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# A-level past papers

## Paper 32 Feb March 2017 Pure Math III – 9709/32/F/M/17

Check out my complete solution here: » Full Solutions « Like and subscribe too! =) 1.     Solve the equation $\ \ln(1+2^{x}) = 2$, giving your answer correct to 3 decimal places. $$\tag*{[3]}$$ 2.     Solve the inequality $\ |x − 4| \lt 2|3x + 1|$. $$\tag*{[4]}$$ 3.   …

## Paper 32 Feb March 2019 Pure Math III – 9709/32/F/M/19

Check out my complete solution here: » Full Solutions « Like and subscribe too! =) 1.     (i)     Show that the equation $\ \log_{10} (x \ − \ 4) = 2 \ − \ \log_{10} x \$ can be written as a quadratic equation in $x$. $$\tag*{[3]}$$     …

## Paper 33 May June 2019 Pure Math III – 9709/33/M/J/19

Check out my complete solution here: » Full Solutions « Like and subscribe too! =) 1.     Use logarithms to solve the equation $5^{3−2x} = 4(7^{x})$, giving your answer correct to 3 decimal places. $$\tag*{[4]}$$ 2.     Show that $\displaystyle \int_{0}^{\frac{1}{4}\pi} x^{2} \cos 2x \textrm{d}x = \frac{1}{32}(\pi^{2} \ – \ 8)$. …