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Cambridge AS & A Level Mathematics

1Pure Mathematics 1 (Paper 1)

Pure Mathematics 1 (Paper 1) in Cambridge AS & A Level Mathematics: what the syllabus expects you to know, the learning objectives and how to practise.
Syllabus section374 practice questions20 lessons

Overview

AS Level and A Level (compulsory for both).

In this topic

Lessons

  • Completing the square and the discriminant

    40 min

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  • Quadratic equations, inequalities and simultaneous equations

    45 min

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  • Composite and inverse functions

    40 min

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  • Functions and relations: mappings, domain and range

    35 min

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  • Transformations of graphs

    40 min

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  • Coordinate geometry of straight lines

    40 min

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  • The equation of a circle

    45 min

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  • Radians, arcs, sectors and segments

    45 min

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  • Basic trigonometric identities and equations

    50 min

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  • Trigonometric graphs, exact values and inverse functions

    45 min

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  • Geometric progressions and the sum to infinity

    45 min

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  • Sequences, sigma notation and arithmetic progressions

    45 min

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  • The binomial expansion for a positive integer index

    45 min

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  • Differentiating powers of x and the chain rule

    40 min

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  • Stationary points, optimisation and curve sketching

    50 min

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  • Tangents, normals, increasing functions and rates of change

    45 min

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  • The gradient of a curve and differentiation from first principles

    40 min

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  • Definite integrals and areas

    45 min

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  • Integration as the reverse of differentiation

    40 min

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  • Volumes of revolution

    40 min

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Sample question

A sample question on this topic. Answer it, check it, then read the worked answer.

Pure Mathematics 1 (Paper 1): sample question

1 mark

Find the centre and radius of the circle x2+y2+8x−2y−8=0x^2 + y^2 + 8x - 2y - 8 = 0.

Choose one answer

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