Download and practise with this ZIMSEC A-Level Pure Mathematics Paper 2 2023 question paper. Useful for exam revision, past paper practice, and preparation in Zimbabwe.
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Answers: ZIMSEC A-Level Pure Mathematics Paper 2 2023 Marking Scheme
This is the ZIMSEC A-Level Pure Mathematics question paper for Paper 2 from 2023. Use it for exam practice under timed conditions, then check your work against the marking scheme. See the marking scheme.
2
Answer all questions
[3]
1
(a) Simplify $\frac{3^{2 x-3} 81^{x+\frac{1}{2}}}{27^{x}}$.
(b) Hence or otherwise solve the equation
\[
\frac{3^{2 x-3} \cdot 81^{x+\frac{1}{2}}}{27^{x}}=\frac{1}{5^{x-1}}
\]
giving the answer in exact form.
2
(a) Show that 1 is a root of the polynomial $Q(x)=2 x^{3}+3 x^{2}-4 x-1$.
(b) Hence find the polynomial $P(x)$ such that
[3] $Q(x)=(x-1) P(x)$
(c) (I) Express $P(x)$ in the form $A(x+B)^{2}+C$.
[3]
(II) Hence state the minimum value of $P(x)$.
[1]
3
The curved surface area, $A$ of a cylindrical drum varies jointly as its circular base diameter $d$, and its height $l$. Given that the curved surface area of the drum is $2.64 \mathrm{~m}^{2}$ when its base radius is 0.35 m and its height is 1.2 m ,
(a) find the relationship between $A, d$ and $l$,
[5]
(b) calculate the radius of a cylinder whose surface area is $14,52 \mathrm{~m}^{2}$ and height is 3 m to 2 decimal places.
[4]
4 Given that $f(x)=k x^{2}+3 x+3$ and $g(x)=k x+7$, find the range of values of $k$ for which $f(x)=g(x)$ has two distinct solutions.
[5]
5 (a) Given that $2 x^{3}+a x^{2}+x-3 \equiv\left(b x^{2}+c\right)(x-3)$, find the constants $a_{1} b$ and $c$.
[4]
(b) Hence express $\frac{1+6 x}{2 x^{3}+a x^{2}+x-3}$ in partial fractions.
[6]
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