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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
AS

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

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 areas

Mathematical requirements question 1

[Maximum number: 2]

The electric field strength E at a distance x from an isolated point charge Q is given by the equation

E=Qx2bE=\frac{Q}{x^{2} b}

where b is a constant.

Use the units for E given in (b)(i) to determine the SI base units of b.

SI base units of b

Mathematical requirements question 2

[Maximum number: 1]

A pendulum consists of a solid sphere suspended by a string from a fixed point P , as shown in Fig. 3.1.

Fig. 3.1 (not to scale)

Fig. 3.1 (not to scale)

The sphere swings from side to side. At one instant the sphere is at its lowest position X , where it has kinetic energy 0.86 J and momentum 0.72 Ns in a horizontal direction. A short time later the sphere is at position Y , where it is momentarily stationary at a maximum vertical height h above position X.

The string has a fixed length and negligible weight. Air resistance is also negligible.

The distance between point P and the centre of the sphere is 0.93 m . When the sphere is at position Y , the string is at an angle θ\theta to the vertical.

Show that θ\theta is 47∘47^{\circ}.

Mathematical requirements question 3

[Maximum number: 2]

A diffraction grating is used with different wavelengths of light. The angle θ\theta of the second order maximum is measured for each wavelength. The variation with wavelength λ\lambda of sin⁡θ\sin \theta is shown in Fig. 5.1.

Fig. 5.1

Fig. 5.1

Determine the gradient of the line shown in Fig. 5.1.

gradient =
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