2025 · practice · Mathematical Literacy · Grade 11

Grade 11 Mathematical Literacy — KwaZulu-Natal practice

Notes

Answer every question. Show the formula, the substitution, and the answer with units. Calculators allowed. These are original practice papers in the style of the province, not a copy of a department PDF.

90 min · 90 Marks · 30 questions

Learn the paper in the app: notes, a marks breakdown, the formula you need, and the board working. You do not need to download it.

Sit it timed Formula sheet

Question breakdown

1.1 · 6 Marks
An invoice in Durban shows R1000 excluding VAT. VAT is 15%. VAT amount?
Notes: An invoice in Durban shows R1000 excluding VAT. VAT is 15%. VAT 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: An invoice in Durban shows R1000 excluding VAT. VAT is 15%. VAT amount?
Before any working — hunt first
Given
Numbers and units already in the sentence: R1000 excluding · 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: VAT amount. Circle that word — that is the missing variable.
Find
We are required to find: VAT amount. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: VAT = 0. Then substitute the given, one line at a time, to get VAT amount.
In other words — as if you have never seen this before
VAT=0.15×1000=150.
2. What do we already know?
An invoice in Durban shows R1000 excluding VAT. VAT is 15%. VAT amount?
3. Which method — and why this one?
VAT=0.15×1000=150.
4. Step-by-step working
1. 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.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: R1000 excluding · 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: VAT amount. Circle that word — that is the missing variable. Find: We are required to find: VAT amount. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: VAT = 0. Then substitute the given, one line at a time, to get VAT amount.
  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).
3. 03 / 08
  Step B — Write the given in a column
  An invoice in Durban shows R1000 excluding VAT. VAT is 15%. VAT amount?
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  VAT=0.15×1000=150.
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Working
  VAT=0.15×1000=150.
  Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  R150.00
  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.
8. 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
R150.00
Copy onto your answer sheet — in this order
Answer: R150.00
6. Check it like a marker
VAT=0.15×1000=150.
7. A trap first-timers fall into
R1150.00
1.2 · 6 Marks
Total including that VAT
Notes: Total including that VAT
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: Total including that VAT
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: Total including that VAT. Circle that word — that is the missing variable.
Find
We are required to find: Total including that VAT. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Total = 1000 + 150 = 1150. Then substitute the given, one line at a time, to get Total including that VAT.
In other words — as if you have never seen this before
Total=1000+150=1150.
2. What do we already know?
Total including that VAT
3. Which method — and why this one?
Total=1000+150=1150.
4. Step-by-step working
1. 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.
2. 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: Total including that VAT. Circle that word — that is the missing variable. Find: We are required to find: Total including that VAT. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: Total = 1000 + 150 = 1150. Then substitute the given, one line at a time, to get Total including that VAT.
  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).
3. 03 / 08
  Step B — Write the given in a column
  Total including that VAT
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  Total=1000+150=1150.
  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.
5. 05 / 08
  Working
  Total=1000+150=1150.
  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.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  R1150.00
  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.
8. 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
R1150.00
Copy onto your answer sheet — in this order
Answer: R1150.00
6. Check it like a marker
Total=1000+150=1150.
7. A trap first-timers fall into
R150.00
2.1 · 8 Marks · Simple and compound interest
R6000 at 8% per year simple interest for 2 years. Interest earned?
Formulas
A=P(1 + in)A=P(1 + i)ⁿ
Simple interest vs compound interest
Notes: R6000 at 8% per year simple interest for 2 years. Interest earned?
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: R6000 at 8% per year simple interest for 2 years. Interest earned?
Before any working — hunt first
Given
Numbers and units already in the sentence: R6000 at · 8% · 2 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: I = Pin = 6000 × 0. Then substitute the given, one line at a time, to get Interest earned.
In other words — as if you have never seen this before
I=Pin=6000×0.08×2=960.
2. What do we already know?
R6000 at 8% per year simple interest for 2 years. Interest earned?
3. Which method — and why this one?
I=Pin=6000×0.08×2=960.
4. Step-by-step working
1. 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.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: R6000 at · 8% · 2 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: I = Pin = 6000 × 0. 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).
3. 03 / 08
  Step B — Write the given in a column
  R6000 at 8% per year simple interest for 2 years. Interest earned?
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  I=Pin=6000×0.08×2=960.
  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.
5. 05 / 08
  Working
  I=Pin=6000×0.08×2=960.
  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.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  R960.00
  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.
8. 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
R960.00
Copy onto your answer sheet — in this order
Answer: R960.00
6. Check it like a marker
I=Pin=6000×0.08×2=960.
7. A trap first-timers fall into
R6960.00
2.2 · 6 Marks
Two towns are 7 km apart. Map scale 1:100 000. Map distance?
Notes: Two towns are 7 km apart. Map scale 1:100 000. Map distance?
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Two towns are 7 km apart. Map scale 1:100 000. Map distance?
Before any working — hunt first
Given
Numbers and units already in the sentence: 7 km · 1 · 100 · 000. 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: Map distance. Circle that word — that is the missing variable.
Find
We are required to find: Map distance. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 7 km = 700000 cm on the ground. Then substitute the given, one line at a time, to get Map distance.
In other words — as if you have never seen this before
7 km = 700000 cm on the ground. Divide by 100 000: 7 cm on the map.
2. What do we already know?
Two towns are 7 km apart. Map scale 1:100 000. Map distance?
3. Which method — and why this one?
7 km = 700000 cm on the ground. Divide by 100 000: 7 cm on the map.
4. Step-by-step working
1. 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.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 7 km · 1 · 100 · 000. 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: Map distance. Circle that word — that is the missing variable. Find: We are required to find: Map distance. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 7 km = 700000 cm on the ground. Then substitute the given, one line at a time, to get Map distance.
  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).
3. 03 / 08
  Step B — Write the given in a column
  Two towns are 7 km apart. Map scale 1:100 000. Map distance?
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  7 km = 700000 cm on the ground. Divide by 100 000: 7 cm on the map.
  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.
5. 05 / 08
  Working
  7 km = 700000 cm on the ground. Divide by 100 000: 7 cm on the map.
  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.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  7 cm
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 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
7 cm
Copy onto your answer sheet — in this order
Answer: 7 cm
6. Check it like a marker
7 km = 700000 cm on the ground. Divide by 100 000: 7 cm on the map.
7. A trap first-timers fall into
70 cm
3.1 · 4 Marks
A till slip that already includes VAT. To find the VAT inside it you
Notes: A till slip that already includes VAT. To find the VAT inside it you
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 till slip that already includes VAT. To find the VAT inside it you
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: the VAT inside it you. Circle that word — that is the missing variable.
Find
We are required to find: the VAT inside it you. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Inclusive price is 115%. Then substitute the given, one line at a time, to get the VAT inside it you.
In other words — as if you have never seen this before
Inclusive price is 115%. Exclusive = inclusive1.15. VAT is the difference.
2. What do we already know?
A till slip that already includes VAT. To find the VAT inside it you
3. Which method — and why this one?
Inclusive price is 115%. Exclusive = inclusive1.15. VAT is the difference.
4. Step-by-step working
1. 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.
2. 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: the VAT inside it you. Circle that word — that is the missing variable. Find: We are required to find: the VAT inside it you. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: Inclusive price is 115%. Then substitute the given, one line at a time, to get the VAT inside it you.
  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).
3. 03 / 08
  Step B — Write the given in a column
  A till slip that already includes VAT. To find the VAT inside it you
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  Inclusive price is 115%. Exclusive = inclusive1.15. VAT is the difference.
  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.
5. 05 / 08
  Working
  Inclusive price is 115%. Exclusive = inclusive1.15. VAT is the difference.
  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.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  divide by 1.15, then subtract from the total
  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.
8. 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
divide by 1.15, then subtract from the total
Copy onto your answer sheet — in this order
Answer: divide by 1.15, then subtract from the total
6. Check it like a marker
Inclusive price is 115%. Exclusive = inclusive1.15. VAT is the difference.
7. A trap first-timers fall into
take 15% of the inclusive price
3.2 · 6 Marks · Tree diagrams and relative frequency
Probability of a red marble from 3 red and 7 blue
Formulas
P(A then B)=P(A)×P(B given A)
Compound events
Notes: Probability of a red marble from 3 red and 7 blue
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: Probability of a red marble from 3 red and 7 blue
In other words — as if you have never seen this before
3 favourable out of 10 marbles.
2. What do we already know?
Probability of a red marble from 3 red and 7 blue
3. Which method — and why this one?
3 favourable out of 10 marbles.
4. Step-by-step working
1. 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.
2. 02 / 07
  Step B — Write the given in a column
  Probability of a red marble from 3 red and 7 blue
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
3. 03 / 07
  Step C — Name the method in words
  3 favourable out of 10 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.
4. 04 / 07
  Working
  3 favourable out of 10 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.
5. 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.
6. 06 / 07
  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.
7. 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
310
Copy onto your answer sheet — in this order
Answer: 310
6. Check it like a marker
3 favourable out of 10 marbles.
7. A trap first-timers fall into
37
7 · 2 Marks · Simple and compound interest
R4000 at 8% per year simple interest for 2 years. Interest earned?
Formulas
A=P(1 + in)A=P(1 + i)ⁿ
Simple interest vs compound interest
Notes: R4000 at 8% per year simple interest for 2 years. Interest earned?
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: R4000 at 8% per year simple interest for 2 years. Interest earned?
Before any working — hunt first
Given
Numbers and units already in the sentence: R4000 at · 8% · 2 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: I = Pin = 4000 × 0. Then substitute the given, one line at a time, to get Interest earned.
In other words — as if you have never seen this before
I=Pin=4000×0.08×2=640.
2. What do we already know?
R4000 at 8% per year simple interest for 2 years. Interest earned?
3. Which method — and why this one?
I=Pin=4000×0.08×2=640.
4. Step-by-step working
1. 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.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: R4000 at · 8% · 2 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: I = Pin = 4000 × 0. 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).
3. 03 / 08
  Step B — Write the given in a column
  R4000 at 8% per year simple interest for 2 years. Interest earned?
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  I=Pin=4000×0.08×2=640.
  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.
5. 05 / 08
  Working
  I=Pin=4000×0.08×2=640.
  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.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  R640.00
  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.
8. 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
R640.00
Copy onto your answer sheet — in this order
Answer: R640.00
6. Check it like a marker
I=Pin=4000×0.08×2=640.
7. A trap first-timers fall into
R4640.00
8 · 2 Marks · Inflation and exchange rates
Inflation 4% on R50. New price?
Formulas
new price=old price×(1 + inflation rate)
One-year inflation
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: Inflation 4% on R50. New price?
Before any working — hunt first
Given
Numbers and units already in the sentence: 4% · R50. 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: New price. Circle that word — that is the missing variable.
Find
We are required to find: New price. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: R52. Then substitute the given, one line at a time, to get New price.
In other words — as if you have never seen this before
R52.00
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 4% · R50. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
R52.00
4. Step-by-step working
1. 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.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 4% · R50. 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: New price. Circle that word — that is the missing variable. Find: We are required to find: New price. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: R52. Then substitute the given, one line at a time, to get New price.
  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).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 4% · R50. 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.
4. 04 / 08
  Step C — Name the method in words
  R52.00
  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.
5. 05 / 08
  Working
  50×1.04=52.
  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.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  R52.00
  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.
8. 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
R52.00
Copy onto your answer sheet — in this order
Answer: R52.00
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
9 · 2 Marks · Simple and compound interest
R5 000 at 10% p.a. simple for 2 years. Amount A?
Formulas
A=P(1 + in)A=P(1 + i)ⁿ
Simple interest vs 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 10% p.a. simple for 2 years. Amount A?
Before any working — hunt first
Given
Numbers and units already in the sentence: R5 · 000 at · 10% · 2 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: Amount A. Circle that word — that is the missing variable.
Find
We are required to find: Amount A. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: A = 5000(1+0. Then substitute the given, one line at a time, to get Amount A.
In other words — as if you have never seen this before
A=5000(1+0.1×2)=6000.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: R5 · 000 at · 10% · 2 years. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
A=5000(1+0.1×2)=6000.
4. Step-by-step working
1. 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.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: R5 · 000 at · 10% · 2 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: Amount A. Circle that word — that is the missing variable. Find: We are required to find: Amount A. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: A = 5000(1+0. Then substitute the given, one line at a time, to get Amount A.
  Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
3. 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 · 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.
4. 04 / 08
  Step C — Name the method in words
  A=5000(1+0.1×2)=6000.
  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.
5. 05 / 08
  Working
  A=5000(1+0.1×2)=6000.
  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.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  R6 000
  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.
8. 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
R6 000
Copy onto your answer sheet — in this order
Answer: R6 000
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 · 4 Marks · Tree diagrams and relative frequency
A bag 3 red, 2 blue. Two drawn without replacement. P(both red)?
Formulas
P(A then B)=P(A)×P(B given A)
Compound events
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 3 red, 2 blue. Two drawn without replacement. P(both red)?
Before any working — hunt first
Given
Numbers and units already in the sentence: 3 red · 2 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(both red). Circle that word — that is the missing variable.
Find
We are required to find: P(both red). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 35 × 24=620=310. Then substitute the given, one line at a time, to get P(both red).
In other words — as if you have never seen this before
35×24=620=310.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 3 red · 2 blue. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
35×24=620=310.
4. Step-by-step working
1. 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.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 3 red · 2 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(both red). Circle that word — that is the missing variable. Find: We are required to find: P(both red). Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 35 × 24=620=310. Then substitute the given, one line at a time, to get P(both red).
  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).
3. 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 · 2 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.
4. 04 / 08
  Step C — Name the method in words
  35×24=620=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.
5. 05 / 08
  Working
  35×24=620=310.
  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.
6. 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.
7. 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.
8. 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…”
11 · 2 Marks · Inflation and exchange rates
A loaf R16. Inflation 10%. Next year?
Formulas
new price=old price×(1 + inflation rate)
One-year inflation
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 loaf R16. Inflation 10%. Next year?
Before any working — hunt first
Given
Numbers and units already in the sentence: R16 · 10%. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Next year. Circle that word — that is the missing variable.
Find
We are required to find: Next year. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: R17. Then substitute the given, one line at a time, to get Next year.
In other words — as if you have never seen this before
R17.60
2. What do we already know?
Copy these onto the left of your page, one per line, with units: R16 · 10%. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
R17.60
4. Step-by-step working
1. 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.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: R16 · 10%. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Next year. Circle that word — that is the missing variable. Find: We are required to find: Next year. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: R17. Then substitute the given, one line at a time, to get Next year.
  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).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: R16 · 10%. Mixing cm with m, or minutes with seconds, loses a method mark.
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  R17.60
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Working
  16×1.10=17.60.
  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.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  R17.60
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 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
R17.60
Copy onto your answer sheet — in this order
Answer: R17.60
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
12 · 2 Marks · Simple and compound interest
Compound R1 000 at 10% p.a. for 2 years. A?
Formulas
A=P(1 + in)A=P(1 + i)ⁿ
Simple interest vs 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: Compound R1 000 at 10% p.a. for 2 years. A?
Before any working — hunt first
Given
Numbers and units already in the sentence: R1 · 000 at · 10% · 2 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: A. Circle that word — that is the missing variable.
Find
We are required to find: A. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: R1 210. Then substitute the given, one line at a time, to get A.
In other words — as if you have never seen this before
R1 210
2. What do we already know?
Copy these onto the left of your page, one per line, with units: R1 · 000 at · 10% · 2 years. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
R1 210
4. Step-by-step working
1. 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.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: R1 · 000 at · 10% · 2 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: A. Circle that word — that is the missing variable. Find: We are required to find: A. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: R1 210. Then substitute the given, one line at a time, to get A.
  Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: R1 · 000 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.
4. 04 / 08
  Step C — Name the method in words
  R1 210
  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.
5. 05 / 08
  Working
  1000×1.1×1.1=1210.
  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.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  R1 210
  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.
8. 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 210
Copy onto your answer sheet — in this order
Answer: R1 210
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
An invoice in Cape Town shows R1400 excluding VAT. VAT is 15%. VAT amount?
Notes: An invoice in Cape Town shows R1400 excluding VAT. VAT is 15%. VAT 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: An invoice in Cape Town shows R1400 excluding VAT. VAT is 15%. VAT amount?
Before any working — hunt first
Given
Numbers and units already in the sentence: R1400 excluding · 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: VAT amount. Circle that word — that is the missing variable.
Find
We are required to find: VAT amount. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: VAT = 0. Then substitute the given, one line at a time, to get VAT amount.
In other words — as if you have never seen this before
VAT=0.15×1400=210.
2. What do we already know?
An invoice in Cape Town shows R1400 excluding VAT. VAT is 15%. VAT amount?
3. Which method — and why this one?
VAT=0.15×1400=210.
4. Step-by-step working
1. 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.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: R1400 excluding · 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: VAT amount. Circle that word — that is the missing variable. Find: We are required to find: VAT amount. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: VAT = 0. Then substitute the given, one line at a time, to get VAT amount.
  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).
3. 03 / 08
  Step B — Write the given in a column
  An invoice in Cape Town shows R1400 excluding VAT. VAT is 15%. VAT amount?
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  VAT=0.15×1400=210.
  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.
5. 05 / 08
  Working
  VAT=0.15×1400=210.
  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.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  R210.00
  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.
8. 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
R210.00
Copy onto your answer sheet — in this order
Answer: R210.00
6. Check it like a marker
VAT=0.15×1400=210.
7. A trap first-timers fall into
R1610.00
14 · 2 Marks
1:50 plan. 20 mm on the plan is
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: 1:50 plan. 20 mm on the plan is
Before any working — hunt first
Given
Numbers and units already in the sentence: 1 · 50 plan · 20 mm. 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: 20 mm on the plan is. Circle that word — that is the missing variable.
Find
We are required to find: 20 mm on the plan is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 1 000 mm. Then substitute the given, one line at a time, to get 20 mm on the plan is.
In other words — as if you have never seen this before
1 000 mm
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1 · 50 plan · 20 mm. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
1 000 mm
4. Step-by-step working
1. 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.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 1 · 50 plan · 20 mm. 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: 20 mm on the plan is. Circle that word — that is the missing variable. Find: We are required to find: 20 mm on the plan is. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 1 000 mm. Then substitute the given, one line at a time, to get 20 mm on the plan 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).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 1 · 50 plan · 20 mm. 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.
4. 04 / 08
  Step C — Name the method in words
  1 000 mm
  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.
5. 05 / 08
  Working
  20×50=1 000 mm=1 m.
  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.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  1 000 mm
  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.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
1 000 mm
Copy onto your answer sheet — in this order
Answer: 1 000 mm
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
R18.50 = 1 US dollar. R370 is how many dollars?
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: R18.50 = 1 US dollar. R370 is how many dollars?
Before any working — hunt first
Given
Numbers and units already in the sentence: R18.50 · 1 US · R370 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: how many dollars. Circle that word — that is the missing variable.
Find
We are required to find: how many dollars. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 37018. Then substitute the given, one line at a time, to get how many dollars.
In other words — as if you have never seen this before
37018.50=20.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: R18.50 · 1 US · R370 is. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
37018.50=20.
4. Step-by-step working
1. 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.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: R18.50 · 1 US · R370 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: how many dollars. Circle that word — that is the missing variable. Find: We are required to find: how many dollars. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 37018. Then substitute the given, one line at a time, to get how many dollars.
  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).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: R18.50 · 1 US · R370 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.
4. 04 / 08
  Step C — Name the method in words
  37018.50=20.
  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.
5. 05 / 08
  Working
  37018.50=20.
  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.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  20
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 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
20
Copy onto your answer sheet — in this order
Answer: 20
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
16 · 4 Marks · Simple and compound interest
Which is larger after 2 years on R1 000 at 10%: simple or annual compound?
Formulas
A=P(1 + in)A=P(1 + i)ⁿ
Simple interest vs 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: Which is larger after 2 years on R1 000 at 10%: simple or annual compound?
In other words — as if you have never seen this before
Simple A=1200. Compound A=1210.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2 years · R1 · 000 at · 10%. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Simple A=1200. Compound A=1210.
4. Step-by-step working
1. 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.
2. 02 / 07
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 2 years · R1 · 000 at · 10%. Mixing cm with m, or minutes with seconds, loses a method mark.
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
3. 03 / 07
  Step C — Name the method in words
  Simple A=1200. Compound A=1210.
  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.
4. 04 / 07
  Working
  Simple A=1200. Compound A=1210.
  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.
5. 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.
6. 06 / 07
  Step F — Box the answer with its unit
  compound (R1 210 vs 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.
7. 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
compound (R1 210 vs R1 200)
Copy onto your answer sheet — in this order
Answer: compound (R1 210 vs 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…”
17 · 2 Marks · Cost, income and break-even
Break-even is where
Formulas
break-even: income=cost
Break-even point
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: Break-even is where
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: Break-even is where. Circle that word — that is the missing variable.
Find
We are required to find: Break-even is where. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: The graphs meet: no profit, no loss. Then substitute the given, one line at a time, to get Break-even is where.
In other words — as if you have never seen this before
The graphs meet: no profit, no loss.
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?
The graphs meet: no profit, no loss.
4. Step-by-step working
1. 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.
2. 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: Break-even is where. Circle that word — that is the missing variable. Find: We are required to find: Break-even is where. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: The graphs meet: no profit, no loss. Then substitute the given, one line at a time, to get Break-even is where.
  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).
3. 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.
4. 04 / 08
  Step C — Name the method in words
  The graphs meet: no profit, no loss.
  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.
5. 05 / 08
  Working
  The graphs meet: no profit, no loss.
  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.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  income equals cost
  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.
8. 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
income equals cost
Copy onto your answer sheet — in this order
Answer: income equals cost
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 · Tree diagrams and relative frequency
Independent P(A)=0.2, P(B)=0.4. P(A and B)?
Formulas
P(A then B)=P(A)×P(B given A)
Compound events
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Independent P(A)=0.2, P(B)=0.4. P(A and B)?
Before any working — hunt first
Given
Numbers and units already in the sentence: 0.2 · 0.4. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: P(A and B). Circle that word — that is the missing variable.
Find
We are required to find: P(A and B). Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 0. Then substitute the given, one line at a time, to get P(A and B).
In other words — as if you have never seen this before
0.08
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 0.2 · 0.4. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
0.08
4. Step-by-step working
1. 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.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 0.2 · 0.4. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: P(A and B). Circle that word — that is the missing variable. Find: We are required to find: P(A and B). Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 0. Then substitute the given, one line at a time, to get P(A and B).
  Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 0.2 · 0.4. Mixing cm with m, or minutes with seconds, loses a method mark.
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  0.08
  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.
5. 05 / 08
  Working
  0.2×0.4=0.08.
  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.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  0.08
  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.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
0.08
Copy onto your answer sheet — in this order
Answer: 0.08
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
19 · 2 Marks
1 m³ of water is
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: 1 m³ of water is
Before any working — hunt first
Given
Numbers and units already in the sentence: 1 m³. 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: 1 m³ of water is. Circle that word — that is the missing variable.
Find
We are required to find: 1 m³ of water is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 1 m³ = 1 000 ℓ. Then substitute the given, one line at a time, to get 1 m³ of water is.
In other words — as if you have never seen this before
1 m³=1 000 ℓ.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1 m³. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
1 m³=1 000 ℓ.
4. Step-by-step working
1. 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.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 1 m³. 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: 1 m³ of water is. Circle that word — that is the missing variable. Find: We are required to find: 1 m³ of water is. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 1 m³ = 1 000 ℓ. Then substitute the given, one line at a time, to get 1 m³ of water 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).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 1 m³. 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.
4. 04 / 08
  Step C — Name the method in words
  1 m³=1 000 ℓ.
  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.
5. 05 / 08
  Working
  1 m³=1 000 ℓ.
  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.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  1 000 litres
  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.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
1 000 litres
Copy onto your answer sheet — in this order
Answer: 1 000 litres
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
20 · 2 Marks
Two towns are 6 km apart. Map scale 1:100 000. Map distance?
Notes: Two towns are 6 km apart. Map scale 1:100 000. Map distance?
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Two towns are 6 km apart. Map scale 1:100 000. Map distance?
Before any working — hunt first
Given
Numbers and units already in the sentence: 6 km · 1 · 100 · 000. 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: Map distance. Circle that word — that is the missing variable.
Find
We are required to find: Map distance. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 6 km = 600000 cm on the ground. Then substitute the given, one line at a time, to get Map distance.
In other words — as if you have never seen this before
6 km = 600000 cm on the ground. Divide by 100 000: 6 cm on the map.
2. What do we already know?
Two towns are 6 km apart. Map scale 1:100 000. Map distance?
3. Which method — and why this one?
6 km = 600000 cm on the ground. Divide by 100 000: 6 cm on the map.
4. Step-by-step working
1. 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.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 6 km · 1 · 100 · 000. 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: Map distance. Circle that word — that is the missing variable. Find: We are required to find: Map distance. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 6 km = 600000 cm on the ground. Then substitute the given, one line at a time, to get Map distance.
  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).
3. 03 / 08
  Step B — Write the given in a column
  Two towns are 6 km apart. Map scale 1:100 000. Map distance?
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  6 km = 600000 cm on the ground. Divide by 100 000: 6 cm on the map.
  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.
5. 05 / 08
  Working
  6 km = 600000 cm on the ground. Divide by 100 000: 6 cm on the map.
  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.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  6 cm
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
6 cm
Copy onto your answer sheet — in this order
Answer: 6 cm
6. Check it like a marker
6 km = 600000 cm on the ground. Divide by 100 000: 6 cm on the map.
7. A trap first-timers fall into
60 cm
21 · 2 Marks · Simple and compound interest
I=Pin. P=R2 000, i=0.09, n=2. Interest?
Formulas
A=P(1 + in)A=P(1 + i)ⁿ
Simple interest vs 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: I = Pin. P=R2 000, i=0.09, n=2. Interest?
Before any working — hunt first
Given
Numbers and units already in the sentence: R2 · 000 · 0.09 · 2. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Interest. Circle that word — that is the missing variable.
Find
We are required to find: Interest. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: R360. Then substitute the given, one line at a time, to get Interest.
In other words — as if you have never seen this before
R360
2. What do we already know?
Copy these onto the left of your page, one per line, with units: R2 · 000 · 0.09 · 2. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
R360
4. Step-by-step working
1. 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.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: R2 · 000 · 0.09 · 2. Copy each one into a column. A name without a number is not given. Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Interest. Circle that word — that is the missing variable. Find: We are required to find: Interest. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: R360. Then substitute the given, one line at a time, to get Interest.
  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).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: R2 · 000 · 0.09 · 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.
4. 04 / 08
  Step C — Name the method in words
  R360
  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.
5. 05 / 08
  Working
  2000×0.09×2=360.
  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.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  R360
  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.
8. 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
R360
Copy onto your answer sheet — in this order
Answer: R360
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
Two towns are 9 km apart. Map scale 1:100 000. Map distance?
Notes: Two towns are 9 km apart. Map scale 1:100 000. Map distance?
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Two towns are 9 km apart. Map scale 1:100 000. Map distance?
Before any working — hunt first
Given
Numbers and units already in the sentence: 9 km · 1 · 100 · 000. 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: Map distance. Circle that word — that is the missing variable.
Find
We are required to find: Map distance. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 9 km = 900000 cm on the ground. Then substitute the given, one line at a time, to get Map distance.
In other words — as if you have never seen this before
9 km = 900000 cm on the ground. Divide by 100 000: 9 cm on the map.
2. What do we already know?
Two towns are 9 km apart. Map scale 1:100 000. Map distance?
3. Which method — and why this one?
9 km = 900000 cm on the ground. Divide by 100 000: 9 cm on the map.
4. Step-by-step working
1. 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.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 9 km · 1 · 100 · 000. 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: Map distance. Circle that word — that is the missing variable. Find: We are required to find: Map distance. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 9 km = 900000 cm on the ground. Then substitute the given, one line at a time, to get Map distance.
  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).
3. 03 / 08
  Step B — Write the given in a column
  Two towns are 9 km apart. Map scale 1:100 000. Map distance?
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  9 km = 900000 cm on the ground. Divide by 100 000: 9 cm on the map.
  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.
5. 05 / 08
  Working
  9 km = 900000 cm on the ground. Divide by 100 000: 9 cm on the map.
  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.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  9 cm
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 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
9 cm
Copy onto your answer sheet — in this order
Answer: 9 cm
6. Check it like a marker
9 km = 900000 cm on the ground. Divide by 100 000: 9 cm on the map.
7. A trap first-timers fall into
90 cm
23 · 2 Marks
Two towns are 8 km apart. Map scale 1:100 000. Map distance?
Notes: Two towns are 8 km apart. Map scale 1:100 000. Map distance?
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Two towns are 8 km apart. Map scale 1:100 000. Map distance?
Before any working — hunt first
Given
Numbers and units already in the sentence: 8 km · 1 · 100 · 000. 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: Map distance. Circle that word — that is the missing variable.
Find
We are required to find: Map distance. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 8 km = 800000 cm on the ground. Then substitute the given, one line at a time, to get Map distance.
In other words — as if you have never seen this before
8 km = 800000 cm on the ground. Divide by 100 000: 8 cm on the map.
2. What do we already know?
Two towns are 8 km apart. Map scale 1:100 000. Map distance?
3. Which method — and why this one?
8 km = 800000 cm on the ground. Divide by 100 000: 8 cm on the map.
4. Step-by-step working
1. 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.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 8 km · 1 · 100 · 000. 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: Map distance. Circle that word — that is the missing variable. Find: We are required to find: Map distance. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 8 km = 800000 cm on the ground. Then substitute the given, one line at a time, to get Map distance.
  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).
3. 03 / 08
  Step B — Write the given in a column
  Two towns are 8 km apart. Map scale 1:100 000. Map distance?
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  8 km = 800000 cm on the ground. Divide by 100 000: 8 cm on the map.
  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.
5. 05 / 08
  Working
  8 km = 800000 cm on the ground. Divide by 100 000: 8 cm on the map.
  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.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  8 cm
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 08 / 08
  Step H — What the marker is looking for
  On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
  Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
8 cm
Copy onto your answer sheet — in this order
Answer: 8 cm
6. Check it like a marker
8 km = 800000 cm on the ground. Divide by 100 000: 8 cm on the map.
7. A trap first-timers fall into
80 cm
24 · 4 Marks
Pula 1 = R1.25. R500 is how many pula?
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: Pula 1 = R1.25. R500 is how many pula?
Before any working — hunt first
Given
Numbers and units already in the sentence: 1 · R1.25 · R500 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: how many pula. Circle that word — that is the missing variable.
Find
We are required to find: how many pula. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 5001. Then substitute the given, one line at a time, to get how many pula.
In other words — as if you have never seen this before
5001.25=400 pula.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1 · R1.25 · R500 is. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
5001.25=400 pula.
4. Step-by-step working
1. 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.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 1 · R1.25 · R500 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: how many pula. Circle that word — that is the missing variable. Find: We are required to find: how many pula. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 5001. Then substitute the given, one line at a time, to get how many pula.
  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).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 1 · R1.25 · R500 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.
4. 04 / 08
  Step C — Name the method in words
  5001.25=400 pula.
  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.
5. 05 / 08
  Working
  5001.25=400 pula.
  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.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  400
  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.
8. 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
400
Copy onto your answer sheet — in this order
Answer: 400
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 · Simple and compound interest
R3000 at 8% per year simple interest for 2 years. Interest earned?
Formulas
A=P(1 + in)A=P(1 + i)ⁿ
Simple interest vs compound interest
Notes: R3000 at 8% per year simple interest for 2 years. Interest earned?
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: R3000 at 8% per year simple interest for 2 years. Interest earned?
Before any working — hunt first
Given
Numbers and units already in the sentence: R3000 at · 8% · 2 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: I = Pin = 3000 × 0. Then substitute the given, one line at a time, to get Interest earned.
In other words — as if you have never seen this before
I=Pin=3000×0.08×2=480.
2. What do we already know?
R3000 at 8% per year simple interest for 2 years. Interest earned?
3. Which method — and why this one?
I=Pin=3000×0.08×2=480.
4. Step-by-step working
1. 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.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: R3000 at · 8% · 2 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: I = Pin = 3000 × 0. 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).
3. 03 / 08
  Step B — Write the given in a column
  R3000 at 8% per year simple interest for 2 years. Interest earned?
  Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
4. 04 / 08
  Step C — Name the method in words
  I=Pin=3000×0.08×2=480.
  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.
5. 05 / 08
  Working
  I=Pin=3000×0.08×2=480.
  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.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  R480.00
  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.
8. 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
R480.00
Copy onto your answer sheet — in this order
Answer: R480.00
6. Check it like a marker
I=Pin=3000×0.08×2=480.
7. A trap first-timers fall into
R3480.00
26 · 2 Marks · Simple and compound interest
R4 000 at 10% simple for 3 years. Amount?
Formulas
A=P(1 + in)A=P(1 + i)ⁿ
Simple interest vs 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: R4 000 at 10% simple for 3 years. Amount?
Before any working — hunt first
Given
Numbers and units already in the sentence: R4 · 000 at · 10% · 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: Amount. Circle that word — that is the missing variable.
Find
We are required to find: Amount. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: R5 200. Then substitute the given, one line at a time, to get Amount.
In other words — as if you have never seen this before
R5 200
2. What do we already know?
Copy these onto the left of your page, one per line, with units: R4 · 000 at · 10% · 3 years. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
R5 200
4. Step-by-step working
1. 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.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: R4 · 000 at · 10% · 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: Amount. Circle that word — that is the missing variable. Find: We are required to find: Amount. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: R5 200. Then substitute the given, one line at a time, to get Amount.
  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).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: R4 · 000 at · 10% · 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.
4. 04 / 08
  Step C — Name the method in words
  R5 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.
5. 05 / 08
  Working
  A=4000(1+0.1×3)=5200.
  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.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  R5 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.
8. 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
R5 200
Copy onto your answer sheet — in this order
Answer: R5 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…”
27 · 2 Marks
Q₁=12, Q₃=28. IQR?
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: Q₁=12, Q₃=28. IQR?
Before any working — hunt first
Given
Numbers and units already in the sentence: 12 · 28. 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: IQR. Circle that word — that is the missing variable.
Find
We are required to find: IQR. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 16. Then substitute the given, one line at a time, to get IQR.
In other words — as if you have never seen this before
16
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 12 · 28. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
16
4. Step-by-step working
1. 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.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 12 · 28. 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: IQR. Circle that word — that is the missing variable. Find: We are required to find: IQR. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 16. Then substitute the given, one line at a time, to get IQR.
  Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 12 · 28. 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.
4. 04 / 08
  Step C — Name the method in words
  16
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Working
  28−12=16.
  Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
6. 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.
7. 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.
8. 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…”
28 · 2 Marks · Simple and compound interest
Simple interest on R3 000 at 12% for 1 year?
Formulas
A=P(1 + in)A=P(1 + i)ⁿ
Simple interest vs compound interest
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Simple interest on R3 000 at 12% for 1 year?
In other words — as if you have never seen this before
R360
2. What do we already know?
Copy these onto the left of your page, one per line, with units: R3 · 000 at · 12% · 1 year. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
R360
4. Step-by-step working
1. 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.
2. 02 / 07
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: R3 · 000 at · 12% · 1 year. 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.
3. 03 / 07
  Step C — Name the method in words
  R360
  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.
4. 04 / 07
  Working
  I=3000×0.12×1=360.
  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.
5. 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.
6. 06 / 07
  Step F — Box the answer with its unit
  R360
  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.
7. 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
R360
Copy onto your answer sheet — in this order
Answer: R360
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
29 · 2 Marks · Cost, income and break-even
Fixed R100, variable R8 each, sell at R20. Break-even n?
Formulas
break-even: income=cost
Break-even point
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: Fixed R100, variable R8 each, sell at R20. Break-even n?
Before any working — hunt first
Given
Numbers and units already in the sentence: R100 · R8 each · R20. 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: Break-even n. Circle that word — that is the missing variable.
Find
We are required to find: Break-even n. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Profit R12 each. Then substitute the given, one line at a time, to get Break-even n.
In other words — as if you have never seen this before
Profit R12 each. 10012=8.33, so 9 items.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: R100 · R8 each · R20. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
Profit R12 each. 10012=8.33, so 9 items.
4. Step-by-step working
1. 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.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: R100 · R8 each · R20. 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: Break-even n. Circle that word — that is the missing variable. Find: We are required to find: Break-even n. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: Profit R12 each. Then substitute the given, one line at a time, to get Break-even n.
  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).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: R100 · R8 each · R20. 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.
4. 04 / 08
  Step C — Name the method in words
  Profit R12 each. 10012=8.33, so 9 items.
  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.
5. 05 / 08
  Working
  Profit R12 each. 10012=8.33, so 9 items.
  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.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  9
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 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
9
Copy onto your answer sheet — in this order
Answer: 9
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 · 2 Marks · Cost, income and break-even
C=50+10n, Income=15n. Break-even n?
Formulas
break-even: income=cost
Break-even point
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: C = 50 + 10n, Income = 15n. Break-even n?
Before any working — hunt first
Given
Numbers and units already in the sentence: 50 · 10n · 15n. 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: Break-even n. Circle that word — that is the missing variable.
Find
We are required to find: Break-even n. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 10. Then substitute the given, one line at a time, to get Break-even n.
In other words — as if you have never seen this before
10
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 50 · 10n · 15n. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
10
4. Step-by-step working
1. 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.
2. 02 / 08
  Step A2 — Hunt: Given, Missing, Find, Calculate
  Given: Numbers and units already in the sentence: 50 · 10n · 15n. 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: Break-even n. Circle that word — that is the missing variable. Find: We are required to find: Break-even n. Write that as a symbol on the left, with a question mark, before you touch a formula. Calculate: What we need to calculate: 10. Then substitute the given, one line at a time, to get Break-even n.
  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).
3. 03 / 08
  Step B — Write the given in a column
  Copy these onto the left of your page, one per line, with units: 50 · 10n · 15n. 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.
4. 04 / 08
  Step C — Name the method in words
  10
  Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
5. 05 / 08
  Working
  15n=50+10n→5n=50→n=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.
6. 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.
7. 07 / 08
  Step F — Box the answer with its unit
  10
  Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
8. 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
10
Copy onto your answer sheet — in this order
Answer: 10
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”