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Cambridge International AS and A Level Mathematics Pure Mathematics 1

(Michael S) #1

  • Algebra The Cambridge A & AS Level Mathematics 9709 syllabus viii

  • Background algebra

  • Linear equations

  • Changing the subject of a formula

  • Quadratic equations

  • Solving quadratic equations

  • Equations that cannot be factorised

  • The graphs of quadratic functions

  • The quadratic formula

  • Simultaneous equations

  • Inequalities

  • Co-ordinate geometry

  • Co-ordinates

  • Plotting, sketching and drawing

  • The gradient of a line

  • The distance between two points

  • The mid-point of a line joining two points

  • The equation of a straight line

  • Finding the equation of a line

  • The intersection of two lines

  • Drawing curves

  • The intersection of a line and a curve

  • Sequences and series

  • Definitions and notation

  • Arithmetic progressions

  • Geometric progressions

  • Binomial expansions

  • Chapter

  • Chapter

  • Chapter

    • Vectors iv

    • Vectors in two dimensions

    • Vectors in three dimensions

    • Vector calculations

    • The angle between two vectors

    • Answers

    • Index

    • Functions 106 Chapter

    • The language of functions

    • Composite functions

    • Inverse functions

    • Differentiation

    • The gradient of a curve

    • Finding the gradient of a curve

    • Finding the gradient from first principles

    • Differentiating by using standard results

    • Using differentiation

    • Tangents and normals

    • Maximum and minimum points

    • Increasing and decreasing functions

    • Points of inflection

    • The second derivative

    • Applications

    • The chain rule

    • Integration

    • Reversing differentiation

    • Finding the area under a curve

    • Area as the limit of a sum

    • Areas below the x axis

    • The area between two curves

    • The area between a curve and the y axis

    • The reverse chain rule

    • Improper integrals

    • Finding volumes by integration

    • Trigonometry

    • Trigonometry background

    • Trigonometrical functions

    • Trigonometrical functions for angles of any size

    • The sine and cosine graphs

    • The tangent graph

    • Solving equations using graphs of trigonometrical functions

    • Circular measure

    • The length of an arc of a circle

    • The area of a sector of a circle

    • Other trigonometrical functions



  • Chapter

  • Chapter

  • Chapter

  • Chapter

    • Vectors vv

    • Vectors in two dimensions

    • Vectors in three dimensions

    • Vector calculations

    • The angle between two vectors

    • Answers

    • Index



  • Chapter

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