A
acute angles 126
acute triangles 134
addition 11–17
and decimals 59–60
and fractions 74–6
quizzes 17
rounding up and cutting down 16
splitting numbers in your head 15
totaling columns 13
algebra 110–16
brackets 114–15
equation solving 117–23
formulae 111–12
quizzes 116
simplifying 113–14
and substitution 112–13
angles 124–31
acute 126
corresponding 130
measuring and drawing 126–8
obtuse 126
opposite 129
and parallel lines 129–30
and pie charts 213–15
quizzes 131
in a regular polygon 160–1
right 126
translating between degrees and revolutions 126
types of 126
using a protractor 127–8
Archimedes 154
area 149–51
calculating 150–1
parallelograms 151
squared units versus units squared 150
arrowhead (chevron) 159
averages 198–200
axes 183–6
B
bar charts 215–16
segmented 216–18
billion 88
bow-ties 159
brackets 8–9
and algebra 114–15
C
calculators
cosine 177
logarithms 98
π (pi) 143
powers 81
canceling 76–7
Cartesian coordinates 183–6
Celsius, converting into Fahrenheit 195
centimeters 91
charts 212–19
bar 215–16
pie 213–15
quizzes 218–19
segmented bar 216–18
chunking 37–8
circles 140–7
circumference 142–4
definition 141
diameter 141
quizzes 156–7
collecting like terms 120–1
common denominator 74
compass 141
compass (navigation) and measuring angles 126–7
composite numbers 45
cone, volume of 153
and axes 183–6
finding distance between 184–5, 186
mnemonic to remember order of 184
quizzes 187
3-dimensional 185–6
corresponding angles 130
cubic meters 152
cubing 81
cumulative frequency table 201, 202
cylinders, volume of 152–3
D
decimal point 58–9
adding 59–60
and fractions 70–1
multiplying 60–2
quizzes 65
recurring 71
rounding 63–4
subtracting 60
translating between percentages and 103–4
translating into standard form 92–3
degrees 125
denominators 68
common 74
Descartes, René 183
diameter (circle) 141
diamond 157
divisibility tests and multiples 46–7, 49
carrying 39–41
chunking 37–8
long 41–2
and negative numbers 55
quizzes 43
short 38–9
using times tables
backward 36
E
equation of a line 190–2
collecting like terms 120–1
quizzes 123
equilateral triangles 133, 134, 136, 159
even numbers 46
as sum of two prime numbers 48
expanding brackets 114–15
exponential decay 82–3
exponential growth 81–2
F
factors 46
formulae, algebraic 111–12
fractional powers 97
adding 74–6
canceling 76–7
converting into percentages 104
converting ratios into 106
and decimals 70–1
multiplying 76–7
subtracting 76
top-heavy (improper) 69–70
fundamental theorem of arithmetic 46
G
Goldbach’s conjecture 48
gradients 192–5
grams 89
graphs 188–96
equation of a line 190–2
negative gradients 194
plotting 191–2
quizzes 196
steepness and gradients 192–5
H
horizontal axis (x-axis) 183, 184, 185, 190
I
improper fractions 69–70
strict 121
weak 121
interest rates and percentages 106–7
interquartile range 202
inverse sine 180
isosceles trapezium 158
isosceles triangles 133, 134, 136
J
Jones, William 142
K
kilograms 89
kite 158
L
liters 89
and meters 152
logarithms 98–100
and calculators 98
quizzes 101
usefulness of 99–100
long division 41–2
long multiplication 27–9
Loomis, Elisha 170
mean 198–9
megagram (ton) 90
meters
and liters 152
metric system 88–90
milliliters 91
mixed numbers 69
multiples 46
and divisibility tests 46–7, 49
carrying 28–9
column method 32–3
and decimals 60–2
and fractions 76–7
grid method 31–2
long 27–9
and negative numbers 54–5
of powers 83–4
quizzes 34
and times tables 26–7
N
negative gradient 194
dividing 55
multiplying 54–5
and number line 51–3
quizzes 56
subtracting 53–4
uses of 52–3
negative powers of 10: 90
Newton 89
numerators 68
O
obtuse angles 126
obtuse triangles 134
odd numbers 46
opposite angles 129
outliers 198
P
parallel lines 129–30, 157, 195
parallelograms 158
areas 151
percentages 103–9
converting fractions into 104
increase and decrease 104–5
and interest rates 106–7
quizzes 108–9
translating between decimals and 103–4
percentiles 203
plane 183
Platonic solids 162–4
angles in regular 160–1
irregular 160
quizzes 165
and calculators 81
exponential decay 82–3
exponential growth 81–2
fractional 97
and logarithms 98
multiplying 83–4
quizzes 85
and roots 96–7
and Sessa’s chessboard 81–2
of 10: 87–94
prefixes, metric 89–91
breaking numbers down into 45–6, 48
and Goldbach’s conjecture 48
quizzes 49
probability 205–11
combining events “and” 207–8
combining events “or” 208–9
and counting successes 207
quizzes 210–11
proportion 104
protractor 127–8
pyramids 161
Pythagoras’ theorem 166–73, 179, 184–5, 186
Pythagorean triples 171
Q
quadrilateral shapes 157–9
quartiles 202
R
ratios 105–6
converting into fractions 106
rectangles 158
recurring decimals 71
reflex quadrilaterals 159
regular shapes 133
revolution 125–6
rhombus 157
right angle 126
right trapezium 158
right-angled triangles 134, 137
and Pythagoras’ theorem 166–71
rounding 63–4
S
segmented bar charts 216–17
self-intersecting quadrilaterals 159
semicircle, area 151
Sessa’s chessboard 81–2
short division 38–9
signs
π 142
= 7
simplifying algebra 113–14
inverse 180
solids 161–4
spheres
area 153
volume 152
square numbers 27
square roots 96
standard form 91–3
statistics 197–204
cumulative frequency table 201, 202
interquartile range 202
mean 198–9
percentiles 203
quartiles 202
quizzes 204
strict inequalities 121
substitution and algebra 112–13
subtraction 18–23
borrowing 20–1
columns 20
and decimals 60
and fractions 76
and negative numbers 53–4
quizzes 23
rounding up and adding on 22
splitting numbers in your head 21–2
symbols 5–6
T
taking away see subtraction
10
negative powers of 90–1
powers of 87–94
ton (megagram) 90
top-heavy fractions 69–70
trapeziums 158
isosceles 158
right 158
triangles 132–9
acute 134
equilateral 133, 134, 136, 159
obtuse 134
quizzes 139
types of 133–4
within a rectangle 138
see also Pythagoras’ theorem; trigonometry
trigonometry 174–81
calculating angles of triangle from length 179–80
calculating length of triangle from angles 176–9
quizzes 181
SOH-CAH-TOA 178
U
units 88–9
unknowns 118
V
vertical axis (y-axis) 183, 184, 185, 190
volume 151–4
irregular shapes 154
quizzes 155
solid objects 152–3
W
weak inequalities 121
writing mathematics 6–7
X
x-coordinate 190–1
Y
y-coordinate 190–1
y-intercept 195
Z
z-axis 185–6