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This is the A-Level Pure Mathematics question paper for Test 2 from 2024. Use it for exam practice under timed conditions.
2024 PURE MATHEMATICS L6 TEST 2
MR SHARE +263784089807; MUTARE
29/06/2024
L6 PURE MATHEMATICS 2024 -TEST 2
1. Show that,
\[
\frac{6\left(2^{n+1}\right)-4\left(2^{n-1}\right)}{2^{n+1}-2^{n}}=10
\]
[3]
2. Solve the following equations;
(a) $9^{x}+81=10\left(3^{x+1}\right)$
[3]
(b) $2 e^{2 x}=7 e^{x}-3$
[3]
(c) $2 \log _{3}(x-5)-\log _{3}(2 x-13)=1$
[4]
3. Caren received 5000 from his mother after graduating from a local university. Caren chose to invest the money with an annual interest rate of 3 percent compounded quarterly.
[3]
(a) Write down an exponential function to model this relation.
[2]
(b) How much will Caren have invested after 5 years.
[3]
4. The table below shows the values of a variable $p$ obtained experimentally from the values of $q$
$q$ | 2 | 3 | 4 | 5
$p$ | 3.55 | 1.93 | 1.26 | 0.90
The variables $p$ and $q$ are related by the relation $\log p=b \log q+\log a$.
By plotting the graph of logp against logq, determine the approximate values of $a$ and $b$.
[6]
5. Given,
\[
f(x)=\frac{4 x+6}{(x+2)(x+1)(x+3)}
\]
(a) Express $f(x)$ in partial fraction.
[3]
1