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Past papers · Mathematics

WMA13
Pure Mathematics 3

16 papers indexed since 2019, question by question. Next sitting: Fri, 15 Jan 2027. Pick a topic to see every question that tested it.

All topics

383 question parts · 1142 marks

SittingQuestionMarksAsks you to
June 2025Q1(a)· short2find
June 2025Q1(b)· short2find
June 2025Q1(c)· short2find
June 2025Q1(d)· short2solve
June 2025Q2(a)· short3express, give your answer to ...
June 2025Q2(b)· short4use, find, give your answer to ...
June 2025Q3(a)· short2find
June 2025Q3(b)· short3hence or otherwise, express
June 2025Q4(a)· short3show that
June 2025Q4(b)· short2hence, find, simplify
June 2025Q5(i)· short2find
June 2025Q5(ii)· short2find
June 2025Q6(a)· short2find
June 2025Q6(b)· short3find, give your answer to ...
June 2025Q6(c)· short3find, give your answer to ...
June 2025Q7(a)· short4show that, use
June 2025Q7(b)· short3find, give your answer to ...
June 2025Q7(c)· short2use, show that, state
June 2025Q8(a)· short3prove
June 2025Q8(b)· long5hence, solve, give your answer to ...
June 2025Q9(a)· short3find the exact value
June 2025Q9(b)· short4show that, find
June 2025Q10(a)· short3find, simplify
June 2025Q10(b)· short3find
June 2025Q10(c)· short4find
January 2025Q1(a)· short2show that
January 2025Q1(b)· short1show that
January 2025Q1(c)· short3find, give your answer to ...
January 2025Q2(a)· short1find
January 2025Q2(b)· short2find, give your answer to ...
January 2025Q3· long6use, find
January 2025Q4(a)· short4find, show that
January 2025Q4(b)· long5hence, use, find
January 2025Q5(a)· short1find
January 2025Q5(b)· short2sketch, state
January 2025Q5(c)· short3find, give your answer to ...
January 2025Q5(d)· short3show that, find
January 2025Q6(a)· short3find
January 2025Q6(b)· short3show that, find
January 2025Q6(c)· short2find
January 2025Q7(a)· long6sketch
January 2025Q7(b)· short2solve
January 2025Q8(i)· long5solve, give your answer to ...
January 2025Q8(ii)· short4solve, give your answer to ...
January 2025Q9(a)· short1state
January 2025Q9(b)· long5use, find
January 2025Q9(c)· short2hence, find
January 2025Q10(a)· short2find
January 2025Q10(b)· short3hence, show that, find
January 2025Q10(c)· short4find
October 2024Q1· long5solve, give your answer to ...
October 2024Q2(a)· short2find
October 2024Q2(b)· short3find
October 2024Q3(a)· short3solve
October 2024Q3(b)· short4find
October 2024Q4(a)· short1find
October 2024Q4(b)· short3show that, find, give your answer to ...
October 2024Q4(c)· short2hence, find
October 2024Q5(a)· short4show that, find
October 2024Q5(b)· short4hence or otherwise, solve, give your answer to ...
October 2024Q6(a)· short2find
October 2024Q6(b)· short3find
October 2024Q6(c)· short3solve
October 2024Q7(a)· short4show that, find
October 2024Q7(c)· short2hence, find
October 2024Q7(d)· short2find
October 2024Q8(a)· short1state
October 2024Q8(b)· short1state
October 2024Q8(c)· long5find, give your answer to ...
October 2024Q8(d)· short2show that
October 2024Q8(e)· short3find, give your answer to ...
October 2024Q9(a)· short3find, simplify
October 2024Q9(b)· short3show that
October 2024Q9(c)· short3write in the form
October 2024Q9(d)· long5use, find
June 2024Q1(a)· short2state
June 2024Q1(b)· short2use, solve
June 2024Q2(a)· short3write in the form
June 2024Q2(b)· short4hence, use, show that
June 2024Q3(i)· short3sketch
June 2024Q3(ii)· short3show that, find
June 2024Q4(a)· short3write in the form
June 2024Q4(b)· short3use, write in the form, give your answer to ...
June 2024Q4(c)· short3hence or otherwise, state, find, give your answer to ...
June 2024Q5(a)· short2find
June 2024Q5(b)· short3use, prove
June 2024Q5(c)· short3find
June 2024Q5(d)· short2find
June 2024Q6(a)· long5use, show that
June 2024Q6(b)· short4use, find
June 2024Q7(a)· short4show that
June 2024Q7(b)· short4hence or otherwise, solve
June 2024Q8(a)· short3find, give your answer to ...
June 2024Q8(b)· short4show that
June 2024Q8(c)· short3find, give your answer to ...
June 2024Q9(b)· long6find, hence, show that
January 2024Q1(c)· short1find
January 2024Q2(a)· short2show that
January 2024Q2(b)· short1show that
January 2024Q2(c)· short3find, give your answer to ...
January 2024Q3(a)· short3write in the form, give your answer to ...
January 2024Q3(b)· short2find, give your answer to ...
January 2024Q3(c)· short2determine
January 2024Q4(a)· short3show that
January 2024Q4(b)· short3show that, explain
January 2024Q4(c)· short3find
January 2024Q4(d)· short4find the exact value
January 2024Q5(a)· short1find
January 2024Q5(b)· short3find, give your answer to ...
January 2024Q5(c)· short2find, give your answer to ...
January 2024Q5(d)· short1explain
January 2024Q6(b)· short4show that
January 2024Q6(c)· short2hence, find, give your answer to ...
January 2024Q7(a)· short2find, simplify
January 2024Q7(b)· short3find
January 2024Q7(c)· short3find
January 2024Q7(d)· short4show that, use
January 2024Q8(a)· long5find
January 2024Q8(b)· short2sketch
January 2024Q8(c)· short4find
January 2024Q9(a)· short3show that
January 2024Q9(b)· long5hence, solve, give your answer to ...
October 2023Q1(a)· short2show that
October 2023Q1(b)· short3find, give your answer to ...
October 2023Q2(a)· short2find
October 2023Q2(b)· short3find
October 2023Q2(c)· short3find the exact value
October 2023Q3(a)· short2use, prove
October 2023Q3(b)· short4hence, find the exact value
October 2023Q4(a)· short1state
October 2023Q4(b)· short3find, give your answer to ...
October 2023Q4(c)· short2find, give your answer to ...
October 2023Q4(d)· short1use, give a reason
October 2023Q5(a)· short3show that, find
October 2023Q5(b)· short3find
October 2023Q5(c)· short1find
October 2023Q6(a)· short2find
October 2023Q6(b)· short3find, give your answer to ...
October 2023Q6(c)· short1interpret
October 2023Q7(a)· short2find
October 2023Q7(b)· short4show that, find
October 2023Q8(a)· short4prove
October 2023Q8(b)· short4hence, solve, give your answer to ...
October 2023Q9(a)· short1state
October 2023Q9(b)· short3find
October 2023Q9(c)· long5find
October 2023Q10(a)· short2find
October 2023Q10(b)· short2find
October 2023Q10(c)· short3hence, show that, find
June 2023Q1(a)· short2show that
June 2023Q1(b)· short3use, find, give your answer to ...
June 2023Q2(a)· short3find, hence, find the exact value
June 2023Q2(b)· short3find
June 2023Q3(i)· short2find, simplify
June 2023Q3(ii)(a)· short2find
June 2023Q3(ii)(b)· short3hence, show that, find
June 2023Q4(a)· short1state
June 2023Q4(b)· short2sketch
June 2023Q4(c)· short3find
June 2023Q5(i)· short3solve
June 2023Q5(ii)· short4solve
June 2023Q6(a)· short2find
June 2023Q6(b)· short2find
June 2023Q6(c)· short2solve
June 2023Q6(d)· short3solve
June 2023Q7(a)· short3find the exact value, find, give your answer to ...
June 2023Q7(b)· short2find, give your answer to ...
June 2023Q7(c)· short3find, give your answer to ...
June 2023Q8(a)· short4show that, find
June 2023Q8(c)· short2find
June 2023Q9(a)· short3show that
June 2023Q9(b)· long5hence, solve, give your answer to ...
June 2023Q9(c)· short2use, find the exact value
June 2023Q10(a)· short4find, simplify
June 2023Q10(b)· short4use, find
January 2023Q1(a)· short1write down
January 2023Q1(b)· short2find
January 2023Q1(c)· short3find
January 2023Q2(a)· short3express, give your answer to ...
January 2023Q2(b)· short3use, write down, find, give your answer to ...
January 2023Q3(a)· short2write down
January 2023Q3(b)· short3hence or otherwise, express, give your answer to ...
January 2023Q4(a)· short4find
January 2023Q4(b)· short3hence, find
January 2023Q5(a)· short4prove
January 2023Q5(b)· long5hence, solve, give your answer to ...
January 2023Q6(a)· short4find, simplify
January 2023Q6(b)· short4find, simplify
January 2023Q7(a)· short4show that, find
January 2023Q8· long5find, simplify
January 2023Q9(a)· short2find, simplify
January 2023Q9(b)· short3show that
January 2023Q9(c)· short2hence, show that
January 2023Q9(d)· short1show that
January 2023Q9(e)· short3use, find, give your answer to ...
January 2023Q10(a)· short1find
January 2023Q10(b)· short3show that
January 2023Q10(c)· long5find, give your answer to ...
October 2022Q1(a)· short4show that, find
October 2022Q1(b)· long5hence, find, give your answer in the form
October 2022Q2(a)· short2find
October 2022Q2(b)· short3find, write down
October 2022Q2(c)· short2find
October 2022Q3(a)· long5use, find
October 2022Q4(b)· short3hence, find
October 2022Q5(a)· short2show that
October 2022Q5(b)· short2show that
October 2022Q5(c)· short2show that
October 2022Q5(d)· short3use, find, give your answer to ...
October 2022Q5(e)· short2hence, find
October 2022Q6· long6show that, find
October 2022Q7(a)· short2write down
October 2022Q7(b)· short2find
October 2022Q7(d)· long5find
October 2022Q8(a)· short3express, give your answer to ...
October 2022Q8(b)· short4find
October 2022Q8(c)· short1state
October 2022Q8(d)· short1state
October 2022Q9(a)· short4prove
October 2022Q9(b)· long5hence, solve, give your answer to ...
June 2022Q1(a)· short2find
June 2022Q2(a)· short2find
June 2022Q2(b)· short3find
June 2022Q2(c)· short4solve
June 2022Q3(a)· short2find
June 2022Q3(b)· short4find
June 2022Q4(a)· short2use, find
June 2022Q4(b)· short3find, give your answer to ...
June 2022Q4(c)· short2find
June 2022Q5(a)· short2find
June 2022Q5(b)· short3find
June 2022Q5(c)· short3find
June 2022Q6(a)· short4show that, find
June 2022Q6(d)· short3find
June 2022Q7(a)· short4show that
June 2022Q7(b)· short4hence, solve, give your answer to ...
June 2022Q8(a)· long5find
June 2022Q8(b)· short4show that
June 2022Q8(c)· short3use, find, give your answer to ...
June 2022Q9(a)· short4show that
June 2022Q9(b)· long5hence, find, give your answer to ...
January 2022Q1· short4find
January 2022Q2(a)· short3show that, find
January 2022Q3(i)· short2find, simplify
January 2022Q3(ii)· short4show that, find
January 2022Q4(a)· short2show that
January 2022Q4(b)· short4find, give your answer to ...
January 2022Q4(c)· short1find
January 2022Q5(a)· short2show that
January 2022Q5(b)· short3use, find, give your answer to ...
January 2022Q5(c)· short4use, find
January 2022Q6(a)· short3show that
January 2022Q6(b)· short3find
January 2022Q6(c)· long5show that, find, deduce
January 2022Q7(a)· short2state
January 2022Q7(b)· short4solve
January 2022Q7(c)· short4sketch, state
January 2022Q8(a)· short4show that, find, give your answer to ...
January 2022Q8(b)· short1interpret
January 2022Q8(c)· short3use, find, give your answer to ...
January 2022Q9(i)· short4solve, give your answer to ...
January 2022Q9(ii)· short4prove
January 2022Q10(a)· short4show that
January 2022Q10(b)· short3find
October 2021Q1(a)· short3show that
October 2021Q1(b)· short3find
October 2021Q1(c)· short3find, simplify, hence, state, give a reason
October 2021Q2(a)· short2state
October 2021Q2(b)· short2state, find
October 2021Q2(c)· short4solve
October 2021Q2(d)· short2find
October 2021Q3(a)· short3find, hence
October 2021Q3(b)· short2find
October 2021Q3(c)· short1state
October 2021Q4(a)· short4show that
October 2021Q4(b)· short3hence or otherwise, solve, give your answer to ...
October 2021Q5(i)· short4find the exact value
October 2021Q5(ii)· short2find, simplify
October 2021Q6(i)· short4show that, find
October 2021Q6(ii)· short4show that, find, hence, state
October 2021Q7(a)· short2find, give your answer to ...
October 2021Q7(b)· short3show that, give your answer to ...
October 2021Q7(c)· short1interpret
October 2021Q8(a)· short1sketch
October 2021Q8(b)· short3show that, find
October 2021Q8(c)· short3find, write in the form
October 2021Q9(a)· short2find
October 2021Q9(b)· short4show that
October 2021Q9(c)· short3use, find, give your answer to ...
October 2021Q10(a)· short2show that, find
October 2021Q10(b)· long5find, simplify
June 2021Q1(a)· short4show that
June 2021Q1(b)· short3use, find, give your answer to ...
June 2021Q2(a)· short3show that, find
June 2021Q2(b)· long6hence, solve, give your answer to ...
June 2021Q3(i)· short2find, simplify
June 2021Q3(ii)· long6write in the form, hence, find the exact value, simplify
June 2021Q4(a)· short4solve
June 2021Q4(b)· short3find
June 2021Q4(c)· short3sketch, label
June 2021Q5(a)· short4find, give your answer to ...
June 2021Q5(b)· short3use, find, give your answer to ...
June 2021Q6(a)· short4sketch
June 2021Q6(b)· short4hence, find, simplify
June 2021Q7· long5show that, find
June 2021Q8(a)· short1find
June 2021Q8(b)· short1find
June 2021Q8(c)· short4find, give your answer to ...
June 2021Q8(d)· short3show that, find
June 2021Q8(e)· short4find, give your answer to ...
June 2021Q9(a)· short3express, give your answer to ...
June 2021Q9(b)· short3find
June 2021Q9(c)· short2find
January 2021Q1· short3find, simplify
January 2021Q2(i)· short3sketch
January 2021Q2(ii)· short3sketch
January 2021Q3(a)· short4show that, find
January 2021Q3(b)· short2hence, find
January 2021Q3(c)· short2find
January 2021Q4(a)· short2find
January 2021Q4(b)· short2sketch
January 2021Q4(c)· long5find
January 2021Q5(a)· short2find
January 2021Q5(b)· short4show that, find
January 2021Q5(c)· short2hence, find, give your answer to ...
January 2021Q5(d)· short3hence, find, give your answer to ...
January 2021Q6(a)· short2find
January 2021Q6(b)· short2show that, find
January 2021Q6(c)· short2use, calculate, give your answer to ...
January 2021Q6(d)· short2use, show that
January 2021Q7(a)· short3prove
January 2021Q7(b)· long6hence, solve, give your answer to ...
January 2021Q8(a)· short4find, give your answer to ...
January 2021Q8(b)· short1interpret
January 2021Q8(c)· short2use, estimate
January 2021Q9(i)· short2find
January 2021Q9(ii)· short2find
January 2021Q10(a)· short2find
January 2021Q10(b)· short3hence, show that, state
October 2020Q1· long5solve, give your answer to ...
October 2020Q2(a)· short4show that, find, give your answer to ...
October 2020Q2(b)· short2use, find, give your answer to ...
October 2020Q3(a)· short4find, simplify
October 2020Q3(b)· short3hence, find
October 2020Q4(a)· short2find
October 2020Q4(b)· short2solve
October 2020Q4(c)· short2state
October 2020Q4(d)· short2find
October 2020Q5(a)· short4show that
October 2020Q5(b)· short4hence, find
October 2020Q6(a)· short3find, give your answer in the form
October 2020Q6(b)· short3use, show that
October 2020Q6(c)· short3use, find, give your answer to ...
October 2020Q7(a)· short3express, give your answer to ...
October 2020Q7(b)· short2find, give your answer to ...
October 2020Q7(c)· short4find, give your answer to ...
October 2020Q8(i)(a)· short2find
October 2020Q8(ii)· short4show that, find
October 2020Q9(a)· short4find, show that
October 2020Q9(b)· long5find, give your answer in the form
October 2020Q9(c)· long5find, give your answer in the form
January 2020Q1(a)· short1calculate
January 2020Q1(b)· short4find, give your answer to ...
January 2020Q1(c)· short1explain
January 2020Q2(a)· short2find, simplify
January 2020Q2(b)· short3find
January 2020Q2(c)· short3hence or otherwise, find
January 2020Q3(a)· short2find
January 2020Q3(b)· short3hence or otherwise, express
January 2020Q4(i)· long6find, hence
January 2020Q4(ii)· long5show that, find
January 2020Q5(a)· short4use, show that
January 2020Q6(a)· short2state
January 2020Q6(b)· short4solve
January 2020Q6(c)· short3find
January 2020Q7(a)· short2show that
January 2020Q7(b)· short3use, find, give your answer to ...
January 2020Q7(c)· long6find the exact value
January 2020Q8(i)· short4find the exact value, simplify
January 2020Q8(ii)· long6find
January 2020Q9(a)· short3express, give your answer to ...
January 2020Q9(b)· short2describe
January 2020Q9(c)· short2find

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