"At this level - never rely on mark schemes to assist with answers. Instead, allocate extra time and refer to tools such as flashcards or formulae pages."
Tutor tip
Pure 3 is the third 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 3
Pure 3 covers eight topics: algebraic methods; functions and graphs, including the modulus function and composite and inverse functions; trigonometric functions — secant, cosecant and cotangent, and the inverse trig functions; trigonometric formulae — addition, double angle and the R form; exponentials and logarithms with e and the natural logarithm; differentiation using the chain, product and quotient rules; integration of standard functions; and numerical methods. This is the unit where the calculus rules multiply. Pure 1 needed only the power rule; Pure 3 expects you to recognise a composite, a product or a quotient and pick the right rule before differentiating. Students who apply the power rule term by term through a product lose the marks without realising why. Trigonometry is the other step up. The addition and double angle formulae are on the formula sheet, but choosing which one turns a given equation into something solvable is not, and that judgement is what the questions test.
How Pure 3 is examined
Pure 3 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. Expect questions that chain topics: differentiate a function involving e and a logarithm, then use the result to find a stationary point. Numerical methods questions often ask you to show a root lies in an interval before iterating, and the change-of-sign argument is worth marks in its own right.
Practise Pure 3 by topic
Algebra — functions, domain and range, modulus, composite and inverse Trigonometry — reciprocal and inverse functions, addition and double angle, R form Exponentials & Logarithms — e and natural logarithms Differentiation — chain, product and quotient rules, standard functions Integration — standard functions
Pure 3 questions — common questions
How long is the Pure 3 exam? 1 hour 30 minutes, worth 75 marks. What is the hardest part of Pure 3? Choosing the right differentiation rule, and knowing which trigonometric identity turns an equation into one you can actually solve. Both are judgement rather than recall. Is Pure 3 harder than Pure 2? Most students find it a clear step up, mainly because the calculus and trigonometry both become rule-selection problems rather than single-method ones. Do I need to memorise the trig formulae? The addition and double angle formulae are given in the formula booklet. Knowing which to reach for is not, and that is what the marks are for.