Contents - Mathematics 4 ESO

Contents

 

ARITHMETIC


1 REAL NUMBERS ........................................ 4
1.1 CLASSIFICATION ..................................... 4
1.2 THE NUMBER LINE .................................. 6
1.3 TRANSCENDENTAL NUMBERS ............. 9
1.4 ROUNDING ERRORS ................................ 9

2 POWERS AND ROOTS .................................................. 14
2.1 INDEX LAWS ................................................................ 15
2.2 STANDARD INDEX FORM .......................................... 16
2.3 POWERS AND RADICALS ........................................... 17
2.4 HOW MANY ROOTS DOES A RADICAL HAVE? ...... 17
2.5 EQUIVALENT RADICALS ........................................... 18
2.6 HOW TO SIMPLIFY RADICALS ................................. 18
2.7 ADDING AND SUBTRACTING RADICALS ............... 19
2.8 PRODUCT AND DIVISION OF RADICALS ............... 19
2.9 PRODUCT AND DIVISION OF RADICALS . . . . . . . . . . . .
. . . WITH DIFFERENT INDEXES ....................................... 20
2.10 RATIONALIZING DENOMINATORS WITH . . . . . . . . . . .
. . . . RADICALS ................................................................... 20
2.11 LOGARITHMS ............................................................. 21

 

ALGEBRA


3 POLYNOMIALS .......................................................... 26
3.1 IMPORTANT EQUALITIES ....................................... 27
3.2 OPERATIONS WITH POLYNOMIALS .................... 27
3.3 REMAINDER THEOREM .......................................... 29
3.4 FACTOR THEOREM ................................................. 29
3.5 FACTORIZATION OF A POLYNOMIAL ............... 30
3.6 ALGEBRAIC FRACTIONS ....................................... 30

4 EQUATIONS & INEQUALITIES .............................................. 36
4.1 1ST DEGREE EQUATIONS WITH ONE VARIABLE .............. 37
4.2 SECOND DEGREE (QUADRATIC) EQUATIONS ................... 38
4.3 NUMBER OF REAL SOLUTIONS TO A . . . . . . . . . . . . . . . . . . .
. . . 2ND DEGREE EQUATION ........................................................ 40
4.4 OTHER TYPES OF EQUATIONS .............................................. 41
4.5 INEQUALITIES ........................................................................... 43
4.6 SOLUTIONS TO SYSTEMS OF LINEAR INEQUALITIES ...... 47

5 SYSTEMS OF EQUATIONS ....................................................... 54
5.1 SYSTEMS OF LINEAR EQUATIONS ...................................... 55
5.2 SYSTEMS OF NON-LINEAR EQUATIONS ........................... 58

FUNCTIONS


6 FUNCTIONS ................................................. 64
6.1 HOW TO EXPRESS FUNCTIONS ............ 65
6.2 DOMAIN AND RANGE ............................. 66
6.3 CONTINUITY & DISCONTINUITY ......... 66
6.4 PERIODICITY ............................................. 67
6.5 SYMMETRY ................................................ 67
6.6 VARIATION AND CRITICAL POINTS ..... 68
6.7 ASYMPTOTES ............................................ 69

7 ELEMENTARY FUNCTIONS .............................................. 74
7.1 TYPES OF LINEAR FUNCTIONS ....................................... 74
7.2 QUADRATIC FUNCTIONS ................................................. 76
7.3 INVERSELY PROPORTIONAL FUNCTIONS ................... 77
7.4 RADICAL FUNCTIONS ...................................................... 78
7.5 EXPONENTIAL FUNCTIONS ............................................ 79
7.6 LOGARITHMIC FUNCTIONS ............................................ 80
7.7 RELATION BETWEEN EXPONENTIAL FUNCTIONS . . .
. . . . AND LOGARITHMIC FUNCTIONS ................................ 81

 

GEOMETRY

8 SIMILARITY ...................................................... 86
8.1 THALES’ INTERCEPT THEOREM .................. 87
8.2 SIMILARITY CRITERIA FOR TRIANGLES .... 88
8.3 SIMILARITY OF RIGHT TRIANGLES ............. 89

9 TRIGONOMETRY ................................................................. 92
9.1 TRIGONOMETRIC RATIOS ................................................ 92
9.2 RELATIONS BETWEEN RATIOS ....................................... 94
9.3 TRIGONOMETRIC RATIOS OF 30° 45° 60° ...................... 95
9.4 TRIGONOMETRIC RATIOS IN THE “UNIT CIRCLE” ...... 96
9.5 SOLVING RIGHT TRIANGLES ........................................... 98
9.6 SOLVING OBLIQUE TRIANGLES ...................................... 99
9.7 APPLICATIONS ................................................................. 100
9.8 MEASURING ANGLES ...................................................... 101

10 ANALYTIC GEOMETRY.................................. 106
10.1 VECTORS ......................................................... 106
10.2 EQUATIONS OF A STRAIGHT LINE .............. 110
10.3 RELATIVE POSITIONS .................................... 112
10.4 THE CIRCUMFERENCE ................................... 113

 

STATISTICS & PROBABILITY

11 STATISTICS .......................................................................... 118
11.1 SAMPLING .......................................................................... 119
11.2 FREQUENCY ...................................................................... 120
11.3 CHARTS .............................................................................. 121
11.4 STATISTICAL CONCENTRATION PARAMETERS ....... 122
11.5 STATISTICAL POSITION PARAMETERS ....................... 123
11.6 STATISTICAL DISPERSION PARAMETERS .................. 124

12 COMBINATORICS AND PROBABILITY ............ 130
12.1 PERMUTATIONS .................................................... 131
12.2 COMBINATIONS ................................................... 133
12.3 EVENTS IN RANDOM EXPERIMENTS ............... 134
12.4 LAW OF LARGE NUMBERS ................................ 136
12.5 LAPLACE’S RULE OF SUCCESSION .................. 137
12.6 COMPLEX EXPERIMENTS ................................... 138