Ю.Н.Макарычев, Н.Г.Миндюк, К.И.Нешков. Алгебра 9-сынып, 2009

1.1. Angles and arcs

1.1.1. Angles and arcs

1.1.2. Radian measure of an angle

1.1.3. Coordinate circle

1.2. Trigonometric functions of an angle

1.2.1. Definition of sine, cosine, tangent and cotangent of an angle

1.2.2. Table of trigonometric function values for selected angles

1.3. Basic properties of trigonometric functions

1.3.1. Periodicity of trigonometric functions

1.3.2. Evenness and oddness of trigonometric functions

1.3.3. Signs of trigonometric function values in quadrants

Exercises for Sections 1.2–1.3

1.4. Basic trigonometric identities

1.4.1. Relations between trigonometric functions of one argument

1.4.2. Reduction formulas

1.4.3. Addition formulas and their consequences

1.4.3.1. Trigonometric functions of the sum and difference of two arguments

1.4.3.2. Double-angle formulas

1.4.3.3. Sum and difference formulas for trigonometric functions

1.4.4. Product-to-sum formulas for cosα·cosβ, sinα·cosβ and sinα·sinβ

1.5. Graphs and properties of trigonometric functions

1.5.1. Graph and properties of y = sin x

1.5.2. Graph and properties of y = cos x

1.5.3. Graph and properties of y = tan x

1.5.4. Graph and properties of y = cot x

1.5.5. Transformations of trigonometric function graphs

Additional exercises for Chapter I

On the origins of trigonometry

2.1. Numerical sequence

2.1.1. Definition of a numerical sequence

2.1.2. Methods of defining a numerical sequence

2.2. Arithmetic progression

2.2.1. Definition of an arithmetic progression

2.2.2. Properties of an arithmetic progression

2.2.3. Formula for the nth term of an arithmetic progression

2.2.4. Formula for the sum of the first n terms of an arithmetic progression

2.3. Geometric progression

2.3.1. Definition of a geometric progression

2.3.2. Properties of a geometric progression

2.3.3. Formula for the nth term of a geometric progression

2.3.4. Formula for the sum of the first n terms of a geometric progression

2.3.5. Formula for the sum of an infinite decreasing geometric progression

Additional exercises for Chapter II

2.4. Method of mathematical induction

2.4.1. Complete and incomplete induction

2.4.2. Method of mathematical induction

2.4.3. Generalization of the principle of mathematical induction

3.1. Power function with an integer exponent

3.2. nth root

3.2.1. Definition of an nth root. Arithmetic nth root

3.2.2. Basic properties of the arithmetic nth root

3.3. Power with a rational exponent and its properties

3.3.1. Definition of a power with a fractional exponent

3.3.2. Properties of powers with rational exponents

3.3.3. Transforming expressions with fractional exponents

3.4. Power with an irrational exponent. Power function

3.4.1. On powers with irrational exponents

3.4.2. The function y = x^α

3.4.3. Irrational equations

3.4.4. Systems of irrational equations

3.4.5. Irrational inequalities

3.4.6. Means. Classical inequalities

Additional exercises for Chapter III

4.1. Exponential functions

4.1.1. Definition of the exponential function

4.1.2. Properties of the exponential function

4.1.3. Basic exponential equations and inequalities. Systems of equations

4.2. Logarithmic function

4.2.1. Definition of a logarithm

4.2.2. Fundamental logarithmic identity

4.2.3. Basic properties of logarithms

4.2.4. Change-of-base formula. Common and natural logarithms

4.2.5. Logarithmization and exponentiation of expressions

4.2.6. Properties of the logarithmic function

4.2.7. Graph of the logarithmic function

4.2.8. Basic logarithmic equations

4.2.9. Systems of logarithmic equations

4.2.10. Logarithmic inequalities

Additional exercises for Chapter IV

5.1. Translation

5.1.1. Graph of y = f(x) + a

5.1.2. Graph of y = f(x + a)

5.2. Deformation of graphs

5.2.1. Graph of y = b·f(x)

5.2.2. Graph of y = f(ax)

5.3. Reflection

5.3.1. Graph of y = -f(x)

5.3.2. Graph of y = f(-x)

5.4. Plotting graphs of functions containing absolute value

5.4.1. Graph of y equal to f of the absolute value of x

5.4.2. Graph of y equal to the absolute value of f(x)

5.4.3. Graph of y equal to the absolute value of f of the absolute value of x

5.5. Graphs of sums, products and quotients

6.1. Set. Characteristic property of a set

6.1.1. A set and its elements

6.1.2. Characteristic properties of a set

6.1.3. Numerical sets

6.1.4. Sets of points in the plane

6.1.5. Subset

Exercises for Section 6.1

6.2. Operations on sets

6.2.1. Intersection of sets

6.2.2. Union of sets

6.2.3. Difference of sets

6.2.4. Algebra of sets

6.2.5. Inclusion-exclusion formula

6.3. Cardinality of a set

7.1. Combinatorial arrangements

7.1.1. Arrangements

7.1.2. Permutations

7.1.3. Combinations

7.2. Arrangements with repetition

7.2.1. Arrangements with repetition

7.2.2. Permutations with repetition

7.2.3. Combinations with repetition

7.3. Newton's binomial theorem

7.3.1. Newton's binomial formula

7.3.2. Properties of Newton's binomial formula

Additional exercises for Chapter VII

8.1. Subject of probability theory

8.1.1. Two types of phenomena

8.1.2. Subject of probability theory

8.2. Foundations of probability theory

8.2.1. Sample space

8.2.2. Basic relations between events. Operations

8.2.3. Axioms

Exercises for Section 8.2

8.3. Definition of probability. Finding the probability of an event

8.3.1. Statistical definition

8.3.2. Classical definition

8.3.3. Geometric probability

8.3.4. Subjective probability

Exercises for Chapter VIII

Tests

Answers