CAIE A-Level Physics Mathematical, Data and Formula Skills

Practise using CAIE Physics mathematical tools—units, algebra, geometry, graphs, supplied formulae and circuit symbols—to interpret and solve written and practical questions.

Exam points

use mathematical notation, units, equations, graphs and physical constants accurately in calculations
apply geometry, trigonometry, vectors and algebraic manipulation to physical situations
select, rearrange and interpret supplied physical formulae rather than substituting blindly
analyse experimental graphs through gradients, intercepts, curves, tangents, logarithmic plots and uncertainty
recognise and draw circuit symbols and connect them to component behaviour and measurement

Covered syllabus points

Mathematical requirements Key quantities, symbols and units Supplied data and formulae Circuit symbols

[Maximum number: 1]

Which circuit symbol does not represent an electric component that is designed to emit sound

waves?

Figure for Question Mathematical, data, formula and circuit-symbol skills question 1 — CAIE A-Level Physics AS

Option A shown in diagram

Option B shown in diagram

Option C shown in diagram

Option D shown in diagram

[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

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

C1

$=\mathrm{A}^{2} \mathrm{~s}^{4} \mathrm{~kg}^{-1} \mathrm{~m}^{-3}$

A1

[Maximum number: 1]

The diagram shows two resistor networks.

network 1

network 2

What is the ratio $\frac{\text { total resistance of network } 1}{\text { total resistance of network } 2} ?$

$\frac{4}{5}$

$\frac{5}{4}$

$\frac{1}{2}$

$\frac{2}{1}$

[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)

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 $\theta$ to the vertical.

Show that $\theta$ is $47^{\circ}$ .

$\cos \theta=(0.93-0.29) / 0.93$ so $\theta=47^{\circ}$

A1

All question bank results loaded

Covered syllabus points

Mathematical, data, formula and circuit-symbol skills question 1

Mathematical, data, formula and circuit-symbol skills question 2

Mathematical, data, formula and circuit-symbol skills question 3

Mathematical, data, formula and circuit-symbol skills question 4