Cambridge 3 Unit Mathematics Year 11 Enhanced Version

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
7K Extension — Implicit Differentiation

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
10J Primitive Functions

Chapter 11. Integration
11A Finding Areas by a Limiting Process
11B The Fundamental Theoremof 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 sin x Near the Origin
14G The Derivatives of the Trigonometric
14H Applications of Differentiation
14I Integration of the Trigonometric Functions
14J Applications of Integration

Answers to Exercises
Index