A Polokwane taxi covers 210 km at 70 kmh. Time in hours?
Notes: Distance s = 210 km. Speed v = 70 kmh. Unknown: time t in hours.
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 Polokwane taxi covers 210 km at 70 kmh. Time in hours?
Before any working — hunt first
Given
Numbers and units already in the sentence: 210 km · 70 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 in hours. Circle that word — that is the missing variable.
Find
We are required to find: Time in hours. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write t = sv with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Time in hours.
In other words — as if you have never seen this before
Time is distance divided by speed. In words: “how many seventies fit into 210?”
2. What do we already know?
Distance s = 210 km. Speed v = 70 kmh. Unknown: time t in hours.
3. Which method — and why this one?
Time is distance divided by speed. In words: “how many seventies fit into 210?”
4. Step-by-step working
01 / 06
Write the formula in words
time = distancespeed. Symbols: t = sv.
t=sv
Why this step: We write the formula empty first so the marker can award a method mark even if a number later slips.
02 / 06
Substitute, do not calculate yet
t = 21070. Both numbers are in km and kmh, so the km cancel and hours remain.
t=21070
Why this step: Matching units is the whole trick. If the paper had given 70 km/h and 210 m you would convert first.
03 / 06
Calculate one step
21070=3. So t=3 h. Check: 3×70=210 km. It lands exactly.
t=3 h
Why this step: The reverse multiply is the marker’s favourite check. If it does not rebuild 210, you divided the wrong way round.
04 / 06
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
05 / 06
Step F — Box the answer with its unit
3 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.
06 / 06
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
3 h
Copy onto your answer sheet — in this order
Formula: t=sv
Answer: 3 h
6. Check it like a marker
3 × 70 = 210. Units are hours, which is what was asked. 14 h would be 21015 — a calculator slip.
7. A trap first-timers fall into
Doing 70210=0.33 h. That is speeddistance, which is the reciprocal of time. Always say the formula in words first.
1.2 · 8 Marks
Expand (x + 7)(x − 3).
Notes: Two brackets. First: x + 7. Second: x − 3. Unknown: the 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 + 7)(x − 3).
Before any working — hunt first
Given
Numbers and units already in the sentence: 7 · 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: Expand (x + 7)(x − 3). Circle that word — that is the missing variable.
Find
We are required to find: Expand (x + 7)(x − 3). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write x² − 3x + 7x − 21 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Expand (x + 7)(x − 3).
In other words — as if you have never seen this before
FOIL: First, Outer, Inner, Last. Then collect the two middle (x) terms.
2. What do we already know?
Two brackets. First: x + 7. Second: x − 3. Unknown: the expanded trinomial.
3. Which method — and why this one?
FOIL: First, Outer, Inner, Last. Then collect the two middle (x) terms.
Why this step: Write all four even if two will later cancel or add. Skipping Inner is the classic first-timer miss.
02 / 05
Collect like terms
−3x + 7x = +4x. Nothing else is an x-term. So x² + 4x − 21.
x²+4x−21
Why this step: The signs ride with the numbers. 7x is plus because 7 is plus; −3x is minus because of −3.
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 + 4x − 21
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 + 4x − 21
Copy onto your answer sheet — in this order
Formula: x² − 3x + 7x − 21
Answer: x² + 4x − 21
6. Check it like a marker
Pick x = 1: (8)(−2) = −16. And 1 + 4 − 21 = −16. Same number, so the expansion is right.
7. A trap first-timers fall into
Writing x² − 21 and dropping the middle. That would be (x+√21)(x−√21), a different identity.
2.1 · 10 Marks · Analytical geometry
Gradient of the line through (1; 2) and (5; 14).
Analytical geometry
Formulas
d=√[(x₂−x₁)² + (y₂−y₁)²]
Distance
M=((x₁+x₂)/2 ; (y₁+y₂)/2)
Midpoint
Notes: Point A (1; 2), point B (5; 14). Unknown: gradient m.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Gradient of the line through (1; 2) and (5; 14).
In other words — as if you have never seen this before
Gradient is rise over run: change in y divided by change in x, in the same order.
2. What do we already know?
Point A (1; 2), point B (5; 14). Unknown: gradient m.
3. Which method — and why this one?
Gradient is rise over run: change in y divided by change in x, in the same order.
4. Step-by-step working
01 / 06
Write the formula
m = (y₂ − y₁) / (x₂ − x₁). Call (1; 2) point 1 and (5; 14) point 2.
m=(y₂ − y₁)(x₂ − x₁)
Why this step: Order matters. If you subtract the x’s the other way, you must also flip the y’s, or the sign of m flips.
02 / 06
Substitute
m=(14 − 2)(5 − 1)=124.
m=124
Why this step: Rise 12, run 4. A 12-up-for-4-along line is steep, so m around 3 is sensible — not 12, not 1/3.
03 / 06
Simplify
124=3. So m = 3. From x = 1 to x = 5 we add 4; y must add 12, which is 3 × 4.
m=3
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
04 / 06
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
05 / 06
Step F — Box the answer with its unit
3
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
06 / 06
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
3
Copy onto your answer sheet — in this order
Formula: m=(y₂ − y₁)(x₂ − x₁)
Answer: 3
6. Check it like a marker
Start at (1; 2), add 4 to x and 12 to y: (5; 14). Lands on the second point.
7. A trap first-timers fall into
Writing 412=13 — that is run over rise. Gradient is never “along over up”.
2.2 · 12 Marks · Simple & compound interest
Simple interest on R4 000 at 8% p.a. for 3 years.
Simple & compound interest
Formulas
A=P(1 + in)
Simple interest
A=P(1 + i)ⁿ
Compound interest
Notes: P = R4 000 (the starting money). i = 8% = 0.08 per year. n = 3 years. Unknown: interest I, not the amount.
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 R4 000 at 8% p.a. for 3 years.
Before any working — hunt first
Given
Numbers and units already in the sentence: R4 · 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: for 3 years. Circle that word — that is the missing variable.
Find
We are required to find: for 3 years. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write i = 0.08 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives for 3 years.
In other words — as if you have never seen this before
Simple interest: I = P × i × n. The interest is a rectangle — principal, rate, time, multiplied.
2. What do we already know?
P = R4 000 (the starting money). i = 8% = 0.08 per year. n = 3 years. Unknown: interest I, not the amount.
3. Which method — and why this one?
Simple interest: I = P × i × n. The interest is a rectangle — principal, rate, time, multiplied.
4. Step-by-step working
01 / 05
Percent to decimal
8% means 8 per hundred = 8100=0.08. Never leave the 8 sitting next to 4000.
i=0.08
Why this step: If you multiply by 8 you are charging 800% a year. First-timers do this when they are rushing.
02 / 05
Multiply
I=4000×0.08×3. First 4000×0.08=320 (one year’s interest). Then 320×3=960.
I=960
Why this step: Doing one year first is a gift: you can see whether R320 on R4 000 feels like 8% (it does).
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
R960
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
R960
Copy onto your answer sheet — in this order
Formula: i=0.08
Answer: R960
6. Check it like a marker
Amount A = 4000 + 960 = 4960. That is an option — but the paper asked for interest, not amount.
7. A trap first-timers fall into
Picking R4 960. That is A, the total you have after 3 years. The question said “interest on”.
3.1 · 12 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.
6 · 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…”
7 · 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…”
8 · 3 Marks · Simple & compound interest
Simple interest on R5 000 at 8% for 3 years
Simple & compound interest
Formulas
A=P(1 + in)
Simple interest
A=P(1 + i)ⁿ
Compound interest
Notes: P=5000, i=8%=0.08, n=3. Asked for interest I, not amount A.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Simple interest on R5 000 at 8% for 3 years
In other words — as if you have never seen this before
I=Pin.
2. What do we already know?
P=5000, i=8%=0.08, n=3. Asked for interest I, not amount A.
3. Which method — and why this one?
I=Pin.
4. Step-by-step working
01 / 05
Write I = Pin
Change 8% to 0.08.
I=Pin
Why this step: Write the formula before numbers. The memo awards a method mark for the law even if a digit slips later.
02 / 05
Substitute
I=5000×0.08×3=400×3=R1 200.
I=R1 200
Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
03 / 05
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
04 / 05
Step F — Box the answer with its unit
R1 200
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
05 / 05
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
R1 200
Copy onto your answer sheet — in this order
Formula: I=Pin
Answer: R1 200
6. Check it like a marker
8% of 5000 is R400 per year. Three years: R1 200.
7. A trap first-timers fall into
R6 200 is the amount P+I. The paper asked for interest.
9 · 2 Marks · Statistics
Mean of 2, 4, 6 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: Mean of 2, 4, 6 is
Before any working — hunt first
Given
Numbers and units already in the sentence: 2 · 4 · 6 is. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Mean of 2, 4, 6 is. Circle that word — that is the missing variable.
Find
We are required to find: Mean of 2, 4, 6 is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: (2+4+6)3=4. Then substitute the given, one line at a time, to get Mean of 2, 4, 6 is.
In other words — as if you have never seen this before
(2+4+6)3=4.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2 · 4 · 6 is. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
(2+4+6)3=4.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 2 · 4 · 6 is. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Mean of 2, 4, 6 is. Circle that word — that is the missing variable.
Find: We are required to find: Mean of 2, 4, 6 is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: (2+4+6)3=4. Then substitute the given, one line at a time, to get Mean of 2, 4, 6 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 is. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
(2+4+6)3=4.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
(2+4+6)3=4.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
4
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
4
Copy onto your answer sheet — in this order
Answer: 4
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
10 · 2 Marks · Probability
A die is fair. P(rolling a 6)?
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: A die is fair. P(rolling a 6)?
Before any working — hunt first
Given
Numbers and units already in the sentence: 6. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: P(rolling a 6). Circle that word — that is the missing variable.
Find
We are required to find: P(rolling a 6). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: One favourable outcome out of six faces. Then substitute the given, one line at a time, to get P(rolling a 6).
In other words — as if you have never seen this before
One favourable outcome out of six faces.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 6. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
One favourable outcome out of six faces.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 6. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: P(rolling a 6). Circle that word — that is the missing variable.
Find: We are required to find: P(rolling a 6). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: One favourable outcome out of six faces. Then substitute the given, one line at a time, to get P(rolling a 6).
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 6. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
One favourable outcome out of six faces.
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
One favourable outcome out of six faces.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
16
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
16
Copy onto your answer sheet — in this order
Answer: 16
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
11 · 2 Marks
Expand (x+4)(x−1).
Notes: Two brackets: (x+4)(x−1).
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+4)(x−1).
Before any working — hunt first
Given
Numbers and units already in the sentence: 4 · 1. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Expand (x+4)(x−1). Circle that word — that is the missing variable.
Find
We are required to find: Expand (x+4)(x−1). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write x² − x + 4x − 4 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Expand (x+4)(x−1).
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 brackets: (x+4)(x−1).
3. Which method — and why this one?
FOIL: First, Outer, Inner, Last. Then collect like terms.
4. Step-by-step working
01 / 05
FOIL
x·x=x². x·(−1)=−x. 4·x=4x. 4·(−1)=−4.
x²−x+4x−4
Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
02 / 05
Collect
−x+4x=3x. So x²+3x−4.
x²+3x−4
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
x² + 3x − 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.
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 + 3x − 4
Copy onto your answer sheet — in this order
Formula: x² − x + 4x − 4
Answer: x² + 3x − 4
6. Check it like a marker
Let x=1: left (5)(0)=0. Right 1+3−4=0. Matches.
7. A trap first-timers fall into
The middle terms add, they do not cancel. Cancelling would need +x and −x.
12 · 2 Marks · Probability
A bag has 2 red and 3 blue. P(blue) =
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: A bag has 2 red and 3 blue. P(blue) =
Before any working — hunt first
Given
Numbers and units already in the sentence: 2 red · 3 blue. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: P(blue) =. Circle that word — that is the missing variable.
Find
We are required to find: P(blue) =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 3 blue out of 5 marbles. Then substitute the given, one line at a time, to get P(blue) =.
In other words — as if you have never seen this before
3 blue out of 5 marbles.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2 red · 3 blue. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
3 blue out of 5 marbles.
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 red · 3 blue. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: P(blue) =. Circle that word — that is the missing variable.
Find: We are required to find: P(blue) =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 3 blue out of 5 marbles. Then substitute the given, one line at a time, to get P(blue) =.
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 red · 3 blue. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
3 blue out of 5 marbles.
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
3 blue out of 5 marbles.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
35
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
35
Copy onto your answer sheet — in this order
Answer: 35
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
13 · 2 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.
14 · 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…”
15 · 2 Marks
3²×3³=
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: 3² × 3³ =
Before any working — hunt first
Given
Numbers and units already in the sentence: 3² · 3³. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: 3² × 3³ =. Circle that word — that is the missing variable.
Find
We are required to find: 3² × 3³ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 3⁵. Then substitute the given, one line at a time, to get 3² × 3³ =.
In other words — as if you have never seen this before
3⁵
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 3² · 3³. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
3⁵
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 3² · 3³. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: 3² × 3³ =. Circle that word — that is the missing variable.
Find: We are required to find: 3² × 3³ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 3⁵. Then substitute the given, one line at a time, to get 3² × 3³ =.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 3² · 3³. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
3⁵
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Same base: add the indices. 2 + 3 = 5, so 3⁵. Do not multiply the bases.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
3⁵
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
3⁵
Copy onto your answer sheet — in this order
Answer: 3⁵
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
16 · 3 Marks
When you divide −2x ≥ 8 by −2, the inequality
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: When you divide −2x ≥ 8 by −2, the inequality
In other words — as if you have never seen this before
Dividing by a negative reverses ≥ to ≤. 8/−2=−4.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2x · 8 by · 2. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Dividing by a negative reverses ≥ to ≤. 8/−2=−4.
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: 2x · 8 by · 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.
03 / 07
Step C — Name the method in words
Dividing by a negative reverses ≥ to ≤. 8/−2=−4.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
04 / 07
Working
Dividing by a negative reverses ≥ to ≤. 8/−2=−4.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
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
flips: 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.
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
flips: x ≤ −4
Copy onto your answer sheet — in this order
Answer: flips: 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…”
17 · 2 Marks · Factorisation
Factorise fully: 3x² − 12.
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 fully: 3x² − 12.
Before any working — hunt first
Given
Numbers and units already in the sentence: 3x² · 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: Factorise fully: 3x² − 12. Circle that word — that is the missing variable.
Find
We are required to find: Factorise fully: 3x² − 12. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: HCF 3 first: 3(x² − 4) = 3(x−2)(x+2). Then substitute the given, one line at a time, to get Factorise fully: 3x² − 12.
In other words — as if you have never seen this before
HCF 3 first: 3(x² − 4)=3(x−2)(x+2).
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 3x² · 12. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
HCF 3 first: 3(x² − 4)=3(x−2)(x+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: 3x² · 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: Factorise fully: 3x² − 12. Circle that word — that is the missing variable.
Find: We are required to find: Factorise fully: 3x² − 12. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: HCF 3 first: 3(x² − 4) = 3(x−2)(x+2). Then substitute the given, one line at a time, to get Factorise fully: 3x² − 12.
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: 3x² · 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
HCF 3 first: 3(x² − 4)=3(x−2)(x+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
HCF 3 first: 3(x² − 4)=3(x−2)(x+2).
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
3(x−2)(x+2)
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
3(x−2)(x+2)
Copy onto your answer sheet — in this order
Answer: 3(x−2)(x+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…”
18 · 2 Marks
Solve 4x+5=21.
Notes: 4x + 5 on the left. 21 on the right. Unknown x.
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 4x + 5 = 21.
Before any working — hunt first
Given
Numbers and units already in the sentence: 4x · 5 · 21. 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 4x + 5 = 21. Circle that word — that is the missing variable.
Find
We are required to find: Solve 4x + 5 = 21. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write 4x = 16 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Solve 4x + 5 = 21.
In other words — as if you have never seen this before
Undo +5 first (subtract 5), then undo ×4 (divide by 4). Same to both sides.
2. What do we already know?
4x + 5 on the left. 21 on the right. Unknown x.
3. Which method — and why this one?
Undo +5 first (subtract 5), then undo ×4 (divide by 4). Same to both sides.
4. Step-by-step working
01 / 05
Subtract 5
4x+5−5=21−5→4x=16.
4x=16
Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
02 / 05
Divide by 4
x=164=4.
x=4
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=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.
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
x=4
Copy onto your answer sheet — in this order
Formula: 4x=16
Answer: x=4
6. Check it like a marker
4(4)+5=16+5=21. Both sides match.
7. A trap first-timers fall into
Do not divide by 4 first — that splits the +5 and makes a mess. Reverse BODMAS.
19 · 2 Marks · Trigonometry
sin of a right triangle opposite 3, hypotenuse 5
Trigonometry
Formulas
sin θ=opphyp
Sine
tan θ=oppadj
Tangent
Notes: opp=3. hyp=5. A 3-4-5 triangle.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: sin of a right triangle opposite 3, hypotenuse 5
In other words — as if you have never seen this before
sin = oppositehypotenuse.
2. What do we already know?
opp=3. hyp=5. A 3-4-5 triangle.
3. Which method — and why this one?
sin = oppositehypotenuse.
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
opp=3. hyp=5. A 3-4-5 triangle.
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
sin = oppositehypotenuse.
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
SOH
sin=35.
35
Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.
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
35
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
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
35
Copy onto your answer sheet — in this order
Formula: 35
Answer: 35
6. Check it like a marker
cos would be 45. tan would be 34. Match the ratio to the name.
7. A trap first-timers fall into
34 is tan. 45 is cos. Write SOH CAH TOA in the margin.
20 · 2 Marks · Simple & compound interest
Simple interest on R2000 at 10% for 2 years is
Simple & compound interest
Formulas
A=P(1 + in)
Simple interest
A=P(1 + i)ⁿ
Compound interest
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Simple interest on R2000 at 10% for 2 years is
In other words — as if you have never seen this before
I=Pin=2000×0.1×2=400.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: R2000 at · 10% · 2 years. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
I=Pin=2000×0.1×2=400.
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: R2000 at · 10% · 2 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
I=Pin=2000×0.1×2=400.
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=2000×0.1×2=400.
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
R400
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
R400
Copy onto your answer sheet — in this order
Answer: R400
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
21 · 2 Marks · Probability
P(heart) from a 52-card pack
Formulas
P(A)=n(A)n(S)
Classical probability
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: P(heart) from a 52-card pack
Before any working — hunt first
Given
Numbers and units already in the sentence: 52. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: P(heart) from a 52-card pack. Circle that word — that is the missing variable.
Find
We are required to find: P(heart) from a 52-card pack. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 1352. Then substitute the given, one line at a time, to get P(heart) from a 52-card pack.
In other words — as if you have never seen this before
1352
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 52. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
1352
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 52. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: P(heart) from a 52-card pack. Circle that word — that is the missing variable.
Find: We are required to find: P(heart) from a 52-card pack. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 1352. Then substitute the given, one line at a time, to get P(heart) from a 52-card pack.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 52. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
1352
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
13 hearts out of 52 cards. Simplify later to 14 if the paper asks. Favourabletotal.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
1352
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
1352
Copy onto your answer sheet — in this order
Answer: 1352
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
22 · 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…”
23 · 3 Marks · Analytical geometry
The line through (1; 2) and (3; 8) has equation
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 (1; 2) and (3; 8) has equation
In other words — as if you have never seen this before
m=(8−2)(3−1)=3. y−2=3(x−1)→y=3x−1.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1 · 2 · 3 · 8. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
m=(8−2)(3−1)=3. y−2=3(x−1)→y=3x−1.
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: 1 · 2 · 3 · 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.
03 / 07
Step C — Name the method in words
m=(8−2)(3−1)=3. y−2=3(x−1)→y=3x−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.
04 / 07
Working
m=(8−2)(3−1)=3. y−2=3(x−1)→y=3x−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.
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
y=3x−1
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
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
y=3x−1
Copy onto your answer sheet — in this order
Answer: y=3x−1
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
24 · 2 Marks · Number patterns
Which number is irrational?
Number patterns
Formulas
Tₙ=a+(n − 1)d
nth term
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Which number is irrational?
Before any working — hunt first
Given
Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Which number is irrational. Circle that word — that is the missing variable.
Find
We are required to find: Which number is irrational. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: √2 cannot be ab. Then substitute the given, one line at a time, to get Which number is irrational.
In other words — as if you have never seen this before
√2 cannot be ab. √9=3 is rational.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
√2 cannot be ab. √9=3 is rational.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Which number is irrational. Circle that word — that is the missing variable.
Find: We are required to find: Which number is irrational. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: √2 cannot be ab. Then substitute the given, one line at a time, to get Which number is irrational.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
√2 cannot be ab. √9=3 is rational.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
√2 cannot be ab. √9=3 is rational.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
√2
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
√2
Copy onto your answer sheet — in this order
Answer: √2
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
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 · 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…”
27 · 3 Marks · Trigonometry
cos θ = adjacenthypotenuse. If adj=9, hyp=15, cos 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: cos θ = adjacenthypotenuse. If adj=9, hyp=15, cos θ =
Before any working — hunt first
Given
Numbers and units already in the sentence: 9 · 15. 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: If adj=9, hyp=15, cos θ =. Circle that word — that is the missing variable.
Find
We are required to find: If adj=9, hyp=15, cos θ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 915=35. Then substitute the given, one line at a time, to get If adj=9, hyp=15, cos θ =.
In other words — as if you have never seen this before
915=35.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 9 · 15. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
915=35.
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: 9 · 15. 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: If adj=9, hyp=15, cos θ =. Circle that word — that is the missing variable.
Find: We are required to find: If adj=9, hyp=15, cos θ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 915=35. Then substitute the given, one line at a time, to get If adj=9, hyp=15, cos 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: 9 · 15. 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
915=35.
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
915=35.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
35
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
35
Copy onto your answer sheet — in this order
Answer: 35
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
28 · 3 Marks · Analytical geometry
Distance (1; 1) to (4; 5)
Analytical geometry
Formulas
d=√[(x₂−x₁)² + (y₂−y₁)²]
Distance
M=((x₁+x₂)/2 ; (y₁+y₂)/2)
Midpoint
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Distance (1; 1) to (4; 5)
Before any working — hunt first
Given
Numbers and units already in the sentence: 1 · 1 · 4 · 5. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Distance (1; 1) to (4; 5). Circle that word — that is the missing variable.
Find
We are required to find: Distance (1; 1) to (4; 5). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 5. Then substitute the given, one line at a time, to get Distance (1; 1) to (4; 5).
In other words — as if you have never seen this before
5
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1 · 1 · 4 · 5. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
5
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 1 · 1 · 4 · 5. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Distance (1; 1) to (4; 5). Circle that word — that is the missing variable.
Find: We are required to find: Distance (1; 1) to (4; 5). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 5. Then substitute the given, one line at a time, to get Distance (1; 1) to (4; 5).
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 1 · 1 · 4 · 5. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
5
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Reason
√9+16=5.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
5
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
5
Copy onto your answer sheet — in this order
Answer: 5
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
29 · 4 Marks
(3²)³=
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: (3²)³ =
Before any working — hunt first
Given
Numbers and units already in the sentence: 3². Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: (3²)³ =. Circle that word — that is the missing variable.
Find
We are required to find: (3²)³ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Power of a power: 3⁶ = 729. Then substitute the given, one line at a time, to get (3²)³ =.
In other words — as if you have never seen this before
Power of a power: 3⁶ = 729.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 3². Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Power of a power: 3⁶ = 729.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 3². Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: (3²)³ =. Circle that word — that is the missing variable.
Find: We are required to find: (3²)³ =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Power of a power: 3⁶ = 729. Then substitute the given, one line at a time, to get (3²)³ =.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 3². Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Power of a power: 3⁶ = 729.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Power of a power: 3⁶ = 729.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
729
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
729
Copy onto your answer sheet — in this order
Answer: 729
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
30 · 3 Marks · Probability
P(red) from 3 red and 7 blue marbles?
Formulas
P(A)=n(A)n(S)
Classical probability
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: P(red) from 3 red and 7 blue marbles?
Before any working — hunt first
Given
Numbers and units already in the sentence: 3 red · 7 blue. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: P(red) from 3 red and 7 blue marbles. Circle that word — that is the missing variable.
Find
We are required to find: P(red) from 3 red and 7 blue marbles. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 310. Then substitute the given, one line at a time, to get P(red) from 3 red and 7 blue marbles.
In other words — as if you have never seen this before
310
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 3 red · 7 blue. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
310
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 3 red · 7 blue. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: P(red) from 3 red and 7 blue marbles. Circle that word — that is the missing variable.
Find: We are required to find: P(red) from 3 red and 7 blue marbles. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 310. Then substitute the given, one line at a time, to get P(red) from 3 red and 7 blue marbles.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 3 red · 7 blue. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
310
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Reason
3 favourable out of 10.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
310
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
310
Copy onto your answer sheet — in this order
Answer: 310
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”