Foundation Maths, 7th Edition


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1292289767 / 9781292289762 Foundation Maths 7th Edition plus MyLab Math with eText — Access Card Package

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9781292289717 Pearson eText of Croft & Davison, Foundation Maths, 7th Edition

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Deepen and broaden subject knowledge to set yourself up for future success

Foundation Maths 7th Edition by Croft and Davison has been written for students taking higher and further education courses who may not have specialised in mathematics on post-16 qualifications, and who require a working knowledge of mathematical and statistical tools. By providing careful and steady guidance in mathematical methods along with a wealth of practice exercises to improve your maths skills, Foundation Maths imparts confidence in its readers. For students with established mathematical expertise, this book will be an ideal revision and reference guide. The style of the book also makes it suitable for self-study and distance learning with self-assessment questions and worked examples throughout.

Foundation Maths is ideally suited for students studying marketing, business studies, management, science, engineering, social science, geography, combined studies and design.


Mathematical processes described in everyday language.

Key points highlighting important results for easy reference

Worked examples included throughout the book to reinforce learning.

Self-assessment questions to test understanding of important concepts, with answers provided at the back of the book.

Demanding Challenge Exercises included at the end of chapters stretch the keenest of students
Test and assignment exercises with answers provided in a lecturer’s Solutions Manual available for download at, allow lecturers to set regular work throughout the course
A companion website containing a student support pack and video tutorials, as well as PowerPoint slides for lecturers, can be found at

New to this edition:

A new section explains the importance of developing a thorough mathematical foundation in order to take advantage of and exploit the full capability of mathematical and statistical technology used in higher education and in the workplace

Extensive sections throughout the book illustrate how readily-available computer software and apps can be used to perform mathematical and statistical calculations, particularly those involving algebra, calculus, graph plotting and data analysis

Table of contents :

Front Cover
Half Title Page
Title Page
Copyright Page
Brief contents
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
Back Cover

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