Cambridge mathematics : 3 unit, Extension 1. Year 12, Enhanced

Preliminary Pages
Contents
Chapter 1 - The Inverse Trigonometric Functions
1A - Restricting the Domain
1B - Defining the Inverse Trigonometric Functions
1C - Graphs Involving Inverse Trigonometric Functions
1D - Differentiation
1E - Integration
1F - General Solutions of Trigonometric Equations
Chapter 2 - Further Trigonometry
2A - Trigonometric Identities
2B - The t-Formulae
2C - Applications of Trigonometric Identities
2D - Trigonometric Equations
2E - The Sum of Sine and Cosine Functions
2F - Extension: Products to Sums and Sums to Products
2G - Three-Dimensional Trigonometry
2H - Further Three-Dimensional Trigonometry
Chapter 3 - Motion
3A - Average Velocity and Speed
3B - Velocity and Acceleration as Derivatives
3C - Integrating with Respect to Time
3D - Simple Harmonic Motion— The Time Equations
3E - Motion Using Functions of Displacement
3F - Simple Harmonic Motion— The Differential Equation
3G - Projectile Motion— The Time Equations
3H - Projectile Motion— The Equation of Path
Chapter 4 - Polynomial Functions
4A - The Language of Polynomials
4B - Graphs of Polynomial Functions
4C - Division of Polynomials
4D - The Remainder and Factor Theorems
4E - Consequences of the Factor Theorem
4F - The Zeroes and the Coefficients
4G - Geometry using Polynomial Techniques
Chapter 5 - The Binomial Theorem
5A - The Pascal Triangle
5B - Further Work with the Pascal Triangle
5C - Factorial Notation
5D - The Binomial Theorem
5E - Greatest Coefficient and Greatest Term
5F - Identities on the Binomial Coefficients
Chapter 6 - Further Calculus
6A - Differentiation of the Six Trigonometric Functions
6B - Integration Using the Six Trigonometric Functions
6C - Integration by Substitution
6D - Further Integration by Substitution
6E - Approximate Solutions and Newton’s Method
6F - Inequalities and Limits Revisited
Chapter 7 - Rates and Finance
7A - Applications of APs and GPs
7B - Simple and Compound Interest
7C - Investing Money by Regular Instalments
7D - Paying Off a Loan
7E - Rates of Change — Differentiating
7F - Rates of Change— Integrating
7G - Natural Growth and Decay
7H - Modified Natural Growth and Decay
Chapter 8 - Euclidean Geometry
8A - Points, Lines, Parallels and Angles
8B - Angles in Triangles and Polygons
8C - Congruence and Special Triangles
8D - Trapezia and Parallelograms
8E - Rhombuses, Rectangles and Squares
8F - Areas of Plane Figures
8G - Pythagoras’ Theorem and its Converse
8H - Similarity
8I - Intercepts on Tranversals
Chapter 9 - Circle Geometry
9A - Circles, Chords and Arcs
9B - Angles at the Centre and Circumference
9C - Angles on the Same and Opposite Arcs
9D - Concyclic Points
9E - Tangents and Radii
9F - The Alternate Segment Theorem
9G - Similarity and Circles
Chapter 10 - Probability and Counting
10E - Counting Ordered Selections
10F - Counting with Identical Elements, and Cases
10G - Counting Unordered Selections
10G - Counting Unordered Selections
10H - Using counting in probability
10I - Arrangements in a Circle
10J - Binomial Probability
Answers
Chapter 1
Exercise 1A
Exercise 1B
Exercise 1C
Exercise 1D
Exercise 1E
Exercise 1F
Chapter 2
Exercise 2A
Exercise 2B
Exercise 2C
Exercise 2D
Exercise 2E
Exercise 2F
Exercise 2G
Chapter 3
Exercise 3A
Exercise 3B
Exercise 3C
Exercise 3D
Exercise 3E
Exercise 3F
Exercise 3G
Exercise 3H
Chapter 4
Exercise 4A
Exercise 4B
Exercise 4C
Exercise 4D
Exercise 4E
Exercise 4F
Exercise 4G
Chapter 5
Exercise 5A
Exercise 5B
Exercise 5C
Exercise 5D
Exercise 5E
Exercise 5F
Chapter 6
Exercise 6A
Exercise 6B
Exercise 6C
Exercise 6D
Exercise 6E
Exercise 6F
Chapter 7
Exercise 7A
Exercise 7B
Exercise 7C
Exercise 7D
Exercise 7E
Exercise 7F
Exercise 7G
Exercise 7H
Chapter 8
Exercise 8A
Exercise 8B
Exercise 8C
Exercise 8D
Exercise 8E
Exercise 8F
Exercise 8G
Exercise 8H
Exercise 8I
Chapter 9
Exercise 9A
Exercise 9B
Exercise 9C
Exercise 9D
Exercise 9E
Exercise 9F
Exercise 9G
Chapter 10
Exercise 10A
Exercise 10B
Exercise 10C
Exercise 10D
Exercise 10E
Exercise 10F
Exercise 10G.)
Exercise 10G
Exercise 10H
Exercise 10I
Exercise 10J
Index