CambridgeMATHS Stage 6. Year 12, Mathematics extension 1

Rationale
Overview
Acknowledgements
About the authors
1 Sequences and series
1A Sequences and how to specify them
1B Arithmetic sequences
1C Geometric sequences
1D Solving problems involving APs and GPs
1E Adding up the terms of a sequence
1F Summing an arithmetic series
1G Summing a geometric series
1H The limiting sum of a geometric series
1I Recurring decimals and geometric series
Chapter 1 Review
2 Mathematical induction
2A Using mathematical induction for series
2B Proving divisibility by mathematical induction
Chapter 2 Review
3 Graphs and equations
3A The sign of a function
3B Vertical and horizontal asymptotes
3C A curve-sketching menu
3D Solving inequations
3E Using graphs to solve equations and inequations
3F Regions in the coordinate plane
3G Review of translations and reflections
3H Dilations
3I Combinations of transformations
3J Trigonometric graphs
Chapter 3 Review
4 Curve-sketching using the derivative
4A Increasing, decreasing and stationary at a point
4B Stationary points and turning points
4C Some less familiar curves
4D Second and higher derivatives
4E Concavity and points of inflection
4F Systematic curve sketching with the derivative
4G Global maximum and minimum
4H Applications of maximisation and minimisation
4I Maximisation and minimisation in geometry
4J Primitive functions
Chapter 4 Review
5 Integration
5A Areas and the definite integral
5B The fundamental theorem of calculus
5C The definite integral and its properties
5D Proving the fundamental theorem
5E The indefinite integral
5F Finding areas by integration
5G Areas of compound regions
5H The trapezoidal rule
5I The reverse chain rule
Chapter 5 Review
6 The exponential and logarithmic functions
6A Review of exponential functions base e
6B Differentiation of exponential functions
6C Applications of differentiation
6D Integration of exponential functions
6E Applications of integration
6F Review of logarithmic functions
6G Differentiation of logarithmic functions
6H Applications of differentiation of loge x
6I Integration of the reciprocal function
6J Applications of integration of 1/x
6K Calculus with other bases
Chapter 6 Review
7 The trigonometric functions
7A The behaviour of sin x near the origin
7B Differentiating the trigonometric functions
7C Applications of differentiation
7D Integrating the trigonometric functions
7E Applications of integration
Chapter 7 Review
8 Vectors
8A Directed intervals and vectors
8B Components and column vectors
8C The dot product (or scalar product)
8D Geometric problems
8E Projections
8F Applications to physical situations
Chapter 8 Review
9 Motion and rates
9A Average velocity and speed
9B Velocity and acceleration as derivatives
9C Integrating with respect to time
9D Rates and differentiation
9E Review of related rates
9F Rates and integration
Chapter 9 Review
10 Projectile motion
10A Projectile motion â•fl the time equations
10B Projectile motion â•fl the equation of path
Chapter 10 Review
11 Trigonometric equations
11A Equations involving compound angles
11B The sum of sine and cosine functions
11C Using the t-formula to solve equations
Chapter 11 Review
12 Further calculus
12A Inverse trigonometric functions â•fl differentiating
12B Inverse trigonometric functions â•fl integrating
12C Further trigonometric integrals
12D Integration by substitution
12E Further integration by substitution
12F Volumes of rotation
Chapter 12 Review
13 Differential equations
13A Differential equations
13B Slope fields
13C Separable differentiable equations
13D y ' = g(y ) and the logistic equation
13E Applications of differential equations
Chapter 13 Review
14 Series and finance
14A Applications of APs and GPs
14B The use of logarithms with GPs
14C Simple and compound interest
14D Investing money by regular instalments
14E Paying off a loan
Chapter 14 Review
15 Displaying and interpreting data
15A Displaying data
15B Grouped data and histograms
15C Quartiles and interquartile range
15D Bivariate data
15E Formulae for correlation and regression
15F Using technology with bivariate data
Chapter 15 Review
16 Continuous probability distributions
16A Relative frequency
16B Continuous distributions
16C Mean and variance of a distribution
16D The standard normal distribution
16E General normal distributions
16F Applications of the normal distribution
16G Investigations using the normal distribution
Chapter 16 Review
Appendix: The standard normal distribution
17 Binomial distributions
17A Binomial probability
17B Binomial distributions
17C Normal approximations to a binomial
17D Sample proportions
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