Notes: m = 50 kg. F_net = 150 N. Unknown: acceleration a. The word net means “already the leftover force”.
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 50 kg kibble, F_net = 150 N down a mine shaft. a =
Before any working — hunt first
Given
Numbers and units already in the sentence: 50 kg · 150 N. 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
Write a = Fnetm with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives a =.
In other words — as if you have never seen this before
Newton 2 in words: leftover force equals mass times acceleration. So a = Fnetm.
2. What do we already know?
m = 50 kg. F_net = 150 N. Unknown: acceleration a. The word net means “already the leftover force”.
3. Which method — and why this one?
Newton 2 in words: leftover force equals mass times acceleration. So a = Fnetm.
4. Step-by-step working
01 / 06
Write Newton 2
F_net = m a, therefore a = Fnetm. Do not add g — net force already includes whatever gravity leftover there is.
a=Fnetm
Why this step: If the paper had given weight and tension separately you would subtract first. Here they already gave F_net.
02 / 06
Substitute
a = 15050. Units: N is kg·m·s⁻², so Nkg=m·s⁻². The unit we want falls out.
a=15050
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
03 / 06
Calculate
15050=3. So a = 3 m·s⁻² downward, same direction as F_net.
a=3 m·s⁻²
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
04 / 06
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
05 / 06
Step F — Box the answer with its unit
3 m·s⁻²
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
06 / 06
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
3 m·s⁻²
Copy onto your answer sheet — in this order
Formula: a=Fnetm
Answer: 3 m·s⁻²
6. Check it like a marker
3 × 50 = 150 N. Rebuilds the given force. 9.8 m·s⁻² would be free fall with no other forces.
7. A trap first-timers fall into
m × F = 7500. That multiplies mass by force, which is not a Newton law. Force over mass, never mass times force.
1.2 · 10 Marks
Two 6 Ω resistors in parallel. R_eq =
Notes: R₁ = 6 Ω, R₂ = 6 Ω, connected in parallel (side by side, two paths).
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 6 Ω resistors in parallel. R_eq =
Before any working — hunt first
Given
Numbers and units already in the sentence: 6 Ω. 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: R_eq =. Circle that word — that is the missing variable.
Find
We are required to find: R_eq =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write 1Req=1R₁ + 1R₂ with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives R_eq =.
In other words — as if you have never seen this before
Parallel: the reciprocals add. Equal parallels always halve. Series would have added to 12 Ω.
2. What do we already know?
R₁ = 6 Ω, R₂ = 6 Ω, connected in parallel (side by side, two paths).
3. Which method — and why this one?
Parallel: the reciprocals add. Equal parallels always halve. Series would have added to 12 Ω.
4. Step-by-step working
01 / 05
Write the parallel law
1Req=1R₁ + 1R₂. For two equals this becomes 1R + 1R=2R, so R_eq = R2.
1Req=1R₁+1R₂
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
02 / 05
Substitute
1Req=16+16=26=13. Flip both sides: Req=3 Ω.
Req=3 Ω
Why this step: Flipping 1/3 gives 3. First-timers stop at 1/3 and write 0.33 Ω — they forgot to invert.
03 / 05
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
04 / 05
Step F — Box the answer with its unit
3 Ω
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
05 / 05
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
3 Ω
Copy onto your answer sheet — in this order
Formula: 1Req=1R₁+1R₂
Answer: 3 Ω
6. Check it like a marker
Equal parallels: half of 6 is 3. Parallel equivalent is always smaller than the smallest resistor (6). 3 < 6. Good.
7. A trap first-timers fall into
Adding 6+6=12. That is series. The question said parallel — two paths, current splits, resistance drops.
2.1 · 12 Marks · Coulomb’s law & fields
If r doubles, Coulomb F becomes
Coulomb’s law & fields
Formulas
F=k Q₁ Q₂r²
Coulomb’s law
Notes: Coulomb: F ∝ 1r². New distance r' = 2r. Charges stay the same.
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: If r doubles, Coulomb F becomes
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: If r doubles, Coulomb F becomes. Circle that word — that is the missing variable.
Find
We are required to find: If r doubles, Coulomb F becomes. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write F ∝ 1r² with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives If r doubles, Coulomb F becomes.
In other words — as if you have never seen this before
Square the factor that r changes by, then flip because of the 1. Double → 2² = 4 → a quarter.
2. What do we already know?
Coulomb: F ∝ 1r². New distance r' = 2r. Charges stay the same.
3. Which method — and why this one?
Square the factor that r changes by, then flip because of the 1. Double → 2² = 4 → a quarter.
4. Step-by-step working
01 / 05
Write the proportion
F=k Q₁ Q₂ / r². Only r changes, so FnewFold=(rold / rnew)².
F ∝ 1r²
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
02 / 05
Square the factor
r_new = 2 r_old, so (1/2)²=14. F becomes a quarter of what it was.
F'=F4
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
03 / 05
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
04 / 05
Step F — Box the answer with its unit
a quarter
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
05 / 05
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
a quarter
Copy onto your answer sheet — in this order
Formula: F ∝ 1r²
Answer: a quarter
6. Check it like a marker
Further apart, force must get weaker, never stronger. “Four times” is the inverse-square going the wrong way.
7. A trap first-timers fall into
Saying “half” because r doubled. Inverse-square is not inverse-linear. You must square.
2.2 · 14 Marks · Refraction & TIR
n=1.33 (water) into air. sin c=
Refraction & TIR
Formulas
n₁ sinθ₁=n₂ sinθ₂
Snell’s law
Notes: Light goes water → air. n₁ = 1.33, n₂ = 1.00. Unknown: sin of the critical angle c.
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: n = 1.33 (water) into air. sin c =
Before any working — hunt first
Given
Numbers and units already in the sentence: 1.33. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: sin c =. Circle that word — that is the missing variable.
Find
We are required to find: sin c =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write sin c = n₂ / n₁ with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives sin c =.
In other words — as if you have never seen this before
Critical angle is the incidence in the denser medium for which refraction skims at 90°. Snell: n₁ sin c = n₂ sin 90°.
2. What do we already know?
Light goes water → air. n₁ = 1.33, n₂ = 1.00. Unknown: sin of the critical angle c.
3. Which method — and why this one?
Critical angle is the incidence in the denser medium for which refraction skims at 90°. Snell: n₁ sin c = n₂ sin 90°.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 1.33. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: sin c =. Circle that word — that is the missing variable.
Find: We are required to find: sin c =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: Write sin c = n₂ / n₁ with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives sin c =.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Light goes water → air. n₁ = 1.33, n₂ = 1.00. Unknown: sin of the critical angle c.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Critical angle is the incidence in the denser medium for which refraction skims at 90°. Snell: n₁ sin c = n₂ sin 90°.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Snell at the critical
n₁ sin c=n₂ sin 90°. sin 90°=1, so sin c=n₂n₁=11.33.
sin c=n₂n₁
Why this step: Denser to rarer is the only setup that has a critical angle. Air to water does not TIR.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
11.33
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
11.33
Copy onto your answer sheet — in this order
Formula: sin c=n₂n₁
Answer: 11.33
6. Check it like a marker
11.33 ≈ 0.75, and c ≈ 49°. A number between 0 and 1, as a sine must be.
7. A trap first-timers fall into
Writing 1.33, which is n, not sin c. Or using n₁/n₂ which is bigger than 1 — sines cannot be 1.33.
3.1 · 14 Marks · Electric fields
F=IℓB at 90°, I=4 A, ℓ=0.5 m, B=0.2 T
Electric fields
Formulas
E=Fq
Field definition
E=Vd
Uniform field between plates
Notes: I = 4 A, ℓ = 0.5 m, B = 0.2 T, θ = 90°. Unknown: magnetic force F on the wire.
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: F = IℓB at 90°, I = 4 A, ℓ = 0.5 m, B = 0.2 T
Before any working — hunt first
Given
Numbers and units already in the sentence: 90° · 4 A · 0.5 m · 0.2 T. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: 2 T. Circle that word — that is the missing variable.
Find
We are required to find: 2 T. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write F = IℓB sinθ with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives 2 T.
In other words — as if you have never seen this before
A current in a magnetic field feels F = I ℓ B sinθ. At 90°, sin = 1, so just multiply the three numbers.
2. What do we already know?
I = 4 A, ℓ = 0.5 m, B = 0.2 T, θ = 90°. Unknown: magnetic force F on the wire.
3. Which method — and why this one?
A current in a magnetic field feels F = I ℓ B sinθ. At 90°, sin = 1, so just multiply the three numbers.
4. Step-by-step working
01 / 05
Write the formula
F=I ℓ B sinθ. sin 90°=1, so F=I ℓ B.
F=IℓB sinθ
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
02 / 05
Multiply slowly
4×0.5=2. Then 2×0.2=0.4. Unit N.
F=0.4 N
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
03 / 05
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
04 / 05
Step F — Box the answer with its unit
0.4 N
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
05 / 05
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
0.4 N
Copy onto your answer sheet — in this order
Formula: F=IℓB sinθ
Answer: 0.4 N
6. Check it like a marker
4 × 0.5 × 0.2 = 0.4. If you forgot sin 90° = 1 you might stall. If you used 0 you would get 0 N — that is parallel, not 90°.
7. A trap first-timers fall into
Adding the numbers (4.7) or multiplying 4×0.5×0.2×90. Degrees do not go into this product — only sinθ.
6 · 2 Marks
A 6 N force does work through 3 m in the direction of F. W?
Notes: F = 6 N. Δx = 3 m. Force parallel to displacement.
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 6 N force does work through 3 m in the direction of F. W?
Before any working — hunt first
Given
Numbers and units already in the sentence: 6 N · 3 m. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: W. Circle that word — that is the missing variable.
Find
We are required to find: W. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write W = 18 J with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives W.
In other words — as if you have never seen this before
W=F Δx cosθ. θ=0 so cos=1.
2. What do we already know?
F = 6 N. Δx = 3 m. Force parallel to displacement.
3. Which method — and why this one?
W=F Δx cosθ. θ=0 so cos=1.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 6 N · 3 m. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: W. Circle that word — that is the missing variable.
Find: We are required to find: W. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: Write W = 18 J with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives W.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
F = 6 N. Δx = 3 m. Force parallel to displacement.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
W=F Δx cosθ. θ=0 so cos=1.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
W = FΔx
W=6×3=18 J.
W=18 J
Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
18 J
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
18 J
Copy onto your answer sheet — in this order
Formula: W=18 J
Answer: 18 J
6. Check it like a marker
Joule is N·m. 6 N through 3 m is 18 J.
7. A trap first-timers fall into
If the force were perpendicular, work would be 0. Here it is parallel.
7 · 3 Marks · Coulomb’s law & fields
Coulomb’s law says F is proportional to
Coulomb’s law & fields
Formulas
F=k Q₁ Q₂r²
Coulomb’s law
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: Coulomb’s law says F is proportional to
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: Coulomb’s law says F is proportional to. Circle that word — that is the missing variable.
Find
We are required to find: Coulomb’s law says F is proportional to. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: F = k Q₁ Q₂ / r². Then substitute the given, one line at a time, to get Coulomb’s law says F is proportional to.
In other words — as if you have never seen this before
F=k Q₁ Q₂r².
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?
F=k Q₁ Q₂r².
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Coulomb’s law says F is proportional to. Circle that word — that is the missing variable.
Find: We are required to find: Coulomb’s law says F is proportional to. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: F = k Q₁ Q₂ / r². Then substitute the given, one line at a time, to get Coulomb’s law says F is proportional to.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
F=k Q₁ Q₂r².
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
F=k Q₁ Q₂r².
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
Q₁Q₂r²
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
Q₁Q₂r²
Copy onto your answer sheet — in this order
Answer: Q₁Q₂r²
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
8 · 2 Marks · Refraction & TIR
TIR happens when light goes
Refraction & TIR
Formulas
n₁ sinθ₁=n₂ sinθ₂
Snell’s law
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: TIR happens when light goes
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: TIR happens when light goes. Circle that word — that is the missing variable.
Find
We are required to find: TIR happens when light goes. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: denser. Then substitute the given, one line at a time, to get TIR happens when light goes.
In other words — as if you have never seen this before
denser → rarer, i > c
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?
denser → rarer, i > c
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: TIR happens when light goes. Circle that word — that is the missing variable.
Find: We are required to find: TIR happens when light goes. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: denser. Then substitute the given, one line at a time, to get TIR happens when light goes.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
denser → rarer, i > c
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Reason
Critical angle condition.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
denser → rarer, i > c
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
denser → rarer, i > c
Copy onto your answer sheet — in this order
Answer: denser → rarer, i > c
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 · Longitudinal waves & sound
Ultrasound has frequency
Longitudinal waves & sound
Formulas
v=f λ
Sound is a wave
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: Ultrasound has frequency
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: Ultrasound has frequency. Circle that word — that is the missing variable.
Find
We are required to find: Ultrasound has frequency. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Audible 20 Hz–20 kHz. Then substitute the given, one line at a time, to get Ultrasound has frequency.
In other words — as if you have never seen this before
Audible 20 Hz–20 kHz.
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?
Audible 20 Hz–20 kHz.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Ultrasound has frequency. Circle that word — that is the missing variable.
Find: We are required to find: Ultrasound has frequency. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Audible 20 Hz–20 kHz. Then substitute the given, one line at a time, to get Ultrasound has frequency.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Audible 20 Hz–20 kHz.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Audible 20 Hz–20 kHz.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
above 20 kHz
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
above 20 kHz
Copy onto your answer sheet — in this order
Answer: above 20 kHz
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
10 · 2 Marks
p=8 kg·ms, m=2 kg. Speed v?
Notes: p=8 kg·ms. m=2 kg. Unknown: v.
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: p = 8 kg·ms, m = 2 kg. Speed v?
Before any working — hunt first
Given
Numbers and units already in the sentence: 8 kg·ms · 2 kg. 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: Speed v. Circle that word — that is the missing variable.
Find
We are required to find: Speed v. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write v = pm with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Speed v.
In other words — as if you have never seen this before
Momentum p=mv so v=pm.
2. What do we already know?
p=8 kg·ms. m=2 kg. Unknown: v.
3. Which method — and why this one?
Momentum p=mv so v=pm.
4. Step-by-step working
01 / 05
Write the definition
p=m v→v=pm.
v=pm
Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.
02 / 05
Substitute
v=82=4 m·s⁻¹.
v=4 ms
Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
03 / 05
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
04 / 05
Step F — Box the answer with its unit
4 ms
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
05 / 05
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
4 ms
Copy onto your answer sheet — in this order
Formula: v=pm
Answer: 4 ms
6. Check it like a marker
p = 2 × 4 = 8. Recovers the given momentum.
7. A trap first-timers fall into
Do not multiply 8 × 2. That inflates momentum, it does not find speed.
11 · 3 Marks · Electric fields
F on 2 A in 0.5 m at 90° in 0.4 T field?
Electric fields
Formulas
E=Fq
Field definition
E=Vd
Uniform field between plates
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: F on 2 A in 0.5 m at 90° in 0.4 T field?
Before any working — hunt first
Given
Numbers and units already in the sentence: 2 A · 0.5 m · 90° · 0.4 T. 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: 4 T field. Circle that word — that is the missing variable.
Find
We are required to find: 4 T field. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: F = IℓB sin90 = 2×0. Then substitute the given, one line at a time, to get 4 T field.
In other words — as if you have never seen this before
F=IℓB sin90=2×0.5×0.4=0.4 N.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 2 A · 0.5 m · 90° · 0.4 T. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
F=IℓB sin90=2×0.5×0.4=0.4 N.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 2 A · 0.5 m · 90° · 0.4 T. 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: 4 T field. Circle that word — that is the missing variable.
Find: We are required to find: 4 T field. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: F = IℓB sin90 = 2×0. Then substitute the given, one line at a time, to get 4 T field.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 2 A · 0.5 m · 90° · 0.4 T. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
F=IℓB sin90=2×0.5×0.4=0.4 N.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
F=IℓB sin90=2×0.5×0.4=0.4 N.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
0.4 N
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
0.4 N
Copy onto your answer sheet — in this order
Answer: 0.4 N
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 · Universal gravitation
If r halves, gravitational F becomes
Formulas
F=G m₁ m₂r²
Gravitational force
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: If r halves, gravitational F becomes
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: If r halves, gravitational F becomes. Circle that word — that is the missing variable.
Find
We are required to find: If r halves, gravitational F becomes. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 4 times larger. Then substitute the given, one line at a time, to get If r halves, gravitational F becomes.
In other words — as if you have never seen this before
4 times larger
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?
4 times larger
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: If r halves, gravitational F becomes. Circle that word — that is the missing variable.
Find: We are required to find: If r halves, gravitational F becomes. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 4 times larger. Then substitute the given, one line at a time, to get If r halves, gravitational F becomes.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
4 times larger
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Reason
1r².
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
4 times larger
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
4 times larger
Copy onto your answer sheet — in this order
Answer: 4 times larger
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
13 · 2 Marks
A wave: f=50 Hz, λ=2 m. Speed v?
Notes: f=50 Hz. λ=2 m. Unknown: wave speed v.
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 wave: f = 50 Hz, λ = 2 m. Speed v?
Before any working — hunt first
Given
Numbers and units already in the sentence: 50 Hz · 2 m. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Speed v. Circle that word — that is the missing variable.
Find
We are required to find: Speed v. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write v = fλ with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Speed v.
In other words — as if you have never seen this before
v = f λ. Frequency times wavelength. Do not divide.
2. What do we already know?
f=50 Hz. λ=2 m. Unknown: wave speed v.
3. Which method — and why this one?
v = f λ. Frequency times wavelength. Do not divide.
4. Step-by-step working
01 / 05
Write the wave equation
v=f λ.
v=fλ
Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.
02 / 05
Substitute
v=50×2=100 m·s⁻¹.
v=100 ms
Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
03 / 05
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
04 / 05
Step F — Box the answer with its unit
100 ms
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
05 / 05
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
100 ms
Copy onto your answer sheet — in this order
Formula: v=fλ
Answer: 100 ms
6. Check it like a marker
T = 1f=0.02 s. In 0.02 s the wave travels 100×0.02 = 2 m = λ. Consistent.
7. A trap first-timers fall into
v = f/λ = 25 would be wrong. Speed is product, not quotient.
14 · 4 Marks · Refraction & TIR
Critical angle exists only when light goes
Refraction & TIR
Formulas
n₁ sinθ₁=n₂ sinθ₂
Snell’s law
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: Critical angle exists only when light goes
In other words — as if you have never seen this before
Need n1>n2.
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?
Need n1>n2.
4. Step-by-step working
01 / 07
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 07
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
03 / 07
Step C — Name the method in words
Need n1>n2.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
04 / 07
Working
Need n1>n2.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
05 / 07
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
06 / 07
Step F — Box the answer with its unit
denser to rarer
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
07 / 07
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
denser to rarer
Copy onto your answer sheet — in this order
Answer: denser to rarer
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 · Friction
Kinetic friction f_k =
Friction
Formulas
fs ≤ μs N
Static friction (maximum at the point of slipping)
fk=μk N
Kinetic friction
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: Kinetic friction f_k =
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: Kinetic friction f_k =. Circle that word — that is the missing variable.
Find
We are required to find: Kinetic friction f_k =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Opposes sliding, magnitude μ_k N. Then substitute the given, one line at a time, to get Kinetic friction f_k =.
In other words — as if you have never seen this before
Opposes sliding, magnitude μ_k N.
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?
Opposes sliding, magnitude μ_k N.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Kinetic friction f_k =. Circle that word — that is the missing variable.
Find: We are required to find: Kinetic friction f_k =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Opposes sliding, magnitude μ_k N. Then substitute the given, one line at a time, to get Kinetic friction f_k =.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Opposes sliding, magnitude μ_k N.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Opposes sliding, magnitude μ_k N.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
μ_k N
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
μ_k N
Copy onto your answer sheet — in this order
Answer: μ_k N
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
16 · 2 Marks · Newton’s laws
Newton I says a body stays at rest or uniform velocity unless
Newton’s laws
Formulas
Fnet=m a
Newton 2
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Newton I says a body stays at rest or uniform velocity unless
In other words — as if you have never seen this before
InertiaN1.
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?
InertiaN1.
4. Step-by-step working
01 / 07
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 07
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
03 / 07
Step C — Name the method in words
InertiaN1.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
04 / 07
Working
InertiaN1.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
05 / 07
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
06 / 07
Step F — Box the answer with its unit
a net force acts
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
07 / 07
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
a net force acts
Copy onto your answer sheet — in this order
Answer: a net force acts
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
17 · 3 Marks
F=IℓB, I=3 A, ℓ=0.4 m, B=0.5 T, 90°
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: F=IℓB, I=3 A, ℓ=0.4 m, B=0.5 T, 90°
Before any working — hunt first
Given
Numbers and units already in the sentence: 3 A · 0.4 m · 0.5 T · 90°. 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: 5 T, 90°. Circle that word — that is the missing variable.
Find
We are required to find: 5 T, 90°. 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 5 T, 90°.
In other words — as if you have never seen this before
0.6 N
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 3 A · 0.4 m · 0.5 T · 90°. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
0.6 N
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 3 A · 0.4 m · 0.5 T · 90°. 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: 5 T, 90°. Circle that word — that is the missing variable.
Find: We are required to find: 5 T, 90°. 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 5 T, 90°.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 3 A · 0.4 m · 0.5 T · 90°. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
0.6 N
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Reason
3×0.4×0.5=0.6.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
0.6 N
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
0.6 N
Copy onto your answer sheet — in this order
Answer: 0.6 N
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 · 4 Marks · Universal gravitation
If r doubles, gravitational F becomes
Formulas
F=G m₁ m₂r²
Gravitational force
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: If r doubles, gravitational F becomes
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: If r doubles, gravitational F becomes. Circle that word — that is the missing variable.
Find
We are required to find: If r doubles, gravitational F becomes. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: F ∝ 1r² so 2² = 4 times smaller. Then substitute the given, one line at a time, to get If r doubles, gravitational F becomes.
In other words — as if you have never seen this before
F ∝ 1r² so 2²=4 times smaller.
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?
F ∝ 1r² so 2²=4 times smaller.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: If r doubles, gravitational F becomes. Circle that word — that is the missing variable.
Find: We are required to find: If r doubles, gravitational F becomes. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: F ∝ 1r² so 2² = 4 times smaller. Then substitute the given, one line at a time, to get If r doubles, gravitational F becomes.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
F ∝ 1r² so 2²=4 times smaller.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
F ∝ 1r² so 2²=4 times smaller.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
a quarter
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
a quarter
Copy onto your answer sheet — in this order
Answer: a quarter
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 · Electric circuits: Ohm’s law and power
A 2.0 kW heater runs for 3.0 h. Electricity costs R3.00 per kWh. Cost?
Electric circuits: Ohm’s law and power
Formulas
V=IR
Ohm’s law (constant temperature)
Rs=R₁+R₂+…1Rp=1R₁+1R₂+…
Series and parallel resistors
P=VI=I²R=V²RW=Pt
Electrical power and energy (1 kWh = 3.6 × 10⁶ J)
Notes: P=2.0 kW, t=3.0 h, tariff R3.00 per kWh.
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 2.0 kW heater runs for 3.0 h. Electricity costs R3.00 per kWh. Cost?
Before any working — hunt first
Given
Numbers and units already in the sentence: 2.0 kW · 3.0 h · R3.00 per. 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: Cost. Circle that word — that is the missing variable.
Find
We are required to find: Cost. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write W = 6.0 kWh with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Cost.
In other words — as if you have never seen this before
Energy in kWh = power in kW × time in hours. Cost = kWh × tariff.
2. What do we already know?
P=2.0 kW, t=3.0 h, tariff R3.00 per kWh.
3. Which method — and why this one?
Energy in kWh = power in kW × time in hours. Cost = kWh × tariff.
4. Step-by-step working
01 / 05
Energy
W=Pt=2.0 kW×3.0 h=6.0 kWh.
W=6.0 kWh
Why this step: One job per line so you can find a slip, and so a marker can follow the marks.
02 / 05
Cost
Cost=6.0×R3.00=R18.00.
R18.00
Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.
03 / 05
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
04 / 05
Step F — Box the answer with its unit
R18.00
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.
05 / 05
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
R18.00
Copy onto your answer sheet — in this order
Formula: W=6.0 kWh
Answer: R18.00
6. Check it like a marker
6.0 kWh=6.0×3.6×10⁶ J=2.16×10⁷ J. R18.00R3.00=6 kWh. Consistent.
7. A trap first-timers fall into
R6.00 stops at the energy; R18 000 uses 2 000 W instead of 2.0 kW.
20 · 3 Marks · Friction
Static friction can be
Friction
Formulas
fs ≤ μs N
Static friction (maximum at the point of slipping)
fk=μk N
Kinetic friction
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: Static friction can be
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: Static friction can be. Circle that word — that is the missing variable.
Find
We are required to find: Static friction can be. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Only the maximum is μ_s N. Then substitute the given, one line at a time, to get Static friction can be.
In other words — as if you have never seen this before
Only the maximum is μ_s N.
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?
Only the maximum is μ_s N.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Static friction can be. Circle that word — that is the missing variable.
Find: We are required to find: Static friction can be. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Only the maximum is μ_s N. Then substitute the given, one line at a time, to get Static friction can be.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Only the maximum is μ_s N.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Only the maximum is μ_s N.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
any value from 0 up to μ_s N
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
any value from 0 up to μ_s N
Copy onto your answer sheet — in this order
Answer: any value from 0 up to μ_s N
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
21 · 3 Marks
F=IℓB at 90°, I=5 A, ℓ=0.2 m, B=0.4 T
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: F = IℓB at 90°, I = 5 A, ℓ = 0.2 m, B = 0.4 T
Before any working — hunt first
Given
Numbers and units already in the sentence: 90° · 5 A · 0.2 m · 0.4 T. 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: 4 T. Circle that word — that is the missing variable.
Find
We are required to find: 4 T. 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 4 T.
In other words — as if you have never seen this before
0.4 N
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 90° · 5 A · 0.2 m · 0.4 T. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
0.4 N
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 90° · 5 A · 0.2 m · 0.4 T. 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: 4 T. Circle that word — that is the missing variable.
Find: We are required to find: 4 T. 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 4 T.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 90° · 5 A · 0.2 m · 0.4 T. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
0.4 N
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
5 × 0.2 × 0.4 × sin 90° = 0.4 N. sin 90° = 1, so just multiply the three numbers.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
0.4 N
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
0.4 N
Copy onto your answer sheet — in this order
Answer: 0.4 N
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…”
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: Efficiency = usefulinput. Useful 80 J, input 100 J
Before any working — hunt first
Given
Numbers and units already in the sentence: 80 J · 100 J. 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: Useful 80 J, input 100 J. Circle that word — that is the missing variable.
Find
We are required to find: Useful 80 J, input 100 J. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write 80% with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Useful 80 J, input 100 J.
In other words — as if you have never seen this before
Efficiency = (useful / input) × 100%.
2. What do we already know?
Useful energy 80 J. Input 100 J.
3. Which method — and why this one?
Efficiency = (useful / input) × 100%.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 80 J · 100 J. 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: Useful 80 J, input 100 J. Circle that word — that is the missing variable.
Find: We are required to find: Useful 80 J, input 100 J. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: Write 80% with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Useful 80 J, input 100 J.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Useful energy 80 J. Input 100 J.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Efficiency = (useful / input) × 100%.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Divide then percent
80100=0.8=80%.
80%
Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
80%
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
80%
Copy onto your answer sheet — in this order
Formula: 80%
Answer: 80%
6. Check it like a marker
20 J was wasted. 80+20=100.
7. A trap first-timers fall into
Writing 80 without % loses the unit the memo wants.
23 · 4 Marks · Longitudinal waves & sound
Particles in a sound wave vibrate
Longitudinal waves & sound
Formulas
v=f λ
Sound is a wave
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: Particles in a sound wave vibrate
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: Particles in a sound wave vibrate. Circle that word — that is the missing variable.
Find
We are required to find: Particles in a sound wave vibrate. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Longitudinal. Then substitute the given, one line at a time, to get Particles in a sound wave vibrate.
In other words — as if you have never seen this before
Longitudinal.
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?
Longitudinal.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Particles in a sound wave vibrate. Circle that word — that is the missing variable.
Find: We are required to find: Particles in a sound wave vibrate. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Longitudinal. Then substitute the given, one line at a time, to get Particles in a sound wave vibrate.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Longitudinal.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Longitudinal.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
parallel to the direction of travel
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
parallel to the direction of travel
Copy onto your answer sheet — in this order
Answer: parallel to the direction of travel
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
24 · 3 Marks · Coulomb’s law & fields
k in Coulomb’s law is
Coulomb’s law & fields
Formulas
F=k Q₁ Q₂r²
Coulomb’s law
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: k in Coulomb’s law is
Before any working — hunt first
Given
Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: k in Coulomb’s law is. Circle that word — that is the missing variable.
Find
We are required to find: k in Coulomb’s law is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: Coulomb constant in airvacuum. Then substitute the given, one line at a time, to get k in Coulomb’s law is.
In other words — as if you have never seen this before
Coulomb constant in airvacuum.
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?
Coulomb constant in airvacuum.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: k in Coulomb’s law is. Circle that word — that is the missing variable.
Find: We are required to find: k in Coulomb’s law is. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: Coulomb constant in airvacuum. Then substitute the given, one line at a time, to get k in Coulomb’s law is.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Coulomb constant in airvacuum.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
Coulomb constant in airvacuum.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
9.0×10⁹ N·m²·C⁻²
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
9.0×10⁹ N·m²·C⁻²
Copy onto your answer sheet — in this order
Answer: 9.0×10⁹ N·m²·C⁻²
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
25 · 2 Marks
A 1.5 kW heater runs for 4 h. Energy used?
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 1.5 kW heater runs for 4 h. Energy used?
Before any working — hunt first
Given
Numbers and units already in the sentence: 1.5 kW · 4 h. 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: Energy used. Circle that word — that is the missing variable.
Find
We are required to find: Energy used. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: W = Pt = 1. Then substitute the given, one line at a time, to get Energy used.
In other words — as if you have never seen this before
W=Pt=1.5 kW×4 h=6 kWh (= 2.16 × 10⁷ J).
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 1.5 kW · 4 h. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
W=Pt=1.5 kW×4 h=6 kWh (= 2.16 × 10⁷ J).
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 1.5 kW · 4 h. 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: Energy used. Circle that word — that is the missing variable.
Find: We are required to find: Energy used. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: W = Pt = 1. Then substitute the given, one line at a time, to get Energy used.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 1.5 kW · 4 h. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
W=Pt=1.5 kW×4 h=6 kWh (= 2.16 × 10⁷ J).
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
W=Pt=1.5 kW×4 h=6 kWh (= 2.16 × 10⁷ J).
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
6 kWh
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
6 kWh
Copy onto your answer sheet — in this order
Answer: 6 kWh
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
26 · 2 Marks
m=0.2 kg, v=10 ms. p?
Notes: m=0.2 kg. v=10 ms.
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: m=0.2 kg, v=10 ms. p?
Before any working — hunt first
Given
Numbers and units already in the sentence: 0.2 kg · 10 ms. 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. Circle that word — that is the missing variable.
Find
We are required to find: p. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write p = 2 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives p.
In other words — as if you have never seen this before
p=mv.
2. What do we already know?
m=0.2 kg. v=10 ms.
3. Which method — and why this one?
p=mv.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 0.2 kg · 10 ms. 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. Circle that word — that is the missing variable.
Find: We are required to find: p. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: Write p = 2 with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives p.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
m=0.2 kg. v=10 ms.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
p=mv.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Multiply
p=0.2×10=2 kg·ms.
p=2
Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
2 kg·ms
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
2 kg·ms
Copy onto your answer sheet — in this order
Formula: p=2
Answer: 2 kg·ms
6. Check it like a marker
A cricket ball order of magnitude. Sensible.
7. A trap first-timers fall into
mv is not momentum.
27 · 3 Marks
g on Earth 9.8, on Moon ≈ 1.6. Mass of 10 kg on Moon?
Notes: m = 10 kg on Earth. Moved to the Moon.
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: g on Earth 9.8, on Moon ≈ 1.6. Mass of 10 kg on Moon?
Before any working — hunt first
Given
Numbers and units already in the sentence: 9.8 · 1.6 · 10 kg. 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: Mass of 10 kg on Moon. Circle that word — that is the missing variable.
Find
We are required to find: Mass of 10 kg on Moon. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
Write m = 10 kg with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Mass of 10 kg on Moon.
In other words — as if you have never seen this before
Mass is the amount of matter. It does not change. Weight does.
2. What do we already know?
m = 10 kg on Earth. Moved to the Moon.
3. Which method — and why this one?
Mass is the amount of matter. It does not change. Weight does.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 9.8 · 1.6 · 10 kg. 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: Mass of 10 kg on Moon. Circle that word — that is the missing variable.
Find: We are required to find: Mass of 10 kg on Moon. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: Write m = 10 kg with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Mass of 10 kg on Moon.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
m = 10 kg on Earth. Moved to the Moon.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
Mass is the amount of matter. It does not change. Weight does.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Mass is invariant
mmoon=10 kg. Weight would be 16 N.
m=10 kg
Why this step: Write the formula before numbers. The memo awards a method mark even if a digit slips later.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
10 kg
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
10 kg
Copy onto your answer sheet — in this order
Formula: m=10 kg
Answer: 10 kg
6. Check it like a marker
W_moon = 10 × 1.6 = 16 N. That is weight, not mass.
7. A trap first-timers fall into
1.6 kg confuses g with mass. 16 N is weight. The asking-word is mass.
28 · 2 Marks
Fnet=20 N, m=4 kg. a=
How we got there
Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.
Explain in another language · 11
1. What is the question asking?
Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: F_net = 20 N, m = 4 kg. a =
Before any working — hunt first
Given
Numbers and units already in the sentence: 20 N · 4 kg. 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: a = Fm=5 m·s⁻². Then substitute the given, one line at a time, to get a =.
In other words — as if you have never seen this before
a=Fm=5 m·s⁻².
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 20 N · 4 kg. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
a=Fm=5 m·s⁻².
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 20 N · 4 kg. 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: a = Fm=5 m·s⁻². Then substitute the given, one line at a time, to get a =.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 20 N · 4 kg. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
a=Fm=5 m·s⁻².
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
a=Fm=5 m·s⁻².
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
5 m·s⁻²
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
5 m·s⁻²
Copy onto your answer sheet — in this order
Answer: 5 m·s⁻²
6. Check it like a marker
Does your answer appear as one of the options? Do the units match what was asked (m, N, J, °)? If you put the number back into the original equation, does it still hold? Estimate: is the size sensible?
7. A trap first-timers fall into
First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”
29 · 2 Marks · Friction
20 kg on horizontal floor, μ_s = 0.4, g = 9.8. Max static friction =
Friction
Formulas
fs ≤ μs N
Static friction (maximum at the point of slipping)
fk=μk N
Kinetic friction
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: 20 kg on horizontal floor, μ_s = 0.4, g = 9.8. Max static friction =
Before any working — hunt first
Given
Numbers and units already in the sentence: 20 kg · 0.4 · 9.8. Copy each one into a column. A name without a number is not given.
Missing
After you copy the given, the letter that still has no number is missing. The paper is pointing at: Max static friction =. Circle that word — that is the missing variable.
Find
We are required to find: Max static friction =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: N = 196 N. Then substitute the given, one line at a time, to get Max static friction =.
In other words — as if you have never seen this before
N=196 N. μs N=78.4 N.
2. What do we already know?
Copy these onto the left of your page, one per line, with units: 20 kg · 0.4 · 9.8. Mixing cm with m, or minutes with seconds, loses a method mark.
3. Which method — and why this one?
N=196 N. μs N=78.4 N.
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: 20 kg · 0.4 · 9.8. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: Max static friction =. Circle that word — that is the missing variable.
Find: We are required to find: Max static friction =. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: N = 196 N. Then substitute the given, one line at a time, to get Max static friction =.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: 20 kg · 0.4 · 9.8. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
N=196 N. μs N=78.4 N.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
N=196 N. μs N=78.4 N.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
78.4 N
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
78.4 N
Copy onto your answer sheet — in this order
Answer: 78.4 N
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 · Universal gravitation
If r triples, gravitational F becomes
Formulas
F=G m₁ m₂r²
Gravitational force
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: If r triples, gravitational F becomes
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: If r triples, gravitational F becomes. Circle that word — that is the missing variable.
Find
We are required to find: If r triples, gravitational F becomes. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate
What we need to calculate: 19 as large. Then substitute the given, one line at a time, to get If r triples, gravitational F becomes.
In other words — as if you have never seen this before
19 as large
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?
19 as large
4. Step-by-step working
01 / 08
Step A — Read the question twice
Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
02 / 08
Step A2 — Hunt: Given, Missing, Find, Calculate
Given: Numbers and units already in the sentence: no numbers yet — only a name, a diagram, or a worded unknown. Copy each one into a column. A name without a number is not given.
Missing: After you copy the given, the letter that still has no number is missing. The paper is pointing at: If r triples, gravitational F becomes. Circle that word — that is the missing variable.
Find: We are required to find: If r triples, gravitational F becomes. Write that as a symbol on the left, with a question mark, before you touch a formula.
Calculate: What we need to calculate: 19 as large. Then substitute the given, one line at a time, to get If r triples, gravitational F becomes.
Why this step: Do not name the letters yet. First hunt: what already has a number (Given), what has no number (Missing), the word the paper wants (Find), and which formula still contains the missing letter (Calculate).
03 / 08
Step B — Write the given in a column
Copy these onto the left of your page, one per line, with units: every number and its unit in the sentence. Mixing cm with m, or minutes with seconds, loses a method mark.
Why this step: A column with units stops you mixing cm with m, or minutes with seconds. Markers can also see you started correctly.
04 / 08
Step C — Name the method in words
19 as large
Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.
05 / 08
Working
F ∝ 1r² so 3²=9 times smaller.
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
06 / 08
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
07 / 08
Step F — Box the answer with its unit
19 as large
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
08 / 08
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.
5. The answer
19 as large
Copy onto your answer sheet — in this order
Answer: 19 as large
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…”