Cambridge mathematics : 3 unit. Year 11, Enhanced

Preliminary Pages
Contents
Chapter 1 - Methods in Algebra
1A Terms, Factors and Indices
1B Expanding Brackets
1C Factorisation
1D Algebraic Fractions
1E Four Cubic Identities
1F Linear Equations and Inequations
1G Quadratic Equations
1H Simultaneous Equations
1I Completing the Square
1J The Language of Sets
Chapter 2 - Numbers and Functions
2A Cardinals, Integers and Rational Numbers
2B The Real Numbers
2C Surds and their Arithmetic
2D Rationalising the Denominator
2E Equality of Surdic Expressions
2F Relations and Functions
2G Review of Known Functions and Relations
2H Inverse Relations and Functions
2I Shifting and Reflecting Known Graphs
2J Further Transformations of Known Graphs
Chapter 3 - Graphs and Inequations
3A Inequations and Inequalities
3B Intercepts and Sign
3C Domain and Symmetry
3D The Absolute Value Function
3E Using Graphs to Solve Equations and Inequations
3F Regions in the Number Plane
3G Asymptotes and a Curve Sketching Menu
Chapter 4 - Trigonometry
4A Trigonometry with Right Triangles
4B Theoretical Exercises on Right Triangles
4C Trigonometric Functions of a General Angle
4D The Quadrant, the Related Angle and the Sign
4E Given One Trigonometric Function, Find Another
4F Trigonometric Identities and Elimination
4G Trigonometric Equations
4H The Sine Rule and the Area Formula
4I The Cosine Rule
4J Problems Involving General Triangles
Chapter 5 - Coordinate Geometry
5A Points and Intervals
5B Gradients of Intervals and Lines
5C Equations of Lines
5D Further Equations of Lines
5E Perpendicular Distance
5F Lines Through the Intersection of Two Given Lines
5G Coordinate Methods in Geometry
Chapter 6 - Sequences and Series
6A Indices
6B Logarithms
6C Sequences and How to Specify Them
6D Arithmetic Sequences
6E Geometric Sequences
6F Arithmetic and Geometric Means
6G Sigma Notation
6H Partial Sums of a Sequence
6I Summing an Arithmetic Series
6J Summing a Geometric Series
6K The Limiting Sum of a Geometric Series
6L Recurring Decimals and Geometric Series
6M Factoring Sums and Differences of Powers
6N Proof by Mathematical Induction
Chapter 7 - The Derivative
7A The Derivative — Geometric Definition
7B The Derivative as a Limit
7C A Rule for Differentiating Powers of x
7D The Notation dy/dx for the Derivative
7E The Chain Rule
7F The Product Rule
7G The Quotient Rule
7H Rates of Change
7I Limits and Continuity
7J Differentiability
Chapter 8 - The Quadratic Function
8A Factorisation and the Graph
8B Completing the Square and the Graph
8C The Quadratic Formulae and the Graph
8D Equations Reducible to Quadratics
8E Problems on Maximisation and Minimisation
8F The Theory of the Discriminant
8G Definite and Indefinite Quadratics
8H Sum and Product of Roots
8I Quadratic Identities
Chapter 9 - The Geometry of the Parabola
9A A Locus and its Equation
9B The Geometric Definition of the Parabola
9C Translations of the Parabola
9D Parametric Equations of Curves
9E Chords of a Parabola
9F Tangents and Normals: Parametric Approach
9G Tangents and Normals: Cartesian Approach
9H The Chord of Contact
9I Geometrical Theorems about the Parabola
9J Locus Problems
Chapter 10 - The Geometry of the Derivative
10A Increasing, Decreasing and Stationary at a Point
10B Stationary Points and Turning Points
10C Critical Values
10D Second and Higher Derivatives
10E Concavity and Points of Inflexion
10F Curve Sketching using Calculus
10G Global Maximum and Minimum
10H Applications of Maximisation and Minimisation
10I Maximisation and Minimisation in Geometry
Chapter 11 - Integration
11A Finding Areas by a Limiting Process
11B The Fundamental Theorem of Calculus
11C The Definite Integral and its Properties
11D The Indefinite Integral
11E Finding Area by Integration
11F Area of a Compound Region
11G Volumes of Solids of Revolution
11H The Reverse Chain Rule
11I The Trapezoidal Rule
11J Simpson’s Rule
Chapter 12 - The Logarithmic Function
12A Review of Logarithmic and Exponential Functions
12B The Logarithmic Function and its Derivative
12C Applications of Differentiation
12D Integration of the Reciprocal Function
12E Applications of Integration
Chapter 13 - The Exponential Function
13A The Exponential Function and its Derivative
13B Applications of Differentiation
13C Integration of the Exponential Function
13D Applications of Integration
13E Natural Growth and Decay
Chapter 14 - The Trigonometric Functions
14A Radian Measure of Angle Size
14B Mensuration of Arcs, Sectors and Segments
14C Graphs of the Trigonometric Functions in Radians
14D Trigonometric Functions of Compound Angles
14E The Angle Between Two Lines
14F The Behaviour of sinx Near the Origin
14G The Derivatives of the Trigonometric Functions
14H Applications of Differentiation
14I Integration of the Trigonometric Functions
14J Applications of Integration
Answers to Exercises
Chapter One
Exercise 1A
Exercise 1B
Exercise 1C
Exercise 1D
Exercise 1E
Exercise 1F
Exercise 1G
Exercise 1H
Exercise 1I
Exercise 1J
Chapter Two
Exercise 2A
Exercise 2B
Exercise 2C
Exercise 2D
Exercise 2E
Exercise 2F
Exercise 2G
Exercise 2H
Exercise 2I
Exercise 2J
Chapter Three
Exercise 3A
Exercise 3B
Exercise 3C
Exercise 3D
Exercise 3E
Exercise 3F
Exercise 3G
Chapter Four
Exercise 4A
Exercise 4B
Exercise 4C
Exercise 4D
Exercise 4E
Exercise 4F
Exercise 4G
Exercise 4H
Exercise 4I
Exercise 4J
Chapter Five
Exercise 5A
Exercise 5B
Exercise 5C
Exercise 5D
Exercise 5E
Exercise 5F
Exercise 5G
Chapter Six
Exercise 6A
Exercise 6B
Exercise 6C
Exercise 6D
Exercise 6E
Exercise 6F
Exercise 6G
Exercise 6H
Exercise 6I
Exercise 6J
Exercise 6K
Exercise 6L
Exercise 6M
Exercise 6N
Chapter Seven
Exercise 7A
Exercise 7B
Exercise 7C
Exercise 7D
Exercise 7E
Exercise 7F
Exercise 7G
Exercise 7H
Exercise 7I
Exercise 7J
Exercise 7K
Chapter Eight
Exercise 8A
Exercise 8B
Exercise 8C
Exercise 8D
Exercise 8E
Exercise 8F
Exercise 8G
Exercise 8H
Exercise 8I
Chapter Nine
Exercise 9A
Exercise 9B
Exercise 9C
Exercise 9D
Exercise 9E
Exercise 9F
Exercise 9G
Exercise 9H
Exercise 9I
Exercise 9J
Chapter Ten
Exercise 10A
Exercise 10B
Exercise 10C
Exercise 10D
Exercise 10E
Exercise 10F
Exercise 10G
Exercise 10H
Exercise 10I
Exercise 10J
Chapter Eleven
Exercise 11A
Exercise 11B
Exercise 11C
Exercise 11D
Exercise 11E
Exercise 11F
Exercise 11G
Exercise 11H
Exercise 11I
Exercise 11J
Chapter Twelve
Exercise 12A
Exercise 12B
Exercise 12C
Exercise 12D
Exercise 12E
Chapter Thirteen
Exercise 13A
Exercise 13B
Exercise 13C
Exercise 13D
Exercise 13E
Chapter Fourteen
Exercise 14A
Exercise 14B
Exercise 14C
Exercise 14D
Exercise 14E
Exercise 14F
Exercise 14G
Exercise 14H
Exercise 14I
Exercise 14J
Index