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First American Edition, 2022
Published in the United States by DK Publishing
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CONSULTANT
Karl Warsi taught mathematics in
schools and colleges for many years.
He has created bestselling textbook
series for secondary-level students
worldwide and is committed to
inclusion in education, and the idea
that people of all ages learn in
different ways.
CONTRIBUTORS
Leo Ball is an Oxford physics graduate,
author, and physics teacher. He also
works with the Institute of Physics,
Oxford University, and the Welsh
Government in preparing students
from under-represented backgrounds
for Oxbridge entrance.
Heather Davis has taught
mathematics for 30 years. She
has published textbooks for Hodder
Education and managed publications
for the UK’s Association of Teachers
of Mathematics.
Julian Emsley is a math teacher
and tutor on the sunny south coast of
England. He enjoys growing fruit and
vegetables, and biking around the hills
and lanes of the South Downs.
Sue Pope is a longstanding
member of the Association of
Teachers of Mathematics and
co-runs workshops on the history
of mathematics in teaching at their
conferences. Published widely,
she recently coedited Enriching
Mathematics in the Primary Curriculum.
Susan Watt studied mathematics
and science at Cambridge University,
and holds postgraduate degrees in
philosophy and psychology. She was
editor of the international magazine
Science in School and has contributed
to many math and science books for
DK and other publishers.
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7 WHAT IS MATH?
NUMBERS
10 NUMBERS ABOVE
AND BELOW ZERO
Integers
11 BREAKING NUMBERS
Fractions
12 POSITIONING THE POINT
Decimals
13 PARTS OF 100
Percentages
14 THE X FACTOR
Factors and multiples
15 PRIME TIME
Prime numbers
16 MULTIPLIED BY ITSELF
Powers and roots
17 PUZZLING POWERS
Negative and zero powers
18 PRIME BUILDERS
Prime factors
20 NOTATING GREAT AND SMALL
Standard form
22 A DIFFERENT WAY
OF THINKING
Complex numbers
23 NUMBER SETS
Types of numbers
24 DIFFERENT BASES
Base arithmetic
25 GROUP RULES
Group theory
CONTENTS
CALCULATIONS
28 TWO STEPS FORWARD,
ONE STEP BACK
Addition and subtraction
30 THREE THREES ARE?
Multiplication
31 EQUAL SPLIT
Division
32 HUNDREDTHS AND
THOUSANDTHS
Calculating decimals
34 MORE OR LESS
Rounding and estimating
36 FRACTION SUMS
Calculating fractions
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GEOMETRY
40 MEASURING TURN
Angles
41 PARALLEL RULES
Angles in parallel lines
42 FLAT SHAPES
2D shapes
44 FLAT WITH THREE SIDES
Types of triangles
46 FOUR-SIDED FIGURES
Types of quadrilaterals
48 THE SUM OF MANY ANGLES
Angles in a polygon
50 3D SHAPES
Types of solids
52 MAKING PLANS
Plans and elevations
53 MULTIPLE COPIES
Symmetry
54 PLOTTING POINTS
Coordinate geometry
56 TRANSFORMING SHAPES
Transformations
58 SHAPE-SHIFTING
Topology
60 4D GEOMETRY
Minkowski space
62 ZOOMING IN
Fractal geometry
ALGEBRA
66 BUILDING BLOCKS
Terms and expressions
67 KEEP IT SIMPLE
Simplifying expressions
68 USING POWERS
Laws of indices
69 RESHAPING EXPRESSIONS
Expanding and factorizing
70 DEFINING RELATIONSHIPS
Formulae
71 A BALANCING ACT
Linear equations
72 WHAT ARE QUADRATIC
EQUATIONS?
Quadratic equations
73 SOLVING BY SUBSTITUTION
Simultaneous equations
74 NOT ALL EQUATIONS
ARE EQUAL
Inequalities
75 WHAT NEXT?
Sequences
76 UNIQUE NUMBER PATTERNS
Special sequences
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GEOMETRY
40 MEASURING TURN
Angles
41 PARALLEL RULES
Angles in parallel lines
42 FLAT SHAPES
2D shapes
44 FLAT WITH THREE SIDES
Types of triangles
46 FOUR-SIDED FIGURES
Types of quadrilaterals
48 THE SUM OF MANY ANGLES
Angles in a polygon
50 3D SHAPES
Types of solids
52 MAKING PLANS
Plans and elevations
53 MULTIPLE COPIES
Symmetry
54 PLOTTING POINTS
Coordinate geometry
56 TRANSFORMING SHAPES
Transformations
58 SHAPE-SHIFTING
Topology
60 4D GEOMETRY
Minkowski space
62 ZOOMING IN
Fractal geometry
ALGEBRA
66 BUILDING BLOCKS
Terms and expressions
67 KEEP IT SIMPLE
Simplifying expressions
68 USING POWERS
Laws of indices
69 RESHAPING EXPRESSIONS
Expanding and factorizing
70 DEFINING RELATIONSHIPS
Formulae
71 A BALANCING ACT
Linear equations
72 WHAT ARE QUADRATIC
EQUATIONS?
Quadratic equations
73 SOLVING BY SUBSTITUTION
Simultaneous equations
74 NOT ALL EQUATIONS
ARE EQUAL
Inequalities
75 WHAT NEXT?
Sequences
76 UNIQUE NUMBER PATTERNS
Special sequences
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GRAPHS
80 FUNCTION MACHINES
Functions
82 PLOTTING A
LINEAR EQUATION
Linear graphs
83 PARABOLAS
Quadratic graphs
84 GRAPHING EQUATIONS
Solving equations with graphs
85 USING REAL-WORLD DATA
Real-life graphs
RATIO AND
PROPORTION
88 COMPARING AMOUNTS
Ratio
90 COMPARISON RELATIONSHIPS
Proportion and percentage
92 CALCULATING CHANGE
Percentage increase and decrease
93 ADDING UP OVER TIME
Compound percentages
94 PROPORTIONAL CHANGES
Direct and inverse proportion
96 IDEAL PROPORTIONS
The golden ratio
98 EXPONENTIAL GROWTH
Exponentials
MEASURE
102 MADE TO MEASURE
Units of measurement
103 A MATTER OF TIME
Time
104 THE AREA OF SHAPES
Area and perimeter
105 TALKING IN CIRCLES
Circles
106 SPACE FILLER
Volume
108 A NET RESULT
Surface area
109 A DEGREE OF ACCURACY
Accuracy and bounds
110 RIGHT-ANGLED TRIANGLES
Pythagoras’ theorem
112 SCALE FACTOR
Scale drawings and maps
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114 SIMILAR OR THE SAME?
Congruence and similarity
116 CALCULATING WITH
TRIANGLES
Trigonometry
118 TRIGONOMETRY IN ACTION
Applications of trigonometry
120 OBLIQUE TRIANGLES
Sine and cosine rules
121 COMBINING UNITS
Compound measures
122 SETS OF POINTS
Constructions and loci
124 MAGNITUDE AND DIRECTION
Vectors
126 WHAT IS THE MATRIX?
Matrices
STATISTICS AND
PROBABILITY
130 ARE STATISTICS VITAL?
Statistics
131 SURVEYS AND SAMPLES
Collecting data
132 DATA CHARTS
Representing data
134 MAKING SENSE OF DATA
Analyzing data
136 WHAT DOES IT MEAN?
Interpreting data
137 FINDING CONNECTIONS
Correlation
138 MEASURING CHANCE
Probability scale
139 COUNTING OUTCOMES
Probability experiments
140 IN A PERFECT WORLD
Theoretical probability
141 TESTING THE ODDS
Comparing experimental and
theoretical probability
142 TREE OF POSSIBILITY
Probability of combined events
143 PART OF THE UNION
Venn diagrams
144 IT DEPENDS
Conditional probability
145 DATA MAPS
Probability distributions
146 VERY UNLIKELY EVENTS
Infinite monkey theorem
CALCULUS
150 MEASURING CHANGE
Rates of change
151 CHANGING VALUES
Derivative of a function
152 SUMMATION OF QUANTITIES
Estimating areas
153 AREA UNDER A CURVE
Integral of a function
154 INVERSE PROCESSES
Fundamental theorem of calculus
155 PRACTICAL CALCULUS
Applications of calculus
156 INDEX
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