The questions are on the uncertainty and vectors test. Take it under real conditions before reading the mark scheme.
Quick answer: Homogeneity means every term of an equation has the same base units, which lets you test formulae. This mark scheme gives the model answers and the marks for the 8 questions of the Physics 11-12 test on uncertainty and vectors, from base units to close readings, with the equivalent answers to accept.
Marks are given for correct method as well as correct answers. Follow-through marks apply when an earlier error is carried into a later part correctly. The marking notes show where each mark is earned.
Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: A Level 1, IB A
Question 1 Base units (2 marks)
- Pressure = force ÷ area = kg m s⁻² ÷ m² = kg m⁻¹ s⁻².
- Power = energy ÷ time = kg m² s⁻² ÷ s = kg m² s⁻³.
Marking: 1 mark for each correct set of base units.
Question 2 Test an equation (3 marks)
- E is in joules: kg m² s⁻². mv is kg m s⁻¹. The base units differ.
- The equation cannot be correct because the two sides have different units; the correct form is ½mv².
Marking: 1 mark for each correct set of base units; 1 mark for the conclusion with reason.
Question 3 Uncertain area (3 marks)
- A = 20.12 × 3.05 = 61.4 m².
- 0.02 ÷ 20.12 = 0.099 %; 0.01 ÷ 3.05 = 0.328 %; total 0.43 %.
- 0.0043 × 61.4 = 0.26 m², so 61.4 ± 0.3 m².
Marking: 1 mark for each part; accept any rounding that agrees with the data.
Question 4 Two forces (4 marks)
- R = √(40² + 30²) = √2500 = 50 N.
- tan θ = 30 ÷ 40 = 0.75, so θ = 36.9°.
Marking: (a) 1 mark for the Pythagoras substitution, 1 for the answer; (b) 1 mark for the tangent ratio, 1 for the angle.
Question 5 Resolve a kick (2 marks)
Horizontal: 18 cos 50° = 18 × 0.643 = 11.6 m/s. Vertical: 18 sin 50° = 18 × 0.766 = 13.8 m/s. Check: √(11.6² + 13.8²) = 18.0 m/s.Marking: 1 mark for each component.
Question 6 Scalar and vector (2 marks)
Speed is a scalar with no direction, while velocity is a vector that includes direction. On a round trip back to the start, the distance travelled is not zero, but the displacement and so the average velocity are zero.Marking: 1 mark for the scalar and vector distinction; 1 mark for a correct journey.
Question 7 Random and systematic (2 marks)
- Mean = 16.5 ÷ 5 = 3.3 s. Half the range = (3.5 − 3.1) ÷ 2 = 0.2 s. 3.3 ± 0.2 s.
- It is a systematic error because it shifts every reading the same way, so repeating and averaging does not remove it.
Marking: 1 mark for the mean with uncertainty; 1 mark for the type of error with reason.
Question 8 Close readings (2 marks)
Extension = 12.9 − 12.4 = 0.5 cm. Absolute uncertainties add for a difference: 0.1 + 0.1 = 0.2 cm. Percentage = 0.2 ÷ 0.5 = 40 %, so the extension is 0.5 ± 0.2 cm.Marking: 1 mark for the extension and absolute uncertainty; 1 mark for the percentage.
