# Contents - Mathematics 1 ESO

### ARITHMETIC

1     NATURAL NUMBERS ............................... 6

1.1 What are natural numbers? .............................. 7
1.2 Equalities and inequalities ............................... 7
1.3 Units, tens, hundreds ....................................... 8
1.4 Properties of addition and multiplication ........ 9
1.5 Order of operations ........................................ 11
1.6 Ancient number systems ................................ 12

2     POWERS AND ROOTS ......... 18
2.1 Powers ........................................ 18
2.2 Operations with powers .............. 20
2.3 Roots ............................................ 22

3     FACTORS AND MULTIPLES ............ 28

3.1 Factors ...................................................... 28
3.2 Multiples ................................................... 29
3.3 Prime & composite numbers .................... 30
3.4 Prime factorization ................................... 31
3.5 Highest common factor ............................ 32
3.6 Lowest common multiple ......................... 33

4     INTEGERS ..................................................... 38
4.1 Graphic representation of integers .................... 39
4.2 Absolute value .................................................. 39
4.3 Adding and subtracting negative numbers ........ 40
4.4 Multiplication and division ............................... 41
4.5 Opposite numbers ............................................. 41

5     FRACTIONS .......................................... 46
5.1 What is a fraction? .................................... 46
5.2 Fractions as operators ............................... 47
5.3 Graphic representation of fractions .......... 47
5.4 Equivalent fractions ................................. 48
5.5 Adding & subtracting fractions ............... 49
5.6 Simplifying fractions ............................... 51
5.7 Multiplying fractions ............................... 52
5.8 Dividing fractions .................................... 53

6     DECIMAL NUMBERS ......................................... 56
6.1 Decimal numbers into fractions and vice versa ........ 57
6.2 Decimal numbers on the number line ....................... 57
6.3 Operations with decimal numbers ............................ 58
6.4 Rounding ................................................................... 61

7     THE METRIC SYSTEM ........ 66

7.1 Length ......................................... 67
7.2 More than one unit ...................... 68
7.3 Mass ............................................ 69
7.4 Area ............................................ 70
7.5 Volume ........................................ 71

8     PROPORTIONALITY .......... 74
8.1 Ratios ......................................... 74
8.2 Direct proportionality ................ 75
8.3 Inverse proportionality .............. 78
8.4 Percentage .................................. 79

### ALGEBRA

9     LINEAR EQUATIONS ....................... 84
9.1 Equivalent equations ............................... 85
9.2 Solving equations with one variable ....... 86

### GEOMETRY

10     2-D GEOMETRY ......... 92
10.1 Points ............................... 92
10.2 Lines ................................ 93
10.3 Angles .............................. 95

11     POLYGONS & THE CIRCUMFERENCE ............ 102
11.1 Triangles ....................................................................... 104
11.2 Points, lines and circles associated with a triangle ....... 106
11.3 Pythagorean Theorem ................................................... 108
11.5 The circumference ......................................................... 110

12     PERIMETERS AND AREAS ........ 116
12.1 Polygons ............................................. 116
12.2 Parallelograms .................................... 117
12.3 Trapeziums ......................................... 119
12.4 Area of a triangle ................................ 120
12.5 Area of any flat shape ......................... 121
12.6 Length of a circumference .................. 122
12.7 Length of an arc .................................. 123

### GRAPHICS, FUNCTIONS, STATISTICS & PROBABILITY

13     GRAPHICS & FUNCTIONS ........ 128
13.1 Coordinates ........................................ 128
13.2 Graphs ................................................ 130
13.3 Functions ............................................ 131

14     STATISTICS & PROBABILITY ......... 134
14.1 Population and sampling ........................... 134
14.2 Frequency ................................................. 135
14.3 Charts ........................................................ 136
14.4 Statistical parameters ................................ 137
14.5 Experiments .............................................. 138
14.6 Frequency and probability ........................ 139