AS CIE Pure Mathematics 1 Textbook
INDEX
Chapter 1: Quadratics
1.1 Solving quadratic equations by factorisation
1.2 Completing the square
1.3 The quadratic formula
1.4 Solving simultaneous equations (one linear and one quadratic)
1.5 Solving more complex quadratic equations
1.6 Maximum and minimum values of a quadratic function
1.7 Solving quadratic inequalities
1.8 The number of roots of a quadratic equation
1.9 Intersection of a line and a quadratic curve
End-of-chapter review exercise 1
Chapter 2: Functions
2.1 Definition of a function
2.2 Composite functions
2.3 Inverse functions
2.4 The graph of a function and its inverse
2.5 Transformations of functions
2.6 Reflections
2.7 Stretches
2.8 Combined transformations
End-of-chapter review exercise 2
Chapter 3: Coordinate Geometry
3.1 Length of a line segment and midpoint
3.2 Parallel and perpendicular lines
3.3 Equations of straight lines
3.4 The equation of a circle
3.5 Problems involving intersections of lines and circles
End-of-chapter review exercise 3
Cross-topic Review Exercise 1
Chapter 4: Circular Measure
4.1 Radians
4.2 Length of an arc
4.3 Area of a sector
End-of-chapter review exercise 4
Chapter 5: Trigonometry
5.1 Angles between 0° and 90°
5.2 The general definition of an angle
5.3 Trigonometric ratios of general angles
5.4 Graphs of trigonometric functions
5.5 Inverse trigonometric functions
5.6 Trigonometric equations
5.7 Trigonometric identities
5.8 Further trigonometric equations
End-of-chapter review exercise 5
Chapter 6: Series
6.1 Binomial expansion of (a + b)ⁿ
6.2 Binomial coefficients
6.3 Arithmetic progressions
6.4 Geometric progressions
6.5 Infinite geometric series
6.6 Further arithmetic and geometric series
End-of-chapter review exercise 6
Cross-topic Review Exercise 2
Chapter 7: Differentiation
7.1 Derivatives and gradient functions
7.2 The chain rule
7.3 Tangents and normals
7.4 Second derivatives
End-of-chapter review exercise 7
Chapter 8: Further Differentiation
8.1 Increasing and decreasing functions
8.2 Stationary points
8.3 Practical maximum and minimum problems
8.4 Rates of change
8.5 Practical applications of connected rates of change
End-of-chapter review exercise 8
Chapter 9: Integration
9.1 Integration as the reverse of differentiation
9.2 Finding the constant of integration
9.3 Integration of expressions of the form (ax + b)ⁿ
9.4 Further indefinite integration
9.5 Definite integration
9.6 Area under a curve
9.7 Area bounded by a curve and a line or by two curves
9.8 Improper integrals
9.9 Volumes of revolution
End-of-chapter review exercise 9