Foundation Maths, 7th Edition By Anthony Croft, Robert Davison [PDF] [eBook]

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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 [Show More]

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