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: 3]

A circuit incorporating an ideal operational amplifier (op-amp) is shown in Fig. 7.1.

Fig. 7.1

The variation with temperature $\theta$ of the resistance $R_{\mathrm{T}}$ of the thermistor is shown in Fig. 7.2.

Fig. 7.2

The output of the op-amp is to be displayed using two light-emitting diodes (LEDs) labelled G and B.
When the temperature of the thermistor is below $4.0^{\circ} \mathrm{C}$ , only the LED labelled G emits light. The LED labelled B emits light only when the temperature of the thermistor is above $4.0^{\circ} \mathrm{C}$ .

On Fig. 7.1, draw and label the symbols for the two LEDs.

correct LED symbol

B1

two diodes shown connected, in parallel and with opposite polarities, between $V_{\text {OUT }}$ and earth

M1

diodes labelled to show correct polarities consistent with (b)
(G pointing from $\mathrm{V}_{\text {OUT }}$ to earth and B pointing from earth to $V_{\text {OUT }}$ if (b) correct)

A1

Question

Marks

[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)

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=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.

$T=2 \pi / \omega$

C1

$2 \pi / 3.3=2 \pi \times(L / 9.81)^{1 / 2}$

C1

$L=0.90 \mathrm{~m}$

A1

[Maximum number: 3]

(a)

An isolated planet is a uniform sphere of radius $3.39 \times 10^{6} \mathrm{~m}$ . Its mass of $6.42 \times 10^{23} \mathrm{~kg}$ may be considered to be a point mass concentrated at its centre. The planet rotates about its axis with a period of 24.6 hours.

For an object resting on the surface of the planet at the equator, calculate, to three significant figures:

[ 3 ]

(i)

the centripetal acceleration
acceleration = $\mathrm{ms}^{-2}$

[ 2 ]

$\begin{aligned} a=r \omega^{2} \text { and } \omega=2 \pi / T \text { or } a=v^{2} / r \text { and } v=2 \pi r / T \end{aligned}$

C1

$\begin{aligned} a =3.39 \times 10^{6} \times(2 \pi /(24.6 \times 3600))^{2} =0.0171 \mathrm{~m} \mathrm{~s}^{-2} \end{aligned}$

A1

(ii)

the force per unit mass exerted on the object by the surface of the planet.
force per unit mass = $\mathrm{Nkg}^{-1}$

[ 1 ]

$\begin{aligned} \text { force per unit mass } =3.73-0.0171 =3.71 \mathrm{~N} \mathrm{~kg}^{-1} \end{aligned}$

A1

[Maximum number: 2]

An ideal op-amp is incorporated into the circuit of Fig. 8.1.

Fig. 8.1

On Fig. 8.1, draw the symbol for a light-emitting diode (LED), connected at the output of the circuit, such that it emits light when the resistance of the thermistor is less than $R_{\mathrm{T}}$ .

correct LED symbol with connection between $V_{\text {OUT }}$ and earth

B1

diode pointing upwards

B1

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

Question (a)

Question (i)

Question (ii)

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