Mathematics 2 ESO

Contents

Arithmetic

1    INTEGERS ……………………………………… 4
1.1 Absolute value …………………………………… 5
1.2 Adding and subtracting integers ………………… 5
1.3 Multiplication and division of integers …………. 6
1.4 Order of operations ……………………………… 7
1.5 Factors …………………………………………… 8
1.6 Multiples ……………………………………….. 10

2    RATIONAL NUMBERS ………………………………….. 16
2.1 Adding and subtracting fractions …………………………… 17
2.2 Multiplying fractions ……………………………………….. 18
2.3 Dividing fractions …………………………………………… 19
2.4 Converting fractions into decimal numbers and vice versa … 20
2.5 Common fractions ………………………………………….. 21
2.6 Adding and subtracting decimal numbers ……………………22
2.7 Multiplication of decimal numbers …………………………. 23
2.8 Division of decimal numbers ……………………………….. 24
2.9 Rounding ……………………………………………………. 25

3    POWERS AND ROOTS ………… 30
3.1 Operations with powers……………. 32
3.2 Scientific notation ………………… 34
3.2 Square roots ………………………. 34
3.4 Cube roots ………………………… 37

4    SEXAGESIMAL NUMBERS ……………. 40
4.1 Angular units………………………………… 41
4.2 Time units …………………………………… 41
4.3 Complex expression of an angle ……………. 42
4.4 Adding angles ……………………………….. 44
4.5 Subtracting angles …………………………… 45
4.6 Multiplying an angle by a number ………….. 46
4.7 Dividing an angle by a number ……………… 47

5    PROPORTIONALITY ……………. 50
5.1 Ratios ……………………………….. 50
5.2 Proportion …………………………… 51
5.3 Directly proportional quantities …….. 52
5.4 Inversely proportional quantities …… 53
5.5 Complex proportionality ……………. 54
5.6 Percentages …………………………. 55

 

Algebra

6    POLYNOMIALS ……………………… 60
6.1 Monomials ……………………………….. 60
6.2 Like terms …………………………………. 61
6.3 Operations with monomials …… 62
6.4 Polynomials ……………………………… 64

7    EQUATIONS ………………………………….. 68
7.1 First degree equations ……………………. 68
7.2 Solving problems with equations ….. 70
7.3 Second degree equations ……………….. 72

8    SYSTEMS OF LINEAR EQUATIONS ……………….. 78
8.1 Linear equation in two variables ………………………. 78
8.2 Solving systems of linear equations ………………… 80
8.3 Writing problems as systems of equations …….. 83

 

Functions

9    FUNCTIONS ………………………………………….. 88
9.1 Coordinate axis ………………………………………… 89
9.2 Discrete and continuous variables ………… 90
9.3 Independent and dependent variables ….. 91
9.4 Domain and range …………………………………… 91
9.5 Draw the graph of a function …………………. 92
9.6 Directly proportional functions ………………. 93
9.7 Slope-intercept form ……………………………….. 94
9.8 Inversely proportional functions ……………..95

Geometry

10    SIMILARITY ……………………………………………….. 98
10.1 Thales’ Theorem ……………………………………………… 98
10.2 Using Thales’ Theorem ………………………………….. 99
10.3 Similarity ………………………………………………………… 100
10.4 Pythagorean Theorem ………………………………….. 101
10.5 Aplications of the Pythagorean Theorem ….. 102

11    AREAS AND VOLUMES ……….. 108
11.1 Polyhedrons …………………………… 109
11.2 Spheres …………………………………… 110
11.3 Cylinders …………………………………. 111
11.4 Cones ……………………………………… 112

 Statistics

12    STATISTICS ………………………… 118
12.1 Basic terms …………………………….. 118
12.2 Frequency ……………………………….. 119
12.3 Charts ………………………………………. 120
12.4 Mean, mode and median ………. 122