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CAIE A-Level Physics Mathematical Requirements

Practise the mathematical methods embedded in CAIE A-Level Physics questions, including geometry, algebra, units, graphs, logarithms and physical interpretation.

Syllabus
2028–2030
Course
Physics 9702
Level
A2

Exam points

  • rearrange physical equations, substitute consistent units and check dimensions
  • apply areas, volumes, Pythagoras, trigonometry and vector resolution to physical diagrams
  • select graph variables and interpret gradients, intercepts, curves, tangents or areas
  • use exponentials, logarithms and logarithmic plots to analyse physical relationships

Covered syllabus points

M.1-Arithmetic, standard form and significant figuresM.2-Algebra, models, units and dimensional consistencyM.3-Geometry, trigonometry and vectorsM.4-Graphs, gradients, intercepts and areasM.5-A Level radians, exponentials and logarithms

Mathematical requirements question 1

[Maximum number: 3]

A simple pendulum consists of a metal sphere suspended from a fixed point by means of a thread, as illustrated in Fig. 3.1.

Fig. 3.1 (not to scale)

Fig. 3.1 (not to scale)

The sphere of mass 94.0 g is displaced to one side through a horizontal distance of 12.7 cm . The centre of gravity of the sphere rises vertically by 0.90 cm .

The sphere is released so that it oscillates. The sphere may be assumed to oscillate with simple harmonic motion.

The period T of oscillation of the pendulum is given by the expression

T=2π(Lg)T=2 \pi \sqrt{\left(\frac{L}{g}\right)}

where g is the acceleration of free fall and L is the length of the pendulum.
Use data from (b) to determine L.

L=

Mathematical requirements question 2

[Maximum number: 1]

A steel sphere of mass 0.29 kg is suspended in equilibrium from a vertical spring. The centre of the sphere is 8.5 cm from the top of the spring, as shown in Fig. 2.1.

Fig. 2.1

Fig. 2.1

The sphere is now set in motion so that it is moving in a horizontal circle at constant speed, as shown in Fig. 2.2.

Fig. 2.2

Fig. 2.2

The distance from the centre of the sphere to the top of the spring is now 10.8 cm .

The angle between the linear axis of the spring and the vertical is 27∘27^{\circ}.

Show that the radius r of the circle is 4.9 cm .

Mathematical requirements question 3

[Maximum number: 1]

A student determines the specific latent heat of vaporisation of a liquid using the apparatus illustrated in Fig. 3.1.

Fig. 3.1

Fig. 3.1

The heater is switched on. When the liquid is boiling at a constant rate, the balance reading is noted at 2.0 minute intervals.

After 10 minutes, the current in the heater is reduced and the balance readings are taken for a further 12 minutes.

The readings of the ammeter and of the voltmeter are given in Fig. 3.2.

Fig. 3.2

Fig. 3.2

The variation with time of the balance reading is shown in Fig. 3.3.
balance reading/g

Fig. 3.3

Fig. 3.3

From time 0 to time 10.0 minutes, the mass of liquid evaporated is 56 g .

Use Fig. 3.3 to determine the mass of liquid evaporated from time 12.0 minutes to time 22.0 minutes.

mass =g [1]
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