Editor/Author
Neill, Hugh

Publication Year: 2013

Publisher: Hodder & Stoughton

Price: Core Collection Only

ISBN: 978-1-44-419106-6

Category: Mathematics & Statistics - Mathematics

Image Count:
76

Book Status: Available

Table of Contents

Algebra--A Complete Introduction provides everything you need to broaden your skills and gain confidence. Assuming only a basic level of arithmetic, this carefully graded and progressive book guides you through the basic principles of the subject with the help of exercises and fully worked examples.

- Introduction
- 1 The meaning of algebra
- 1.1 An illustration from numbers
- 1.2 Substitution
- 1.3 Examples of generalizing patterns
- 1.4 Letters represent numbers, not quantities
- 1.5 Examples of algebraic forms
- 2 Elementary operations in algebra
- 2.1 Use of symbols
- 2.2 Symbols of operation
- 2.3 Algebraic expression – terms
- 2.4 Brackets
- 2.5 Coefficient
- 2.6 Addition and subtraction of like terms
- 2.7 Worked examples
- 2.8 The order of addition
- 2.9 Evaluation by substitution
- 2.10 Multiplication
- 2.11 Powers of numbers
- 2.12 Multiplication of powers of a number
- 2.13 Power of a product
- 2.14 Division of powers
- 2.15 Easy fractions
- 2.16 Addition and subtraction
- 2.17 Multiplication and division
- 3 Brackets and operations with them
- 3.1 Removal of brackets
- 3.2 Addition and subtraction of expressions within brackets
- 3.3 Worked examples
- 3.4 Systems of brackets
- 3.5 Worked examples
- 4 Positive and negative numbers
- 4.1 The scale of a thermometer
- 4.2 Motion in opposite directions
- 4.3 Positive and negative numbers
- 4.4 Negative numbers
- 4.5 Graphical representation of the number line
- 4.6 Addition of positive and negative numbers
- 4.7 Subtraction
- 4.8 Graphical illustrations
- 4.9 Multiplication
- 4.10 Division
- 4.11 Summary of rules of signs for multiplication and division
- 4.12 Powers, squares and square roots
- 5 Equations and expressions
- 5.1 Understanding expressions
- 5.2 Using function machines
- 5.3 Function notation
- 5.4 Inverse functions
- 5.5 An introduction to solving equations
- 6 Linear equations
- 6.1 Meaning of an equation
- 6.2 Solving an equation
- 6.3 Worked examples
- 6.4 Problems leading to simple equations
- 7 Formulae
- 7.1 Practical importance of formulae
- 7.2 Treatment of formulae
- 7.3 Worked examples
- 7.4 Transformation of formulae
- 7.5 Worked examples
- 7.6 Literal equations
- 7.7 Worked examples
- 8 Simultaneous equations
- 8.1 Simple equations with two unknown quantities
- 8.2 Solution of simultaneous equations
- 8.3 Worked examples
- 8.4 Problems leading to simultaneous equations
- 8.5 Worked examples
- 9 Linear inequalities
- 9.1 The idea of an inequality
- 9.2 Representing inequalities
- 9.3 Solving inequalities
- 9.4 A trap for the unwary
- 9.5 Simultaneous inequalities
- 10 Straight-line graphs; coordinates
- 10.1 The straight-line graph
- 10.2 The law represented by a straight-line graph
- 10.3 Graph of an equation of the first degree
- 10.4 Worked examples
- 10.5 Position in a plane; coordinates
- 10.6 A straight line as a locus
- 10.7 Equation of any straight line passing through the origin
- 10.8 Graphs of straight lines not passing through the origin
- 10.9 Graphical solution of simultaneous equations
- 11 Using inequalities to define regions
- 11.1 Defining regions
- 11.2 Regions above and below straight lines
- 11.3 Greatest or least values in a region
- 11.4 Linear programming
- 12 Multiplying algebraical expressions
- 12.1 Multiplying expressions when one factor consists of one term
- 12.2 Product of expressions with two terms
- 12.3 When the coefficients of the first terms are not unity
- 12.4 Multiplication of an expression with three terms
- 12.5 Square of an expression with two terms
- 12.6 Square of an expression with three terms
- 12.7 Cube of an expression with two terms
- 12.8 Product of sum and difference
- 13 Factors
- 13.1 The process of finding factors
- 13.2 Factors consisting of one term only
- 13.3 Worked examples
- 13.4 Factors with two terms
- 13.5 Worked examples
- 13.6 The form x2 + ax + b
- 13.7 Worked examples
- 13.8 The form ax2 + bx + c
- 13.9 Expressions which are squares
- 13.10 Difference of two squares
- 13.11 Worked examples
- 13.12 Evaluation of formulae
- 13.13 Sum and difference of two cubes
- 13.14 Worked examples
- 14 Fractions
- 14.1 Algebraic fractions
- 14.2 Laws of fractions
- 14.3 Reduction of fractions
- 14.4 Multiplication and division
- 14.5 Addition and subtraction
- 14.6 Simple equations involving algebraical fractions
- 15 Graphs of quadratic functions
- 15.1 Constants and variables
- 15.2 Dependent and independent variables
- 15.3 Functions
- 15.4 Graph of a function
- 15.5 Graph of a function of second degree
- 15.6 Some properties of the graph of y = x2
- 15.7 The graph of y = −x2
- 15.8 The graphs of y = ax2
- 15.9 The graphs of y = x2 ± a, where a is any number
- 15.10 Graph of y = (x − 1)2
- 15.11 Graph of y = (x − 1)2 − 4
- 15.12 The graph y = x2 − 2x − 3
- 15.13 Solution of the equation x2 − 2x − 3 = 0 from the graph
- 15.14 Graph of y = 2x2 − 3x − 5
- 15.15 Graph of y = 12 − x − x2
- 15.16 Using graphics calculators
- 15.17 Using graphs to solve quadratic inequalities
- 15.18 Using quadratic inequalities to describe regions
- 16 Quadratic equations
- 16.1 Algebraical solution
- 16.2 The method of solution of any quadratic
- 16.3 Solution of 2x2 + 5x − 3 = .0
- 16.4 Worked examples
- 16.5 Solution of quadratic equations by factorization
- 16.6 Worked examples
- 16.7 General formula for the solution of a quadratic equation
- 16.8 Solution of the quadratic equation ax2 + bx + c = 0
- 16.9 Worked examples
- 16.10 Problems leading to quadratics
- 16.11 Simultaneous equations of the second degree
- 16.12 When one of the equations is of the first degree
- 16.13 Solving quadratic inequalities
- 17 Indices
- 17.1 The meaning of an index
- 17.2 Laws of indices
- 17.3 Extension of the meaning of an index
- 17.4 Graph of 2x
- 17.5 Algebraical consideration of the extension of the meaning of indices
- 17.6 Fractional indices
- 17.7 To find a meaning for a0
- 17.8 Negative indices
- 17.9 Standard forms of numbers17.10 Operations with standard forms
- 18 Logarithms
- 18.1 A system of indices
- 18.2 A system of logarithms
- 18.3 Rules for the use of logarithms
- 18.4 Change of base of a system of logarithms
- 19 Ratio and proportion
- 19.1 Meaning of a ratio
- 19.2 Ratio of two quantities
- 19.3 Proportion
- 19.4 Theorems on ratio and proportion
- 19.5 An illustration from geometry
- 19.6 Constant ratios
- 19.7 Examples of equal ratios
- 20 Variation
- 20.1 Direct variation
- 20.2 Examples of direct variation
- 20.3 The constant of variation
- 20.4 Graphical representation
- 20.5 To find the law connecting two variables
- 20.6 Worked example
- 20.7 y partly constant and partly varying as x
- 20.8 Worked example
- 20.9 y varies as the square of x – that is, y ∝ x2
- 20.10 y varies as the cube of x – that is, y ∝ x3
- 20.11 y varies as or , that is,
- 20.12 Inverse variation:
- 20.13 Graph of
- 20.14 Other forms of inverse variation
- 20.15 Worked examples
- 20.16 Functions of more than one variable
- 20.17 Joint variation
- 20.18 Worked examples
- 21 The determination of laws
- 21.1 Laws which are not linear
- 21.2 y = axn + b. Plotting against a power of a number
- 21.3 Worked example
- 21.4 y = axn. Use of logarithms
- 21.5 Worked example
- 22 Rational and irrational numbers and surds
- 22.1 Rational and irrational numbers
- 22.2 Irrational numbers and the number line
- 22.3 Geometrical representation of surds
- 22.4 Operations with surds
- 23 Arithmetical and geometrical sequences
- 23.1 Meaning of a sequence
- 23.2 The formation of a sequence
- 23.3 Arithmetic sequences, or arithmetic progressions
- 23.4 Any term in an arithmetic sequence
- 23.5 The sum of any number of terms of an arithmetic sequence
- 23.6 Arithmetic mean
- 23.7 Worked examples
- 23.8 Harmonic sequences or harmonic progressions
- 23.9 Geometric sequences or geometric progressions
- 23.10 Connection between a geometric sequence and an arithmetic sequence
- 23.11 General term of a geometric sequence
- 23.12 Geometric mean
- 23.13 The sum of n terms of a geometric sequence
- 23.14 Worked examples
- 23.15 Increasing geometric sequences
- 23.16 Decreasing geometric sequences
- 23.17 Recurring decimals
- 23.18 A geometrical illustration
- 23.19 The sum to infinity
- 23.20 Worked examples
- 23.21 Simple and compound interest
- 23.22 Accumulated value of periodical payments
- 23.23 Annuities
- Appendix
- Answers