CAIE A-Level Physics AS Mathematical Requirements Questions

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

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 figures M.2-Algebra, models, units and dimensional consistency M.3-Geometry, trigonometry and vectors M.4-Graphs, gradients, intercepts and areas

[Maximum number: 2]

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

E=\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

$\begin{aligned} b =Q / X^{2} E =\mathrm{As} / \mathrm{m}^{2} \mathrm{kgmA}^{-1} \mathrm{~s}^{-3} \end{aligned}$ $=\mathrm{A}^{2} \mathrm{~s}^{4} \mathrm{~kg}^{-1} \mathrm{~m}^{-3}$

[Maximum number: 1]

The radius of a small sphere is determined from a measurement of the volume of the sphere. The sphere is submerged in water, displacing some of the water into a measuring cylinder as shown in Fig. 1.1.