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

• Equations that cannot be factorised

• The graphs of quadratic functions

• 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

• 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