Contents - Mathematics 3 ESO

Contents

 

Arithmetic


1 REAL NUMBERS ................................... 4
1.1 FACTORS AND MULTIPLES ............... 5
1.2 FRACTIONS .......................................... 6
1.3 REAL ALGEBRAIC NUMBERS ............ 9
1.4 ROUNDING ........................................... 9
1.5 SCIENTIFIC NOTATION ..................... 9


2 POWERS AND ROOTS .......................... 12
2.1 OPERATIONS WITH POWERS ............ 13
2.2 RADICALS ............................................. 16

3 SEQUENCES ......................................... 20
3.1 TERMS ................................................. 20
3.2 ORDER ................................................. 21
3.3 ARITHMETIC PROGRESSIONS ........ 22
3.4 GEOMETRIC PROGRESSIONS ......... 23
3.5 SIMPLE INTEREST RATE................... 24
3.6 COMPLEX INTEREST RATE ............. 25

4 PROPORTIONALITY ......................................... 28
4.1 DIRECT PROPORTIONALITY .......................... 29
4.2 INVERSE PROPORTIONALITY ....................... 30
4.3 COMPOUND PROPORTIONALITY ................ 31
4.4 APPLICATIONS OF PROPORTIONALITY ..... 32

 

Algebra


5 POLYNOMIALS ................................... 36
5.1 ADDITION .......................................... 38
5.2 MULTIPLICATION ............................ 39
5.3 DIVISION ........................................... 40
5.4 IMPORTANT THEOREMS ................ 41
5.5 IMPORTANT EQUALITIES ............... 41

6 EQUATIONS ........................................................ 44
6.1 SOLVING 1ST DEGREE EQUATIONS ............. 45
6.2 2ND DEGREE EQUATIONS .............................. 46
6.3 SOLUTIONS ....................................................... 48
6.4 SOLVING PROBLEMS WITH EQUATIONS ... 50

7 SYSTEMS OF LINEAR EQUATIONS ……........................ 54
7.1 SOLUTIONS TO SYSTEMS OF LINEAR EQUATIONS ... 55
7.2 SOLVING SYSTEMS OF LINEAR EQUATIONS ………. 56
7.3 WHICH METHOD IS BEST? …………………….....……. 59

Functions and graphs


8 CHARACTERISTICS OF FUNCTIONS ...........62

8.1 HOW TO EXPRESS FUNCTIONS .................. 64
8.2 CONTINUITY .................................................. 65
8.3 ASYMPTOTES ................................................. 65
8.4 TRENDS ........................................................... 66
8.5 PERIODIC FUNCTIONS ................................ 66
8.6 VARIATION AND CRITICAL POINTS.......... 67
8.7 TRANSFORMATIONS OF FUNCTIONS ...... 68


9 FUNCTIONS OF STRAIGHT LINES AND HYPERBOLAS ... 72
9.1 DIRECTLY PROPORTIONAL FUNCTIONS ........................... 73
9.2 FORMS OF WRITING FUNCTIONS ........................................ 74
9.3 INVERSELY PROPORTIONAL FUNCTIONS ......................... 75


Geometry


10 TRANSFORMATIONS.........................................80
10.1 TRANSLATION .................................................. 80
10.2 ROTATION ......................................................... 82
10.3 REFLECTION ..................................................... 83
10.4 ENLARGEMENT ................................................ 83
10.5 COMPOSITION OF TRANSFORMATIONS ... 84
10.6 FRIEZES AND MOSAICS ................................. 85

11 PLANE GEOMETRY .......................88
11.1 POLYGONS .................................. 88
11.2 ANGLES IN A POLYGON ........... 91
11.3 TRIANGLES .................................. 92
11.4 THE CIRCUMFERENCE .............. 94

12 3-D SHAPES .................................. 98
12.1 POLYHEDRONS ........................ 98
12.2 PRISMS ..................................... 100
12.3 PYRAMIDS ............................... 101
12.4 SOLIDS OF REVOLUTION ..... 102
12.5 CYLINDERS ............................. 102
12.6 CONES ..................................... 102
12.7 SPHERES .................................. 104

 

Statistics and probability

13 STATISTICS ............................................. 108
13.1 FREQUENCY TABLES .......................... 109
13.2 CHARTS ................................................. 110
13.3 CONCENTRATION PARAMETERS ..... 112
13.4 DISPERSION PARAMETERS ................ 113

14 PROBABILITY............................................ 116
14.1 EXPERIMENTS ......................................... 116
14.2 EVENTS .................................................... 117
14.3 FREQUENCY ........................................... 120
14.4 LAW OF LARGE NUMBERS ................... 120
14.5 LAPLACE’S RULE OF SUCCESSION .... 121
14.6 SIMPLE EXPERIMENTS ......................... 122
14.7 COMPLEX EXPERIMENTS .................... 123