Ж.У.Кобдикова, Ш.Қ.Нұрманбетова, Р.Октябрь. Математика 6-сынып, 2015

Foreword

Review of the Grade 5 mathematics course

§1. Divisibility of natural numbers. Properties of arithmetic operations

§2. Arithmetic operations with decimal and common fractions

§3. Finding values of expressions with decimal and common fractions

§4. Equation. Solving word problems

§5. Percent. Finding a percent of a number and a number by its percent

§6. Rounding numbers

Chapter I. Ratio and proportion

§7. Ratio. Percentage ratio of two numbers

§8. Proportion

§9. Main property of a proportion

§10. Direct proportional dependence. Inverse proportional dependence

§11. Solving word problems using proportion

§12. Finding a percent of a number and a number by its percent using proportion

§13. Using proportion in drawing diagrams

§14. Scale

§15. Circumference, area of a disk. Ball. Sphere

Chapter II. Rational numbers and operations with them

§16. Positive and negative numbers. Coordinate line

§17. Opposite numbers. Integers. Rational numbers

§18. Absolute value of a number. Simple equations with a variable under the absolute value sign

§19. Comparing rational numbers

§20. Adding rational numbers using a coordinate line

§21. Adding negative rational numbers

§22. Adding rational numbers with different signs

§23. Properties of addition of rational numbers

§24. Subtracting rational numbers with different signs

§25. Subtracting rational numbers with the same signs

§26. Distance between points on a coordinate line

§27. Multiplying rational numbers

§28. Commutative and associative properties of multiplication of rational numbers

§29. Dividing rational numbers. Arithmetic operations with rational numbers

Chapter III. Expressions and identities

§30. Variable. Expression with a variable

§31. Distributive property of multiplication of rational numbers

§32. Expanding brackets. Coefficient. Like terms. Combining like terms

§33. Identical transformation of expressions. Identity

Chapter IV. Linear equations with one variable

§34. Numerical equalities and their properties. Solving equations

§35. Linear equation with one variable. Equivalent equations

§36. Solving equations using transposition of terms and expanding brackets

§37. Solving word problems using a linear equation with one variable

§38. Linear equations with one variable under the absolute value sign

Chapter V. Linear inequalities with one variable and their systems

§39. Numerical inequality and its properties

§40. Number intervals

§41. Intersection and union of number intervals

§42. Linear inequalities with one variable. Equivalent inequalities. Solving linear inequalities with one variable

§43. System of linear inequalities with one variable

§44. Linear inequalities with one variable under the absolute value sign

§45. Solving linear inequalities with one variable under the absolute value sign

Chapter VI. Coordinate plane

§46. Plane. Perpendicular lines and segments

§47. Parallel lines and segments

§48. Coordinate plane. Rectangular coordinate system

§49. Axial and central symmetry

Chapter VII. Function. Linear function

§50. Function. Argument and value of a function

§51. Ways of defining a function: analytic method, defining by formula

§52. Defining a function by a table

§53. Defining a function graphically

§54. Domain of a function. Increasing and decreasing of a function

§55. Linear function and its graph. Properties of a linear function

§56. Relative position of graphs of linear functions

Chapter VIII. Linear equations with two variables and their systems

§57. Linear equation with two variables and its graph

§58. System of linear equations with two variables

§59. Solving a system of linear equations with two variables by the addition method

§60. Solving a system of linear equations with two variables by substitution

§61. Solving a system of linear equations with two variables graphically

§62. Solving word problems using a system of linear equations with two variables

Chapter IX. Review of the Grade 6 mathematics course

§63. Arithmetic operations with rational numbers

§64. Absolute value of a number

§65. Solving equations

§66. Direct and inverse proportional dependencies

§67. Coordinate plane

§68. Linear equation with one variable

§69. Linear inequalities with one variable and their systems

§70. Linear equations and inequalities with one variable under the absolute value sign

§71. Function. Linear function and its graph

§72. System of linear equations with two variables

Answers

References