Contents - 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 Particular powers....................... 33
3.2 Square roots .............................. 34
3.3 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 ......................................... 86
9.1 Coordinate axis ....................................... 87
9.2 Discrete and continuous variables .......... 88
9.3 Independent and dependent variables ..... 89
9.4 Domain and range ................................... 89
9.5 Draw the graph of a function .................. 90
9.6 Directly proportional functions ............... 91
9.7 Slope-intercept form ............................... 92
9.8 Inversely proportional functions ..............93


GEOMETRY

10    SIMILARITY ............................................... 96
10.1 Thales’ Theorem ............................................. 96
10.2 Using Thales’ Theorem .................................. 97
10.3 Similarity ........................................................ 98
10.4 Pythagorean Theorem ..................................... 98
10.5 Aplications of the Pythagorean Theorem ..... 100


11    AREAS AND VOLUMES ......... 106
11.1 Polyhedrons ................................. 107
11.2 Spheres ........................................ 108
11.3 Cylinders ...................................... 109
11.4 Cones ........................................... 110

 

STATISTICS

12    STATISTICS . . . . . . . . . . . . . . 116
12.1 Basic terms ............................... 116
12.2 Frequency ................................. 117
12.3 Charts ........................................ 118
12.4 Mean, mode and median ........... 120