Download and practise with this A-Level Pure Mathematics June 2023 question paper. Useful for revision, practice, and exam preparation in Zimbabwe.
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Answers: ZIMSEC A-Level Pure Mathematics Paper 2 June 2023 Marking Scheme
This is the A-Level Pure Mathematics question paper for Paper 2 from June 2023. Use it for exam practice under timed conditions, then check your work against the marking scheme. See the marking scheme.
U6 PAPER 2 TEST 1
Sharewell B. C [Mr SHARE]
June - 2023
Pay attention to details and show all workings.
Question 1
(a) (i) State any four properties of a group.
(ii) Hence show that $(\mathrm{R}, \mathrm{x})$ is a group.
(b) (i) Construct group tables for $Z_{(2+)}$, addition module 2.
(ii) Verify that $Z_{(2+)}$ is commutative.
Question 2
(a) Given that $I=\int \frac{x^{2}}{\sqrt{4-x^{2}}} d x$, using the substitution of $x=2 \sin \theta$, show that $I=\int 4 \sin ^{2} \theta d \theta$.
(b) Use Taylor's series to expand $\cos x$ as a series of ascending powers of $(x-a)$ up to and including the term in $(x-a)^{2}$.
(c) Hence or otherwise,
(i) state the expansion of $\cos x$ as ascending powers of $x-\frac{\pi}{6}$ up to and including $\left(x-\frac{\pi}{6}\right)^{2}$,
(ii) find an approximate value of $\cos 31^{\circ}$ given that $1^{\circ}=0.017$ radians, giving the answers to 5 decimal places.
1
0784