Contents
1 Sets
1.1 What a set is
1.2 Operations on sets
1.3 Laws of the algebra of sets
1.4 Practice problems
2 Sets of Numbers
2.1 From counting numbers to real numbers
2.2 Interval notation
2.3 Radicals and rational powers
2.4 Complex numbers
2.5 Practice problems
3 Functions
3.1 Ordered pairs and relations
3.2 Functions
3.3 Composite functions
3.4 Odd and even functions
3.5 Inverse of a function
3.6 Practice problems
4 Polynomial Functions
4.1 Linear equations
4.2 Quadratic functions and equations
4.3 Division of polynomials
4.4 Rational functions
4.5 Partial fractions
4.6 Inequalities
4.7 The modulus function
4.8 Practice problems
5 Trigonometry
5.1 Radian measure
5.2 The trigonometric ratios
5.3 Identities
5.4 Trigonometric equations
5.5 Graphs, amplitude and period
5.6 Practice problems
6 Exponential and Logarithmic Functions
6.1 Laws of indices
6.2 Exponential functions
6.3 Logarithmic functions
6.4 Graphs of logarithmic functions
6.5 Practice problems
7 Differentiation
7.1 Limits
7.2 Continuity
7.3 The derivative
7.4 Rules for differentiation
7.5 Implicit differentiation
7.6 The second derivative
7.7 Applications
7.8 Practice problems
8 Integral Calculus
8.1 Reversing differentiation
8.2 Using the integral symbol
8.3 Finding the constant of integration
8.4 Area under a curve
8.5 Methods of integration
8.6 Practice problems
9 Descriptive Statistics
9.1 Introduction
9.2 Some basic definitions
9.3 Frequency distribution
9.4 Histograms
9.5 Frequency polygons
9.6 Cumulative frequency curves (ogives)
9.7 Measures of central tendency
9.8 The median
9.9 The mode
9.10 Measures of dispersion
10 Probability
10.1 Basic ideas
10.2 Probability of an event
10.3 Mutually exclusive events
10.4 Independent events
10.5 Bayes’ theorem