Cover
Chapter 1 โ Sequences and Series
1.01 โ General sequences and series
1.02 โ Arithmetic sequences
1.03 โ Arithmetic series
1.04 โ Geometric sequences
1.05 โ Geometric series
1.06 โ Limiting sum of an infinite geometric series
1.07 โ Proof by mathematical induction
Test yourself
Chapter 2 โ Transformations of Functions
2.01 โ Vertical translations of functions
2.02 โ Horizontal translations of functions
2.03 โ Vertical dilations of functions
2.04 โ Horizontal dilations of functions
2.05 โ Combinations of transformations
2.06 โ Graphs of functions with combined transformations
2.07 โ Equations and inequalities
Test yourself
Chapter 3 โ Vectors
3.01 โ Vectors
3.02 โ Adding and subtracting vectors
3.03 โ Scalar multiplication
3.04 โ Vectors in the Cartesian plane
3.05 โ Magnitude and direction of a vector
3.06 โ Components of a vector
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Chapter 4 โ Trigonometric Functions
4.01 โ Transformations of trigonometric functions
4.02 โ Combined transformations of trigonometric functions
4.03 โ Trigonometric equations
4.04 โ Trigonometric identities
4.05 โ Further trigonometric equations
Test yourself
Practice set 1
Chapter 5 โ Further Differentiation
5.01 โ Differentiation review
5.02 โ Derivative of exponential functions
5.03 โ Derivative of logarithmic functions
5.04 โ Derivative of trigonometric functions
5.05 โ Second derivatives
5.06 โ Anti-derivative graphs
5.07 โ Anti-derivatives
5.08 โ Further anti-derivatives
5.09 โ Derivative of inverse functions
5.10 โ Derivative of inverse trigonometric functions
Test yourself
Chapter 6 โ Geometrical Applications of Differentiation
6.01 โ Increasing and decreasing curves
6.02 โ Stationary points
6.03 โ Concavity and points of inflection
6.04 โ Interpreting rates of change graphically
6.05 โ Stationary points and the second derivative
6.06 โ Curve sketching
6.07 โ Global maxima and minima
6.08 โ Finding formulas for optimisation problems
6.09 โ Optimisation problems
Test yourself
Chapter 7 โ Integration
7.01 โ Approximating areas under a curve
7.02 โ Trapezoidal rule
7.03 โ Definite integrals
7.04 โ Indefinite integrals
7.05 โ Chain rule
7.06 โ Integration involving exponential functions
7.07 โ Integration involving logarithmic functions
7.08 โ Integration involving trigonometric functions
7.09 โ Areas enclosed by the x-axis
7.10 โ Areas enclosed by the y-axis
7.11 โ Sums and differences of areas
Test yourself
Chapter 8 โ Further Integration
8.01 โ Volumes of solids
8.02 โ Integration by substitution
8.03 โ Definite integrals by substitution
8.04 โ Integration of sin2 x and cos2 x
8.05 โ Integrals involving inverse trigonometric functions
Test yourself
Practice set 2
Chapter 9 โ Statistics
9.01 โ Types of data
9.02 โ Displaying numerical and categorical data
9.03 โ Measures of central tendency
9.04 โ Quartiles, deciles and percentiles
9.05 โ Range and interquartile range
9.06 โ Variance and standard deviation
9.07 โ Shape and modality of data sets
9.08 โ Analysing data sets
Test yourself
Chapter 10 โ Further Vectors
10.01 โ Scalar (dot) product
10.02 โ Parallel and perpendicular vectors
10.03 โ Projection of vectors
10.04 โ Proofs using vectors
10.05 โ Motion and vectors
10.06 โ Projectile motion
Test yourself
Chapter 11 โ Correlation and Regression
11.01 โ Bivariate data
11.02 โ Correlation
11.03 โ Line of best fit
11.04 โ Least-squares regression line
Test yourself
Practice set 3
Chapter 12 โ Investments, Annuities and Loans
12.01 โ Arithmetic growth and decay
12.02 โ Geometric growth and decay
12.03 โ Compound interest
12.04 โ Compound interest formula
12.05 โ Annuities
12.06 โ Annuities and geometric series
12.07 โ Reducing balance loans
12.08 โ Loans and geometric series
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Chapter 13 โ Differential Equations
13.01 โ Solving dy/dx = f(x)
13.02 โ Solving dy/dx = g(y)
13.03 โ Solving dy/dx = f(x)g(y)
13.04 โ Applications of differential equations
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Chapter 14 โ Continuous Probability
14.01 โ Probability density functions
14.02 โ Calculating probabilities
14.03 โ Cumulative distribution function
14.04 โ Quantiles
14.05 โ Normal distribution
14.06 โ Empirical rule
14.07 โ z-scores
14.08 โ Applications of the normal distribution
Test yourself
Chapter 15 โ Binomial Distributions
15.01 โ Bernoulli distribution
15.02 โ Binomial distribution
15.03 โ Mean and variance of a binomial distribution
15.04 โ Sample proportions
Test yourself
Practice set 4
Answers
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Practice set 1
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Practice set 2
Chapter 9
Chapter 10
Chapter 11
Practice set 3
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Practice set 4
Index