Жанасбаева Ұ.Б., Жанасбаев Ж.Б., Жанасбаев К.Б., Математика әдістемелік құрал (ҰБТ),2017
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Жанасбаева Ұ.Б.
Жанасбаев Ж.Б.
Жанасбаев К.Б.
ҰБТ
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Жанасбаева Ұ.Б., Жанасбаев Ж.Б., Жанасбаев К.Б., Математика әдістемелік құрал (ҰБТ),2017
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Entries
95
Introduction
Theory
Page 4
Section 1. Algebra. Arithmetic
Theory
Page 5
1.1. Equivalent transformations of numerical expressions
Theory
Page 5
1.1.1. Divisibility rules. Greatest common divisor. Least common multiple
Theory
Page 5
1.1.2. Operations with numbers
Theory
Page 6
1.1.3. Powers. Roots
Theory
Page 8
1.1.4. Special product formulas. Rationalizing expressions
Theory
Page 10
Exercises
Problem
Page 12
1.2. Transforming rational, fractional, and irrational expressions
Theory
Page 15
1.2.1. Factoring polynomials
Theory
Page 15
1.2.2. Equivalent transformations of rational and fractional expressions
Theory
Page 16
1.2.3. Equivalent transformations of irrational expressions
Theory
Page 19
Exercises
Problem
Page 20
1.3. Equivalent transformations of logarithmic expressions
Theory
Page 22
Exercises
Problem
Page 24
1.4. Equivalent transformations of trigonometric expressions
Theory
Page 25
1.4.1. Basic trigonometric formulas
Theory
Page 25
1.4.2. Inverse trigonometric functions
Theory
Page 32
1.4.3. Trigonometric simplifications
Theory
Page 33
Exercises
Problem
Page 36
1.5. Functions
Theory
Page 38
1.5.1. Linear function
Theory
Page 40
1.5.2. Inverse proportionality
Theory
Page 42
1.5.3. Quadratic function and square root
Theory
Page 43
1.5.4. Exponential and logarithmic functions
Theory
Page 46
1.5.5. Trigonometric and inverse trigonometric functions
Theory
Page 47
Exercises
Problem
Page 48
1.6. Range of a function
Theory
Page 50
Exercises
Problem
Page 54
1.7. Progressions
Theory
Page 55
1.7.1. Arithmetic progression
Theory
Page 55
1.7.2. Geometric progression
Theory
Page 58
Exercises
Problem
Page 60
1.8. Equations
Theory
Page 62
1.8.1. Linear equation
Theory
Page 63
1.8.2. Quadratic equation
Theory
Page 63
1.8.3. Rational equations
Theory
Page 66
1.8.4. Equations with absolute value
Theory
Page 67
1.8.5. Irrational equations
Theory
Page 69
1.8.6. Exponential equations
Theory
Page 71
1.8.7. Logarithmic equations
Theory
Page 72
Exercises
Problem
Page 75
1.9. Inequalities
Theory
Page 77
1.9.1. Linear inequality
Theory
Page 77
1.9.2. Quadratic inequality
Theory
Page 78
1.9.3. Interval method
Theory
Page 80
1.9.4. Inequalities with absolute value
Theory
Page 81
1.9.5. Irrational inequalities
Theory
Page 83
1.9.6. Exponential inequalities
Theory
Page 86
1.9.7. Logarithmic inequalities
Theory
Page 87
Exercises
Problem
Page 90
1.10. Systems of equations and inequalities
Theory
Page 93
1.10.1. Systems of equations
Theory
Page 93
1.10.2. Systems of inequalities
Theory
Page 96
Exercises
Problem
Page 97
1.11. Trigonometric equations
Theory
Page 102
1.11.1. Basic trigonometric equations
Theory
Page 102
Exercises
Problem
Page 106
1.11.2. Trigonometric inequalities
Theory
Page 107
Exercises
Problem
Page 111
1.13. Word and logic problems
Theory
Page 113
Exercises
Problem
Page 117
Section 2. Geometry
Theory
Page 121
2.1. Plane geometry
Theory
Page 121
2.1.1. Triangles
Theory
Page 121
Exercises
Problem
Page 128
2.1.2. Quadrilaterals
Theory
Page 130
Exercises
Problem
Page 136
2.1.3. Circle, disk, and regular polygon
Theory
Page 137
Exercises
Problem
Page 139
2.1.4. Vectors. Lines
Theory
Page 140
Exercises
Problem
Page 144
2.2. Solid geometry
Theory
Page 147
2.2.1. Geometric solids
Theory
Page 147
2.2.2. Solids inscribed in and circumscribed about a sphere
Theory
Page 158
Exercises
Problem
Page 162
Section 3. Fundamentals of calculus
Theory
Page 166
3.1. Differential calculus
Theory
Page 166
3.1.1. Derivative
Theory
Page 166
3.1.2. Tangent to the graph of a function
Theory
Page 167
3.1.3. Intervals of increase and decrease, extrema
Theory
Page 168
3.1.4. Maximum and minimum values of a function on an interval
Theory
Page 170
Exercises
Problem
Page 171
3.2. Integral calculus
Theory
Page 173
3.2.1. Antiderivative and indefinite integral
Theory
Page 173
3.2.2. Definite integral and its applications
Theory
Page 175
Exercises
Problem
Page 177
Section 4. Problems with one or multiple answers
Test
Page 179
4.1. Operations with numbers and simplifying expressions
Test
Page 181
4.2. Equations and systems of equations
Test
Page 187
4.3. Inequalities and systems of inequalities
Test
Page 204
4.4. Word problems and progressions
Test
Page 214
4.5. Functions and their properties
Test
Page 224
4.6. Differential and integral calculus
Test
Page 235
4.7. Geometry problems
Test
Page 248
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