ZIMSEC A-Level Pure Mathematics Paper 2 June 2024 Question Paper

About this question paper

This is the ZIMSEC A-Level Pure Mathematics question paper for Paper 2 from June 2024. Use it for exam practice under timed conditions, then check your work against the marking scheme. See the marking scheme.

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Text from the first page

2

Section A (40) marks).
Answer all questions in this section.
1 The extension $y$, of an elastic string varies directly as the magnitude of force $f$. exerted in extending it. If $F=6$ Newtons and $y=0.45 \mathrm{~m}$
(a) Express $F$ as a function of $y$.

[4]
(b) Hence or otherwise find $F$ when $y=0.2 \mathrm{~m}$.

121

2 Set $S$ contains functions $g(x), f(x)$ and $h(x)$ which are defined by
\[
\begin{array}{l}
g: x \rightarrow x
f: x \rightarrow x-1
h: x \rightarrow x+1
\end{array}
\]

A Cayley table is drawn for set $S$ under function composition ( ${ }^{\circ}$ ).

$x$  |  $x$  |  $x-1$  |  $x+1$
$x$  |  $x$  |  $x-1$  |  $x+1$
$x-1$  |  &  |  $x$
$x+1$  |  $x+1$  |  &

(a) Copy and complete the table.

|2|
(b) Use the table to state,
(i) the identity element of the set,
(ii) the inverse of each element of the set.
(iii) why set S is not a group under function composition.

[3]
(2)
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