straight line
Notes: A fair six-face die. Even faces: 2, 4, 6. That is three faces. Total faces: 6.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: A die is fair. P(rolling an even number)?
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(rolling an even number). Circle that word — that is the missing variable.
Find
We are required to find: P(rolling an even number). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write P = 12 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives P(rolling an even number).
In other words — as if you have never seen this before
Probability = favourabletotal, when every face is equally likely.
2. What do we already know?
A fair six-face die. Even faces: 2, 4, 6. That is three faces. Total faces: 6.
3. Which method — and why this one?
Probability = favourabletotal, when every face is equally likely.
4. Step-by-step working
01 / 05
Count favourable
Even numbers on a die: 2, 4 and 6. Three outcomes. Do not include 0 — dice do not have a 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.
02 / 05
Divide
P = 36. Simplify by 3: 12. Leaving 36 is not wrong, but NSC usually wants the simplest form.
P=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.
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
12
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
05 / 05
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
12
Copy onto your answer sheet — in this order
Formula: P=12
Answer: 12
6. Check it like a marker
Odd would also be 12. Together they add to 1. Good.
7. A trap first-timers fall into
Writing 3, or 13 (thinking 2,4,6 out of the even “ideas”). Always divide by 6, the faces.
28 · 3 Marks · Statistics
Data 1,2,2,3,12. The median is
Statistics
Formulas
x̄=Σxn
Mean
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Data 1,2,2,3,12. The median is
Before any working — hunt first
Given
Numbers and units already in the sentence: 1,2 · 2,3 · 12. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: The median is. Circle that word — that is the missing variable.
Find
We are required to find: The median is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Middle of ordered list is 2. Then substitute the given, one line at a time, to get The median is.
In other words — as if you have never seen this before
Middle of ordered list is 2.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1,2 · 2,3 · 12. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Middle of ordered list is 2.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 1,2 · 2,3 · 12. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: The median is. Circle that word — that is the missing variable.
Find: We are required to find: The median is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Middle of ordered list is 2. Then substitute the given, one line at a time, to get The median is.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 1,2 · 2,3 · 12. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Middle of ordered list is 2.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Middle of ordered list is 2.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
2
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
2
Copy onto your answer sheet — in this order
Answer: 2
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
29 · 2 Marks · Factorisation
Factorise x² − 81.
Formulas
a²−b²=(a − b)(a + b)
Difference of squares
x²+(p+q)x+pq=(x+p)(x+q)
Trinomial
Notes: One expression: x² − 81. 81 is 9².
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Factorise x² − 81.
Before any working — hunt first
Given
Numbers and units already in the sentence: 81. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Factorise x² − 81. Circle that word — that is the missing variable.
Find
We are required to find: Factorise x² − 81. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write a = x, b = 9 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Factorise x² − 81.
In other words — as if you have never seen this before
Difference of squares: a² − b² = (a−b)(a+b). a = x, b = 9.
2. What do we already know?
One expression: x² − 81. 81 is 9².
3. Which method — and why this one?
Difference of squares: a² − b² = (a−b)(a+b). a = x, b = 9.
4. Step-by-step working
01 / 05
Name the squares
x² = (x)² and 81 = (9)².
a=x, b=9
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
Write the brackets
(x − 9)(x + 9). One minus, one plus.
(x−9)(x+9)
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
(x−9)(x+9)
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.
Do not write (x−9)². That expands to x² − 18x + 81.
30 · 2 Marks
2⁻³=
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: 2⁻³ =
Before any working — hunt first
Given
Numbers and units already in the sentence: 2⁻³. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: 2⁻³ =. Circle that word — that is the missing variable.
Find
We are required to find: 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: a⁻ⁿ = 1aⁿ=18. Then substitute the given, one line at a time, to get 2⁻³ =.
In other words — as if you have never seen this before
a⁻ⁿ=1aⁿ=18.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2⁻³. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
a⁻ⁿ=1aⁿ=18.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 2⁻³. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: 2⁻³ =. Circle that word — that is the missing variable.
Find: We are required to find: 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: a⁻ⁿ = 1aⁿ=18. Then substitute the given, one line at a time, to get 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: 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
a⁻ⁿ=1aⁿ=18.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
a⁻ⁿ=1aⁿ=18.
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
18
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
18
Copy onto your answer sheet — in this order
Answer: 18
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…”