CambridgeMaths stage 6. Year 11, Mathematics extension 1

Rationale
Overview
Acknowledgements
About the authors
1 Methods in algebra
1A Arithmetic with pronumerals
1B Expanding brackets
1C Factoring
1D Algebraic fractions
1E Solving linear equations
1F Solving quadratic equations
1G Solving simultaneous equations
1H Completing the square
Chapter 1 Review
2 Numbers and surds
2A Whole numbers, integers and rationals
2B Real numbers and approximations
2C Surds and their arithmetic
2D Further simplification of surds
2E Rationalising the denominator
Chapter 2 Review
3 Functions and graphs
3A Functions and function notation
3B Functions, relations and graphs
3C Review of linear graphs
3D Quadratics functions â•fl factoring and the graph
3E Completing the square and the graph
3F The quadratic formulae and the graph
3G Powers, polynomials and circles
3H Two graphs that have asymptotes
3I Four types of relations
Chapter 3 Review
4 Transformations and symmetry
4A Translations of known graphs
4B Reflections in the x-axis and y-axis
4C Even and odd symmetry
4D The absolute value function
4E Composite functions
Chapter 4 Review
5 Further graphs
5A Solving inequations
5B The sign of a function
5C Reciprocals and asymptotes
5D Graphing sums and products
5E Absolute value and square roots
5F Inverse relations and functions
5G Inverse function notation
5H Defining functions and relations parametrically
Chapter 5 Review
6 Trigonometry
6A Trigonometry with right-angled triangles
6B Problems involving right-angled triangles
6C Three-dimensional trigonometry
6D Trigonometric functions of a general angle
6E Quadrant, sign, and related acute angle
6F Given one trigonometric function, find another
6G Trigonometric identities
6H Trigonometric equations
6I The sine rule and the area formula
6J The cosine rule
6K Problems involving general triangles
Chapter 6 Review
7 The coordinate plane
7A Lengths and midpoints of intervals
7B Gradients of intervals and lines
7C Equations of lines
7D Further equations of lines
7E Using pronumerals in place of numbers
Chapter 7 Review
8 Exponential and logarithmic functions
8A Indices
8B Fractional indices
8C Logarithms
8D The laws for logarithms
8E Equations involving logarithms and indices
8F Exponential and logarithmic graphs
8G Applications of these functions
Chapter 8 Review
9 Differentiation
9A Tangents and the derivative
9B The derivative as a limit
9C A rule for differentiating powers of x
9D The notation dy/dx for the derivative
9E The chain rule
9F Differentiating powers with negative indices
9G Differentiating powers with fractional indices
9H The product rule
9I The quotient rule
9J Rates of change
9K Continuity
9L Differentiability
Chapter 9 Review
10 Polynomials
10A The language of polynomials
10B Graphs of polynomial functions
10C Division of polynomials
10D The remainder and factor theorems
10E Consequences of the factor theorem
10F Sums and products of zeroes
10G Multiple zeroes
10H Geometry using polynomial techniques
Chapter 10 Review
11 Extending calculus
11A The exponential function base e
11B Transformations of exponential functions
11C Differentiation of exponential functions
11D Differentiation and the graph
11E The logarithmic function base e
11F Exponential rates using the base e
11G Radian measure of angle size
11H Solving trigonometric equations
11I Arcs and sectors of circles
11J Trigonometric graphs in radians
Chapter 11 Review
12 Probability
12A Probability and sample spaces
12B Sample space graphs and tree diagrams
12C Sets and venn diagrams
12D Venn diagrams and the addition theorem
12E Multi-stage experiments and the product rule
12F Probability tree diagrams
12G Conditional probability
Chapter 12 Review
13 Discrete probability distributions
13A The language of probability distributions
13B Expected value
13C Variance and standard deviation
13D Sampling
Chapter 13 Review
14 Combinatorics
14A Factorial notation
14B Counting ordered selections
14C Ordered selections and grouping
14D Ordered selections with identical elements
14E Counting unordered selections
14F Using counting in probability
14G Arrangements in a circle
14H The pigeonhole principle
Chapter 14 Review
15 The binomial expansion and Pascal's triangle
15A Binomial expansions and Pascal's triangle
15B Further binomial expansions
15C The binomial theorem
15D Identities in Pascal's triangle
15E Enrichment - using the general term
Chapter 15 Review
16 Further rates
16A Related rates
16B Exponential growth and decay
16C Modified natural growth and decay
Chapter 16 Review
17 Further trigonometry
17A Restricting the domain
17B Defining the inverse trigonometric functions
17C Graphs involving inverse trigonometric functions
17D Trigonometric functions of compound angles
17E The double-angle formulae
17F The t-formulae
17G Products to sums
Chapter 17 Review
Answers
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Chapter 16
Chapter 17