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"Show that" questions are a distinctive feature of physics exams. Unlike standard calculations where you work towards an unknown answer, in a "show that" question you are given the answer and your job is to prove it through clear, logical working. These questions are common across all three Edexcel papers and appear frequently in mechanics, fields, waves, and energy calculations.
In a standard calculation, you work from known values to find an unknown. In a "show that" question, the answer is provided — but this does not make it easier. In fact, many students find these questions harder because:
Follow this process for every "show that" question:
graph TD
A["Show That Question"] --> B["Step 1: Identify the physics"]
B --> C["Write the relevant equation in symbols"]
C --> D["Step 2: Extract values from question"]
D --> E["Convert ALL values to SI units"]
E --> F["Step 3: Substitute with units shown"]
F --> G["Step 4: Show EVERY arithmetic step"]
G --> H["Do NOT skip intermediate values"]
H --> I["Step 5: Write answer to MORE\nsig figs than given answer"]
I --> J["Step 6: State 'which rounds to X\nas required'"]
J --> K{"Does your answer\nmatch closely?"}
K -->|Yes| L["Done — move on"]
K -->|"Off by > 2%"| M["Re-check arithmetic\nand unit conversions"]
M --> D
Read the question carefully and determine which principle, law, or equation applies. Write down the equation in symbol form.
Extract values from the question (or from standard constants) and substitute them into the equation. Always include units.
Do not jump from substitution to the final answer. If there are multiple arithmetic steps, show each one. If you need to combine equations, show the combination explicitly.
If the question says "show that the speed is 4.5 m s⁻¹," your final line should read something like "v = 4.52 m s⁻¹ ≈ 4.5 m s⁻¹." The extra significant figure demonstrates that your working genuinely produces the given value.
Question: A ball of mass 0.15 kg is dropped from a height of 1.8 m. Show that its speed just before hitting the ground is approximately 5.9 m s⁻¹. Assume air resistance is negligible.
Solution:
Using conservation of energy: loss in gravitational potential energy = gain in kinetic energy
mgh = ½mv²
The mass cancels:
gh = ½v²
Rearranging for v:
v = √(2gh)
Substituting values:
v = √(2 × 9.81 × 1.8)
v = √(35.316)
v = 5.943 m s⁻¹
This rounds to 5.9 m s⁻¹ as required.
Note: we showed the intermediate value under the square root (35.316) and gave the answer to 4 significant figures (5.943) before stating it rounds to the given value.
Question: Two parallel plates are separated by 5.0 cm and have a potential difference of 2000 V between them. Show that the electric field strength between the plates is 4.0 × 10⁴ V m⁻¹.
Solution:
For a uniform field between parallel plates:
E = V/d
Convert the separation to metres:
d = 5.0 cm = 5.0 × 10⁻² m
Substitute:
E = 2000 / (5.0 × 10⁻²)
E = 2000 / 0.050
E = 40 000 V m⁻¹
E = 4.0 × 10⁴ V m⁻¹
This matches the given value. Note the explicit unit conversion from cm to m — this is exactly the kind of step you must show.
Question: A standing wave on a string has a frequency of 120 Hz and a wavelength of 0.85 m. Show that the speed of waves on the string is approximately 100 m s⁻¹.
Solution:
Using the wave equation:
v = fλ
Substitute:
v = 120 × 0.85
v = 102 m s⁻¹
This is approximately 100 m s⁻¹ as required. Note that we obtained 102 m s⁻¹, which provides more precision than the given "approximately 100 m s⁻¹."
Question: A satellite orbits Earth at a height of 400 km above the surface. The radius of Earth is 6.37 × 10⁶ m and the mass of Earth is 5.97 × 10²⁴ kg. Show that the orbital speed is approximately 7.7 km s⁻¹.
Solution:
The orbital radius is:
r = R + h = 6.37 × 10⁶ + 400 × 10³ = 6.37 × 10⁶ + 0.40 × 10⁶ = 6.77 × 10⁶ m
For a circular orbit, gravitational force provides centripetal force:
GMm/r² = mv²/r
Cancel m and one factor of r:
v² = GM/r
v = √(GM/r)
Substitute:
v = √(6.67 × 10⁻¹¹ × 5.97 × 10²⁴ / 6.77 × 10⁶)
v = √(3.981 × 10¹⁴ / 6.77 × 10⁶)
v = √(5.881 × 10⁷)
v = 7670 m s⁻¹ = 7.67 km s⁻¹
This is approximately 7.7 km s⁻¹ as required.
Note: every intermediate calculation is shown, the unit conversion of 400 km to metres is explicit, and the final answer (7.67) has more precision than the given value (7.7).
Sometimes your calculated answer does not quite match the given value. This can happen because:
If your answer is close but not exact:
If your answer is significantly different:
Writing the given answer first and then justifying it is not showing — it is assuming. The examiner wants to see you arrive at the answer through forward-working logic.
If a distance is given in cm and you substitute it as cm into an equation expecting metres, your answer will be wrong — and in a "show that" question, you cannot adjust your answer to match.
In a normal calculation, you might skip a rearrangement step. In "show that," every step matters. If you skip the rearrangement, the examiner cannot see your method.
Never substitute the "show that" value back into an equation to prove it works. This is circular reasoning and will score zero.
If the question says "show that v = 4.5 m s⁻¹" and you write "v = 4.5 m s⁻¹," you have not demonstrated that your working leads to this value. Write "v = 4.52 m s⁻¹" to show you genuinely calculated it.
| Given answer format | Your answer should show | Example |
|---|---|---|
| "Show that v = 4.5 m s⁻¹" | At least 3 s.f. | 4.52 m s⁻¹ |
| "Show that F ≈ 25 N" | At least 3 s.f. | 25.2 N or 24.8 N |
| "Show that E = 3.0 × 10⁴ J" | At least 3 s.f. | 3.02 × 10⁴ J |
| "Show that the period is about 2 s" | At least 2 s.f. | 1.97 s or 2.03 s |
Before moving on, check:
"Show that" questions are not the same genre as ordinary calculations, even though they look similar on the page. The destination is printed for you, the marks are quietly redistributed away from the final number, and the question becomes a transparent test of your method. Candidates who treat them as standard calculations routinely lose marks they should have banked, while candidates who treat them as a separate genre with their own conventions can use the printed answer to unlock the rest of a multi-part question. The sections below set out how the genre works, where the time goes, what the recurring derivation patterns are, and the procedural habits that earn full credit on Edexcel 9PH0.
A "show that" question is recognisable from its demand verb and from the explicit appearance of the final answer in the question stem. The standard formulations are show that, derive, prove, and deduce, often followed by a target equation, a numerical value, or a relationship between two quantities. The question is signalling that the destination is fixed and that the marks are reserved for the route, not the arrival.
The pattern most often appears as a 4-mark, 5-mark, or 6-mark sub-part inside a longer structured question. A typical three-part question on Paper 2 might run (a) show that the period of a simple pendulum of length L is T = 2π√(L/g), (b) calculate the period of a pendulum of length 0.50 m, (c) explain how the period would change if the same pendulum were taken to the Moon. The stated result in (a) is then re-used in (b) and (c). This is the structural reason "show that" questions matter beyond their own mark allocation: the printed answer becomes a free starting point for the downstream parts, and a candidate who fails to derive it can still secure those downstream marks by quoting the stated result and pressing on.
The marks inside a "show that" sub-part are distributed according to a specific logic. The final printed answer earns no mark by itself — the value is given, so quoting it is not evidence of work. Instead, the marks are awarded for clearly identifiable method steps: stating a relevant starting principle, substituting correctly, performing each algebraic rearrangement explicitly, and arriving at a value that is consistent with the stated result to a higher precision than the printed figure. A 4-mark "show that" typically allocates roughly one mark for the starting equation, two marks for the algebraic chain, and one mark for the final substitution and consistency check. A 6-mark derivation may add an extra mark for an explicit assumption (for example, neglecting air resistance) and an extra mark for a unit consistency or dimensional check.
The structural implication is the single most important habit to internalise: write more steps, not fewer. Skipping a rearrangement that you would normally take in your head costs M-marks, because the marker cannot see what they cannot see. Where a standard calculation rewards efficiency, a "show that" rewards transparency. Each line should advance the algebra by exactly one operation, with the rule or substitution noted alongside.
A 4-mark "show that" question deserves roughly 5 minutes of paper time. The lower bound assumes a derivation you have rehearsed and can write from memory; the upper bound covers an unfamiliar starting point that requires more thought before you commit to the algebra. The Edexcel pacing rule of 1.2 minutes per mark holds here, with one adjustment: the planning fraction is larger than for an ordinary calculation, because a wrong starting equation makes the whole sub-part unrecoverable.
| Mark value | Target time | Realistic upper bound | Typical derivation type |
|---|---|---|---|
| 3 marks | 4 min | 5 min | Single-step rearrangement of a data-sheet formula |
| 4 marks | 5 min | 6 min | Two- or three-step derivation, e.g. SUVAT manipulation |
| 5 marks | 6 min | 8 min | Multi-step derivation linking two principles |
| 6 marks | 7 min | 9 min | Full derivation of a standard result, e.g. SHM period |
Inside a 5-minute budget, the time should split deliberately. Aim for roughly 30–60 seconds of planning before the algebra begins — long enough to identify the starting principle and to write a one-line sketch of the route in the margin. Spend around 3 minutes on the algebra itself, allocating one line per operation. Reserve the final 30–60 seconds for the consistency check: substitute numerical values where appropriate, confirm the result rounds to the printed figure, and re-read the stem to confirm the demand verb has been answered. Candidates who skip the plan typically commit to the wrong starting equation, recognise the mistake two lines in, and then have no time to recover.
The plan itself is a margin sketch, three or four bullets at most: (1) starting principle, (2) substitution to make, (3) rearrangement target, (4) numerical check. For the pendulum derivation, the plan reads (1) Newton's second law along arc, (2) small-angle approximation sin θ ≈ θ, (3) recognise SHM with ω² = g/L, (4) T = 2π/ω. That margin plan is the answer in skeleton form. Writing it costs 45 seconds and converts a 1-mark answer into a 4-mark one.
A small number of derivation patterns recur across Edexcel 9PH0 papers. Drilling these specifically is far more efficient than general derivation practice.
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