This set covers five skills from physics investigations and explanations: naming variables, choosing graph axes, reading gradients with units, separating random and systematic limitations, and writing short explanations. All data is invented for practice. Answer on paper first, then open the working.
Questions run from easier to harder. Units are part of every numerical answer.
Questions
Q1 (easy). A student investigates how the height of a ramp affects the speed of a trolley at the bottom. Name the independent variable, the dependent variable and two controlled variables.
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Independent: the height of the ramp (in cm). Dependent: the speed of the trolley at the bottom (in m/s, found from distance and time, or from a light gate). Controlled: the same trolley and mass, the same ramp surface and length, the same starting point on the ramp.
Q2 (easy). A student tests whether the mass of a pendulum bob changes its period, but uses a longer string for each heavier bob. Explain why the results cannot answer the question.
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Two variables change together: mass and length. A change in period could be caused by either. Only the mass should be changed, with the string length kept the same in every trial.
Q3 (easy). A fixed mass of gas at constant temperature has p = 200 kPa when V = 10 cm³. (a) Find p when V = 40 cm³. (b) Which quantities should be plotted to give a straight line, and what does the gradient equal?
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(a) p × V is constant: 200 × 10 = 2000 kPa cm³. So p = 2000 ÷ 40 = 50 kPa. Check: 50 × 40 = 2000.
(b) Since p = 2000 × (1/V), plot p on the y-axis against 1/V on the x-axis. The gradient equals p × V = 2000 kPa cm³, and the line passes through the origin.
Q4 (medium). Invented data. A small ball is dropped from rest and the time to fall is measured.
| Fall distance h / m | 0.49 | 0.98 | 1.47 | 1.96 |
|---|---|---|---|---|
| t² / s² | 0.10 | 0.20 | 0.30 | 0.40 |
The model is h = ½ g t². Plot h against t². Find the gradient and use it to find g.
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Compare h = (g/2) × t² with y = mx: y = h, x = t², so the gradient is g/2. Using the last point (0.40, 1.96), gradient = 1.96 ÷ 0.40 = 4.9 m/s². Check with the first point: 0.49 ÷ 0.10 = 4.9 m/s². Then g = 2 × 4.9 = 9.8 m/s².
Q5 (medium). A distance-time graph is a straight line through (2 s, 4 m) and (10 s, 28 m). Find the gradient with its unit and say what it represents.
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Gradient = (28 − 4) m ÷ (10 − 2) s = 24 ÷ 8 = 3.0 m/s. It represents the constant speed.
Q6 (medium). A current-voltage graph for a resistor has I (A) on the y-axis and V (V) on the x-axis. The line passes through the origin and (6.0 V, 0.15 A). Find the gradient and then the resistance.
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Gradient = 0.15 A ÷ 6.0 V = 0.025 A/V. This gradient is 1/R, so R = 1 ÷ 0.025 = 40 Ω. Check: 0.15 A × 40 Ω = 6.0 V.
Q7 (medium). On a force-extension graph for a spring, F is in N on the y-axis and x is in mm on the x-axis. The line passes through the origin and (30 mm, 6.0 N). Find the spring constant in N/m.
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Gradient = 6.0 N ÷ 30 mm = 0.20 N/mm. Convert: 1 mm = 0.001 m, so 0.20 N ÷ 0.001 m = 200 N/m. Check: 6.0 N ÷ 200 N/m = 0.030 m = 30 mm.
Q8 (medium). Classify each limitation as random or systematic: (a) a balance reads 0.3 g with nothing on it; (b) repeat timings of the same event differ by up to 0.2 s in both directions; (c) a worn metre rule has the zero end broken off, so every length reads 0.5 cm too short.
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(a) Systematic: zero error shifts every reading the same way. (b) Random: scatter in both directions, probably reaction time. (c) Systematic: a constant offset of 0.5 cm in every reading.
Q9 (harder). Invented data. Four repeat timings of a trolley run are 12.1 s, 12.4 s, 11.9 s and 12.2 s. Find the mean and the half-range. Say what type of limitation the scatter suggests and how to reduce it.
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Sum = 12.1 + 12.4 + 11.9 + 12.2 = 48.6 s. Mean = 48.6 ÷ 4 = 12.15 s. Range = 12.4 − 11.9 = 0.5 s, so half-range = 0.25 s. The readings scatter both above and below the mean, so the limitation is random, likely reaction time. Reduce it by timing over a longer distance, using light gates, or taking more repeats and averaging.
Q10 (harder). Invented data. Two identical cans hold 100 g of water at 80 °C. After ten minutes in the same room the black can has cooled by 24 °C and the shiny can by 15 °C. Write a claim, evidence and reasoning answer.
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Claim: The black can loses thermal energy faster than the shiny can. Evidence: After ten minutes the black can’s temperature fell by 24 °C and the shiny can’s by 15 °C, a difference of 9 °C, so the black can fell by 1.6 times as much (24 ÷ 15 = 1.6). Reasoning: A black surface is a better emitter of infrared radiation than a shiny surface, so more energy is radiated away each second. The result relies on a single trial, so repeating it would show whether the difference is reliable.
If you got these wrong
| If your mistake was | Revisit |
|---|---|
| Mixing up the variables, or missing a control (Q1, Q2) | Identify independent, dependent and controlled variables |
| Plotting a curve instead of a line, or the wrong gradient meaning (Q3, Q4) | Choose graph axes from a model |
| Wrong unit, missing conversion or a small triangle (Q5, Q6, Q7) | Interpret gradient with units |
| Calling every error “human error” or confusing random with systematic (Q8, Q9) | Explain systematic and random limitations |
| Answers that state a conclusion without numbers or a reason (Q10) | Develop a concise claim-evidence-reasoning answer |
Keep a record of the mistake types you find using the mistake log and retest queue. The bounds and rounding explainer and the reasoning board are useful for checking rounded values and relationships. For Physics help that looks at your own working, see online one-to-one Physics tuition.