А.Е.Әбілқасымова, Т.П.Кучер. Алгебра 7-сынып, 2017

Introduction

Exercises for reviewing the Grade 5-6 mathematics course

Chapter 1. Power with an integer exponent

§ 1. Power with a natural exponent

§ 2. Multiplication of powers with the same bases

§ 3. Division of powers with the same bases. Power with zero exponent

§ 4. Raising a power to a power

§ 5. Raising a product and quotient to a power

§ 6. Power with an integer exponent

§ 7. Properties of powers with integer exponents

§ 8. Standard form of a number. Solving word problems with large and small quantities

§ 9. Transforming expressions with powers. Numerical sequences containing powers

Check yourself!

Chapter 2. Polynomials and operations on them

§ 10. Monomial. Standard form of a monomial

§ 11. Polynomial. Standard form of a polynomial. Degree of a polynomial

§ 12. Addition and subtraction of polynomials

§ 13. Multiplication of polynomials

§ 14. Division of a polynomial by a monomial

§ 15. Factoring a polynomial by taking out a common factor

§ 16. Factoring a polynomial by grouping

§ 17. Identical transformation of expressions

Check yourself!

Chapter 3. Function. Graph of a function

§ 18. Function

§ 19. Defining a function by a formula

§ 20. Tabular way of defining a function

§ 21. Graphical way of defining a function

§ 22. Linear function and its graph

§ 23. Relative position of graphs of linear functions

§ 24. Graphical solution of systems of linear equations in two variables

§ 25. Function y = ax², its properties and graph

§ 26. Function y = ax³, its properties and graph

§ 27. Function y = k/x (k ≠ 0), its properties and graph

Check yourself!

Chapter 4. Elements of statistics

§ 28. Variation series

§ 29. Absolute frequency and relative frequency. Frequency table

§ 30. Frequency polygon

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Chapter 5. Special product formulas

§ 31. Formula for the difference of squares of two expressions

§ 32. Formulas for the square of a sum and the square of a difference of two expressions

§ 33. Formulas for the cube of a sum and the cube of a difference of two expressions

§ 34. Formulas for the sum and difference of cubes of two expressions

§ 35. Identical transformation of expressions

§ 36. Solving word problems by forming equations and inequalities

Check yourself!

Chapter 6. Algebraic fractions and operations on them

§ 37. Algebraic fraction

§ 38. Fundamental property of an algebraic fraction

§ 39. Addition and subtraction of algebraic fractions

§ 40. Multiplication, exponentiation and division of algebraic fractions

§ 41. Identical transformation of algebraic expressions

Check yourself!

Exercises for reviewing the Grade 7 algebra course

Answers