Фатих Шахин, Базаров Е.М. Математика, Шың кітап. ҰБТ-ға дайындық оқулық тесті. 2014

1.1. Concept of natural numbers

1.2. Prime factorization of a natural number

1.3. Divisibility test for a number

1.4. Greatest common divisor of several natural numbers

1.5. Least common multiple of several natural numbers

2.1. Even and odd numbers

2.2. Number sequence

2.3. Formulas for finding the sum of a number sequence

2.4. Formula for finding the number of terms or length of a sequence

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3.1. Common fractions

3.2. Equality of fractions. Fundamental properties of fractions. Reducing fractions

3.3. Arithmetic operations with common fractions

3.4. Decimals

3.5. Arithmetic operations with decimals

3.6. Infinite repeating decimal

3.7. Comparing rational numbers

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4.1. Concept of irrational and real numbers

4.2. Power of a real number. Power with a natural exponent

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4.3. Definition and properties of an arithmetic root

4.4. Rationalization

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5.1. Polynomials. Factoring polynomials

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6.1. Linear equations in one variable

6.2. Quadratic equations. Discriminant. Vieta's theorem. Incomplete quadratic equations

6.3. Equations with a variable inside an absolute value

6.4. Rational equations

6.5. Equations of the form P(x)=0

6.6. Exponential equation

6.7. System of linear equations in two variables

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7.1. Linear inequalities in one variable

7.2. Solving systems of inequalities in one variable

7.3. Linear fractional inequalities

7.4. Quadratic inequalities

7.5. Solving rational inequalities

7.6. Solving rational fractional inequalities

7.7. Solving inequalities with a variable inside an absolute value

7.8. Exponential inequalities

7.9. Solving irrational inequalities

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8.1. Problems on relationships between components of arithmetic operations

8.2. Work and productivity problems

8.3. Motion problems

8.4. Problems on concentration and percentage composition

8.5. Percentage problems

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9.1. Definition of a function

9.2. Even and odd functions

9.3. Increasing and decreasing functions

9.4. Composite functions

9.5. Inverse function

9.6. Constant function

9.7. Direct proportion

9.8. Linear function

9.9. Inverse proportion

9.10. Quadratic function

9.11. Function of the form y=x³

9.12. Function of the form y=√x

9.13. Exponential function

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10.1. Number sequence

10.2. Increasing and decreasing sequences

10.3. Arithmetic progression

10.4. Properties of an arithmetic progression

10.5. Geometric progression

10.6. Properties of a geometric progression

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11.1. Degree and radian measure of an angle

11.2. Trigonometric functions of an arbitrary angle

11.3. Fundamental trigonometric identities

11.4. Reduction formulas

11.5. Addition formulas

11.6. Double-angle and half-angle formulas for trigonometric functions

11.7. Formulas for transforming sums of trigonometric functions

11.8. Formulas for transforming products of trigonometric functions

11.9. Graphs of trigonometric functions

11.10. Inverse trigonometric functions

11.11. Basic trigonometric equations and their solutions

11.12. Trigonometric inequalities

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12.1. Exponential function

12.2. Logarithm of a number

12.3. Logarithmic function

12.4. Logarithmic equation

12.5. Logarithmic inequality

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13.1. Definition of the derivative

13.2. Differentiation rules

13.3. Basic derivatives

13.4. Physical and geometric meaning of the derivative

13.5. Slope of a tangent

13.6. Equation of a tangent

13.7. Criteria for increasing and decreasing functions

13.8. Critical points and extrema of a function

13.9. Finding the maximum and minimum values of y=f(x) on the interval from a to b

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14.1. Properties of indefinite integrals

14.2. Basic integration rules

14.3. Substitution method

14.4. Definite integral

14.5. Properties of the definite integral

14.6. Using the definite integral to find areas of plane figures

14.7. Using the definite integral to find volumes of solids of revolution

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15.1. Coordinate system in the plane

15.2. Types of angles

15.3. Parallel lines. Criteria and properties

15.4. Thales' theorem

16.1. Relations between the sides and angles of a triangle

16.2. Triangle congruence criteria

16.3. Triangles

16.4. Types of triangles

16.5. Inscribed and circumscribed circles of a triangle

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17.1. Polygons

17.2. Quadrilaterals

17.3. Parallelogram

17.4. Rhombus

17.5. Rectangle

17.6. Square

17.7. Trapezoid

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18.1. Lines and segments related to a circle

18.2. Angles related to a circle

18.3. Properties of inscribed angles

18.4. Angles between chords, tangents and secants of a circle

18.5. Properties of chords

18.6. Proportionality of chord, tangent and secant segments

18.7. Arc length and circumference

18.8. Common tangents of circles

18.9. Areas of a circle and its parts

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19.1. Coordinate system in the plane

19.2. Equation of a line

19.3. Relative positions of lines given by general equations

19.4. Angle between two lines

19.5. Equation of a circle

19.6. General form of a circle equation

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20.1. Concept of a vector. Vectors in the plane

20.2. Angle between vectors. Relative positions of vectors

20.3. Operations on vectors

20.4. Coordinate vectors

20.5. Vectors in space

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21.1. Parallel line and plane

21.2. Perpendicularity of a line and a plane

21.3. Perpendicular planes

21.4. Perpendicular and oblique segments

21.5. Three perpendiculars theorem

21.6. Angles in space

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22.1. Polyhedra

22.2. Prism. Parallelepiped. Cube

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22.3. Pyramid

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23.1. Cylinder

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23.2. Cone. Truncated cone

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23.3. Ball. Sphere

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24. Combinations of polyhedra and solids of revolution

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Answers to test questions. Algebra

Answers to test questions. Geometry