# A-level past papers

## Paper 32 May June 2020 Pure Math III – 9709/32/M/J/20

Check out my complete solution here: » Full Solutions « Like and subscribe too! =) 1.     Find the quotient and remainder when $6x^4 + x^3 − x^2 + 5x − 6$ is divided by $2x^2 − x + 1$. $$\tag*{[3]}$$ 2.         The variables $x$ and …

## Paper 31 May June 2020 Pure Math III – 9709/31/M/J/20

Check out my complete solution here: » Full Solutions « Like and subscribe too! =) 1.     Find the set of values of $\ x \$ for which $\ 2({3}^{1 \ − \ 2x}) \lt 5x$. Give your answer in a simplified exact form. $$\tag*{[4]}$$ 2.     (a) …

## Paper 12 May June 2020 Pure Math I – 9709/12/M/J/20

Check out my complete solution here: » Full Solutions « Like and subscribe too! =) 1.     (a)     Find the coefficient of $\ x^2 \$ in the expansion of $\ {(x \ – \ \frac{2}{x})}^{6}$. $$\tag*{[2]}$$         (b)     Find the coefficient of …

## Paper 12 Oct Nov 2019 Pure Math I – 9709/12/O/N/19

Check out my complete solution here: » Full Solutions « Like and subscribe too! =) 1.     The coefficient of $\ x^2 \$ in the expansion of $\ (4 + ax) {(1 + \frac{x}{2})}^{6} \$ is $\ 3$. Find the value of the constant $\ a$. $$\tag*{[4]}$$ …

## 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 $\displaystyle \int_{0}^{\frac{1}{4}\pi} x^{2} \cos 2x \textrm{d}x = \frac{1}{32}(\pi^{2} \ – \ 8)$. …

## Paper 52 Feb Mar 2020 Probability & Statistics I – 9709/52/F/M/20

1.     The 40 members of a club include Ranuf and Saed. All 40 members will travel to a concert. 35 members will travel in a coach and the other 5 will travel in a car. Ranuf will be in the coach and Saed will be in the car. In how many ways can …