Cambridge 0 Level Mathematics

Cover
Book title
CONTENTS
INTRODUCTION
1 NUMBER
Types of number
Prime factors
Common factors and common multiples
2 SET LANGUAGE AND NOTATION
The definition of a set
The universal set
Venn diagrams
The relationship between sets
The complement of a set
Subsets
Problem solving with Venn diagrams
Alternative ways to define a set
Three-set problems
3 SQUARES, SQUARE ROOTS, CUBES AND CUBE ROOTS
Squares and square roots
Cubes and cube roots
4 DIRECTED NUMBERS
Numbers below zero
5 VULGAR AND DECIMAL FRACTIONS AND PERCENTAGES
Fractions
Fraction of a quantity
Equivalent fractions
Fractions and decimals
Terminating and recurring decimals
Fractions, decimals and percentages
6 ORDERING
Ordering integers
Inequalities
Ordering decimals
Ordering fractions
Ordering fractions, decimals and percentages
7 STANDARD FORM
Standard form
Calculating with numbers in standard form
8 THE FOUR OPERATIONS
Calculating with negative numbers
Order of operations
Multiplying integers
Multiplying decimals
Dividing integers
Dividing decimals
Adding and subtracting fractions
Multiplying fractions
Dividing fractions
9 ESTIMATION
Estimating lengths
Rounding to a given number of decimal places
Rounding to a given number of significant figures
Estimating answers to problems
Working to a sensible degree of accuracy
10 LIMITS OF ACCURACY
Bounds of measurement
Sums and differences of measurements
Multiplying and dividing measurements
11 RATIO, PROPORTION, RATE
Ratio
Using ratio to find an unknown quantity
Dividing a quantity in a given ratio
Increasing and decreasing in a given ratio
Proportion
Rate
12 PERCENTAGES
Fractions, decimals and percentages
Percentage of a quantity
Expressing one quantity as a percentage of another
Percentage change
Percentage increase and decrease
Percentage increase and decrease using a multiplier
Finding the original quantity
13 USE OF AN ELECTRONIC CALCULATOR
Order of operations
Standard form on your calculator
Checking accuracy
Interpreting the calculator display
Calculating with time
Fractions on a calculator
14 TIME
The 24-hour clock
Calculating with time
Converting between hours and minutes and hours written as a decimal
Time zones
15 MONEY
Value for money
Currency conversion
16 PERSONAL AND SMALL BUSINESS FINANCE
Extracting data from tables and charts
Wages and salaries
Discount, profit and loss
Repeated percentage change
Compound and simple interest
17 ALGEBRAIC REPRESENTATION AND FORMULAE
Letters for unknowns
Substituting numbers into algebraic expressions
Using harder numbers when substituting
Writing formulae
Writing equations
Transforming formulae
Transforming harder formulae
18 ALGEBRAIC MANIPULATION
Adding and subtracting with negative numbers
Multiplying and dividing with negative numbers
Combining operations
Simplifying algebraic expressions
Simplifying more complex algebraic expressions
Expanding a single bracket
Factorising algebraic expressions
Factorising expressions of the form ax + bx + kay + kby
Expanding a pair of brackets
Expanding more complex brackets
Factorising expressions of the form a²x² - b²y²
Factorising expressions of the form x² + bx + c
Factorising expressions of the form a² + 2ab + b²
Factorising quadratic expressions of the form ax² + bx + c
Simplifying algebraic fractions
Adding and subtracting algebraic fractions
19 INDICES
Simplifying numbers with indices
Multiplying numbers in index form
Dividing numbers in index form
Simplifying algebraic expressions using indices
Negative indices
Fractional indices
Using the laws of indices with numerical and algebraic expressions
20 SOLUTION OF EQUATIONS AND INEQUALITIES
Solving simple linear equations
Solving equations with a bracket
Solving equations with the unknown on both sides
Solving equations involving fractions
Solving more complex equations involving fractions
Solving inequalities
Solving linear simultaneous equations
Solving more complex simultaneous equations
Solving quadratic equations of the form x² + bx + c = 0 by factorisation
Solving quadratic equations of the form ax² + bx + c = 0 by factorisation
Solving quadratic equations by completing the square
Solving quadratic equations using the quadratic formula
Solving equations involving algebraic fractions
21 GRAPHICAL REPRESENTATION OF INEQUALITIES
Showing regions on graphs
Representing regions satisfying more than one inequality
22 SEQUENCES
Number patterns
Linear sequences
The nth term
Finding the formula for the nth term
The nth term of quadratic, cubic and exponential sequences
23 VARIATION
Proportion
Variation as a formula
Other types of variation
24 GRAPHS IN PRACTICAL SITUATIONS
Conversion graphs
Travel graphs
Rate of change on a distance–time graph
Rate of change on a speed–time graph
Area under a speed–time graph
25 GRAPHS OF FUNCTIONS
Quadratic graphs
Using graphs to solve equations
Cubic graphs
Reciprocal graphs
Exponential graphs
Estimating the gradient to a curve
26 FUNCTION NOTATION
Function notation
Inverse functions
27 COORDINATE GEOMETRY
The gradient of a straight-line graph
Line segments
The length of a line segment
The general form of the equation of a straight line
Parallel and perpendicular lines
28 GEOMETRICAL TERMS
Dimensions
Angles
Lines
Bearings
Triangles
Quadrilaterals
Polygons
Solids
Congruence and similarity
Circles
Nets of 3-D shapes
29 GEOMETRICAL CONSTRUCTIONS
Measuring angles
Constructing a triangle using a ruler and protractor
Constructing a geometrical figure using compasses
Constructing regular polygons in circles
Constructing angle bisectors and perpendicular bisectors
Scale drawings and maps
30 SIMILARITY AND CONGRUENCE
Congruence
Similarity
The areas and volumes of similar shapes
31 SYMMETRY
Line symmetry
Rotational symmetry
Symmetry properties of shapes and solids
The symmetry properties of the circle
32 ANGLES
Angles formed by straight lines
Angles formed within parallel lines
The angles in a quadrilateral
The angles in a polygon
The angles in a circle
33 LOCI
Simple loci
Problems involving intersection of loci
34 MEASURES
Basic units of length, mass and capacity
Area and volume measures
35 MENSURATION
The perimeter of a two-dimensional shape
The area of a rectangle
The area of a triangle
The area of a parallelogram
The area of a trapezium
The area of shapes made from rectangles and triangles
The circumference of a circle
The area of a circle
Arc length and sector area
The volume of a prism
The surface area of a prism
The volume of a pyramid, a cone and a sphere
The surface area of a pyramid, a cone and a sphere
The area and volume of compound shapes
36 TRIGONOMETRY
Bearings
Pythagoras’ Theorem
Trigonometry
The sine and cosine functions for obtuse angles
Non-right-angled triangles
Finding lengths and angles in three dimensions
37 VECTORS IN TWO DIMENSIONS
Vectors and translations
Vector notation
Multiplying a vector by a scalar
Addition and subtraction of column vectors
Position vectors
The magnitude of a vector
Vector geometry
38 MATRICES
Displaying information as a matrix
Multiplying a matrix by a scalar quantity
Adding and subtracting matrices
Multiplying two matrices
The determinant and the inverse of a matrix
Matrix algebra
39 TRANSFORMATIONS
The language of transformations
Reflection
Rotation
Translation
Enlargement
Recognising and describing transformations
Combining transformations
Matrices of transformations
40 PROBABILITY
The probability of a single event
The probability of an event not occurring
Estimating from a population
Relative frequency and probability
The probability of combined events
Independent events
Tree diagrams for combined events
The probability of dependent events
41 CATEGORICAL, NUMERICAL AND GROUPED DATA
Collecting and grouping data
Surveys
Designing a questionnaire
Two-way tables
Averages and range
Mean and range
Which average to use when comparing data
Working with larger data sets
Working with grouped and continuous data
42 STATISTICAL DIAGRAMS
Bar charts and pictograms
Pie charts
Representing grouped and continuous data
Scatter diagrams
Cumulative frequency diagrams
Median, quartiles and percentiles
Histograms
INDEX
A
B
C
D
E
F
G
H
I
K
L
M
N
O
P
Q
R
S
T
U
V
W
Z