Pure Mathematics 1

Pure 1 is the foundation everything else stands on. The techniques here appear inside Mechanics and Probability & Statistics questions too.

Quadratics

Quadratics is the algebra that the rest of Paper 1 leans on: coordinate geometry needs it, differentiation needs it, and half the trigonometry questions turn into one. Th...

8 questions · 36 marks

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Functions

A function is a rule with a domain attached, and most of the marks in this topic come from the domain and range rather than the rule. This page covers what a function is,...

8 questions · 31 marks

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Coordinate Geometry

Coordinate geometry is the algebra of pictures. From two points you can find a length, a gradient and a midpoint, and from those you can write the equation of any straigh...

8 questions · 26 marks

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Circular Measure

Circular measure is the arithmetic of the circle once angles are measured in radians. One fact, $π$ radians $= 180^{\circ}$ , turns every question into a conversion;...

8 questions · 29 marks

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Trigonometry

Pure 1 trigonometry is where the right-angled triangle work of earlier years becomes a set of functions you can sketch, transform and solve. You need the shapes of the si...

8 questions · 30 marks

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Series

Series is the Pure 1 topic about patterns you can write down in one line. You need to expand $(a + b)^{n}$ for a positive integer $n$ using $(\binom{n}{r})$ and $n!$ ,...

8 questions · 31 marks

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Differentiation

Differentiation answers one question: how steep is the curve here? You find the gradient of a chord, let the second point slide in until the chord becomes a tangent, and ...

8 questions · 32 marks

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Integration

Integration is differentiation run backwards, and the first thing you notice is that it is not quite reversible: $x^{2}$ , $x^{2} + 5$ and $x^{2} - 100$ all differentiate ...

8 questions · 32 marks

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Other areas in AS & A Level Maths