И.П.Рустюмова, С.Т.Рустюмова. Математикадан ҰБТ дайындалуға тренажер, 2013

Foreword

Chapter I. Rational functions

§1. Equivalent transformations of numerical expressions

§2. Equivalent transformations of rational algebraic expressions

§3. Solving rational algebraic equations

§4. Solving systems of algebraic equations

§5. Solving rational inequalities

§6. Solving equations with a variable inside an absolute value

§7. Solving inequalities with a variable inside an absolute value

Chapter II. Irrational functions

§1. Equivalent transformations of algebraic irrational expressions

§2. Solving irrational equations

§3. Solving systems of irrational equations

§4. Solving irrational inequalities

Chapter III. Exponential and logarithmic functions

§1. Solving exponential equations

§2. Solving exponential inequalities

§3. Equivalent transformations of logarithmic expressions

§4. Solving logarithmic equations

§5. Solving logarithmic inequalities

§6. Solving systems of exponential and logarithmic equations

Chapter IV. Trigonometric functions

§1. Trigonometric transformations

§2. Solving trigonometric equations

§3. Solving trigonometric inequalities

Chapter V. Solving problems involving progressions

§1. Arithmetic progression

§2. Geometric progression

Chapter VI. Solving word problems

Chapter VII. Fundamentals of calculus

§1. Function and its properties

§2. Differentiation of functions

§3. Investigating functions using derivatives

§4. Derivative of a function and equation of a tangent

§5. Antiderivative and its calculation. Applications of the definite integral

Chapter VIII. Plane geometry

§1. Triangles

§2. Quadrilaterals

§3. Circle and disk

Chapter IX. Solid geometry

§1. Calculating distances and angles in space

§2. Polyhedra

§3. Solids of revolution

Chapter X. Elements of analytic geometry and vector algebra

§1. Cartesian coordinates

§2. Vectors in the plane and in space

Chapter XI. Logic problems