Tutor tip
"Integration has a huge amount of depth at this level. All questions can rely on Pure 3 trig, so ensure you haven't forgotten key trig formulae which you may need."
Pure 4 is the final Pure unit of the Edexcel International A-Level in Mathematics. Every topic below has exam-style questions and full worked solutions, free to download, plus interactive practice that generates unlimited new questions.
What's on Pure 4
Pure 4 covers seven topics: proof; partial fractions; coordinate geometry with parametric equations; the binomial expansion for negative and fractional powers; differentiation including implicit, parametric and connected rates of change; integration by substitution, by parts and using partial fractions, leading to differential equations; and vectors. Integration is the largest and hardest part of the unit. Unlike Pure 1, where you reversed the power rule, Pure 4 asks you to recognise which technique a given integral needs — and the same integral can often be done more than one way, with only one of them quick. Partial fractions and integration are taught separately but examined together, so a question will frequently split a fraction and then integrate the pieces. Vectors are the topic students most often leave until last and most often regret. The questions are geometric rather than procedural: find where two lines meet, show they are skew, or find the angle between them.
How Pure 4 is examined
Pure 4 is a written paper of 1 hour 30 minutes worth 75 marks, sat in the January, June or October series, counting for one sixth of the full International A-Level. The final questions carry the most marks and almost always combine topics — a parametric curve differentiated to find a tangent, then integrated to find an area, or a differential equation solved using partial fractions. Constants of integration matter: an indefinite integral without one loses a mark every time, and a differential equation needs the initial condition used to find its value.
Practise Pure 4 by topic
Algebra — partial fractions and proof Coordinate Geometry — parametric equations Sequences & Series — binomial expansion for negative and fractional powers Differentiation — implicit, parametric, connected rates of change Integration — substitution, by parts, partial fractions, differential equations Vectors
Pure 4 questions — common questions
How long is the Pure 4 exam? 1 hour 30 minutes, worth 75 marks. What is the hardest topic in Pure 4? Integration, because the difficulty is choosing the technique rather than executing it. Vectors come second, mainly because students leave them until last. Do I need partial fractions for integration? Yes. They are examined together far more often than separately — split the fraction, then integrate each piece, usually giving a sum of logarithms. Is Pure 4 the hardest unit? Most students find it so. It assumes everything from Pure 1 to Pure 3 and adds the techniques that need the most judgement.