Foundation Maths

Front Cover
Half Title Page
Title Page
Copyright Page
Brief contents
Contents
Preface
Publisher\'s acknowledgements
List of videos
Mathematical symbols
Using mathematical and statistical computer software and apps in Foundation Maths
1 Arithmetic of whole numbers
	1.1 Addition, subtraction, multiplication and division
	1.2 The BODMAS rule
	1.3 Prime numbers and factorisation
	1.4 Highest common factor and lowest common multiple
	Test and assignment exercises 1
2 Fractions
	2.1 Introduction
	2.2 Expressing a fraction in equivalent forms
	2.3 Addition and subtraction of fractions
	2.4 Multiplication of fractions
	2.5 Division by a fraction
	Test and assignment exercises 2
3 Decimal numbers
	3.1 Decimal numbers
	3.2 Significant figures and decimal places
	Test and assignment exercises 3
4 Percentage and ratio
	4.1 Percentage
	4.2 Ratio
	Test and assignment exercises 4
5 Algebra
	5.1 What is algebra?
	5.2 Powers or indices
	5.3 Substitution and formulae
	Test and assignment exercises 5
6 Indices
	6.1 The laws of indices
	6.2 Negative powers
	6.3 Square roots, cube roots and fractional powers
	6.4 Multiplication and division by powers of 10
	6.5 Scientific notation
	Challenge Exercise 6
	Test and assignment exercises 6
7 Simplifying algebraic expressions
	7.1 Addition and subtraction of like terms
	7.2 Multiplying algebraic expressions and removing brackets
	7.3 Removing brackets from a(b + c), a(b - c), (a + b)(c + d) and (a + b)(c - d)
	Challenge Exercise 7
	Test and assignment exercises 7
8 Factorisation
	8.1 Factors and common factors
	8.2 Factorising quadratic expressions
	8.3 Difference of two squares
	Challenge Exercise 8
	Test and assignment exercises 8
9 Algebraic fractions
	9.1 Introduction
	9.2 Cancelling common factors
	9.3 Multiplication and division of algebraic fractions
	9.4 Addition and subtraction of algebraic fractions
	9.5 Partial fractions
	Challenge Exercise 9
	Test and assignment exercises 9
10 Transposing formulae
	10.1 Rearranging a formula
	Challenge Exercise 10
	Test and assignment exercises 10
11 Solving equations
	11.1 Solving linear equations
	11.2 Solving simultaneous equations
	11.3 Solving quadratic equations
	Challenge Exercises 11
	Test and assignment exercises 11
12 Sequences and series
	12.1 Sequences
	12.2 Arithmetic progressions
	12.3 Geometric progressions
	12.4 Infinite sequences
	12.5 Series and sigma notation
	12.6 Arithmetic series
	12.7 Geometric series
	12.8 Infinite geometric series
	Challenge Exercises 12
	Test and assignment exercises 12
13 Sets
	13.1 Terminology
	13.2 Sets defined mathematically
	13.3 Venn diagrams
	13.4 Number sets
	Challenge Exercise 13
	Test and assignment exercises 13
14 Number bases
	14.1 The decimal system
	14.2 The binary system
	14.3 Octal system
	14.4 Hexadecimal system
	Challenge Exercise 14
	Test and assignment exercises 14
15 Elementary logic
	15.1 Logic and propositions
	15.2 Symbolic logic
	15.3 Truth tables
	Test and assignment exercises 15
16 Functions
	16.1 Definition of a function
	16.2 Notation used for functions
	16.3 Composite functions
	16.4 The inverse of a function
	Challenge Exercise 16
	Test and assignment exercises 16
17 Graphs of functions
	17.1 The x–y plane
	17.2 Inequalities and intervals
	17.3 Plotting the graph of a function
	17.4 The domain and range of a function
	17.5 Solving equations using graphs
	17.6 Solving simultaneous equations graphically
	Challenge Exercises 17
	Test and assignment exercises 17
18 The straight line
	18.1 Straight line graphs
	18.2 Finding the equation of a straight line from its graph
	18.3 Gradients of tangents to curves
	Challenge Exercise 18
	Test and assignment exercises 18
19 The exponential function
	19.1 Exponential expressions
	19.2 The exponential function and its graph
	19.3 Solving equations involving exponential terms using a graphical method
	Challenge Exercises 19
	Test and assignment exercises 19
20 The logarithm function
	20.1 Introducing logarithms
	20.2 Calculating logarithms to any base
	20.3 Laws of logarithms
	20.4 Solving equations with logarithms
	20.5 Properties and graph of the logarithm function
	Challenge Exercises 20
	Test and assignment exercises 20
21 Measurement
	21.1 Introduction to measurement
	21.2 Units of length
	21.3 Area and volume
	21.4 Measuring angles in degrees and radians
	21.5 Areas of common shapes and volumes of common solids
	21.6 Units of mass
	21.7 Units of time
	21.8 Dimensional analysis
	Challenge Exercise 21
	Test and assignment exercises 21
22 Introduction to trigonometry
	22.1 The trigonometrical ratios
	22.2 Finding an angle given one of its trigonometrical ratios
	Challenge Exercise 22
	Test and assignment exercises 22
23 The trigonometrical functions and their graphs
	23.1 Extended definition of the trigonometrical ratios
	23.2 Trigonometrical functions and their graphs
	Challenge Exercise 23
	Test and assignment exercises 23
24 Trigonometrical identities and equations
	24.1 Trigonometrical identities
	24.2 Solutions of trigonometrical equations
	Challenge Exercises 24
	Test and assignment exercises 24
25 Solution of triangles
	25.1 Types of triangle
	25.2 Pythagoras\' theorem
	25.3 Solution of right-angled triangles
	25.4 The sine rule
	25.5 The cosine rule
	Challenge Exercises 25
	Test and assignment exercises 25
26 Vectors
	26.1 Introduction to vectors and scalars
	26.2 Multiplying a vector by a scalar
	26.3 Adding and subtracting vectors
	26.4 Representing vectors using Cartesian components
	26.5 The scalar product
	Challenge Exercise 26
	Test and assignment exercises 26
27 Matrices
	27.1 What is a matrix?
	27.2 Addition, subtraction and multiplication of matrices
	27.3 The inverse of a 2 * 2 matrix
	27.4 Application of matrices to solving simultaneous equations
	Challenge Exercises 27
	Test and assignment exercises 27
28 Complex numbers
	28.1 Introduction to complex numbers
	28.2 Real and imaginary parts of a complex number
	28.3 Addition, subtraction, multiplication and division of complex numbers
	28.4 Representing complex numbers graphically – the Argand diagram
	28.5 Modulus, argument and the polar form of a complex number
	28.6 The exponential form of a complex number
	Challenge Exercises 28
	Test and assignment exercises 28
29 Tables and charts
	29.1 Introduction to data
	29.2 Frequency tables and distributions
	29.3 Bar charts, pie charts, pictograms and histograms
	Test and assignment exercises 29
30 Statistics
	30.1 Introduction
	30.2 Averages: the mean, median and mode
	30.3 The variance and standard deviation
	Challenge Exercises 30
	Test and assignment exercises 30
31 Probability
	31.1 Introduction
	31.2 Calculating theoretical probabilities
	31.3 Calculating experimental probabilities
	31.4 Independent events
	Challenge Exercise 31
	Test and assignment exercises 31
32 Correlation
	32.1 Introduction
	32.2 Scatter diagrams
	32.3 Correlation coefficient
	32.4 Spearman\'s coefficient of rank correlation
	Challenge Exercise 32
	Test and assignment exercises 32
33 Regression
	33.1 Introduction
	33.2 The regression equation
	Test and assignment exercises 33
34 Gradients of curves
	34.1 The gradient function
	34.2 Gradient function of y = xn
	34.3 Some rules for finding gradient functions
	34.4 Higher derivatives
	34.5 Finding maximum and minimum points of a curve
	Challenge Exercise 34
	Test and assignment exercises 34
35 Techniques of differentiation
	35.1 Introduction
	35.2 The product rule
	35.3 The quotient rule
	35.4 The chain rule
	Challenge Exercise 35
	Test and assignment exercises 35
36 Integration and areas under curves
	36.1 Introduction
	36.2 Indefinite integration: the reverse of differentiation
	36.3 Some rules for finding other indefinite integrals
	36.4 Definite integrals
	36.5 Areas under curves
	Challenge Exercise 36
	Test and assignment exercises 36
37 Techniques of integration
	37.1 Products of functions
	37.2 Integrating products of functions
	37.3 Definite integrals
	37.4 Integration by substitution
	37.5 Integration by partial fractions
	Challenge Exercise 37
	Test and assignment exercises 37
38 Functions of more than one variable and partial differentiation
	38.1 Functions of two independent variables
	38.2 Representing a function of two independent variables graphically
	38.3 Partial differentiation
	38.4 Partial derivatives requiring the product or quotient rules
	38.5 Higher-order derivatives
	38.6 Functions of several variables
	Challenge Exercise 38
	Test and assignment exercises 38
Solutions
Index
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