Turkey Grade 10 High School Curriculum - Mathematics

This information is based on the FutureSchool curriculum.

Year 10 Mathematics

1. Self Assessment – Year 10

• Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.

2. Multiplying and dividing to obtain equivalent fractions

• Objective: Obtain equivalent fractions using a number line or diagram, develop mental strategies to obtain equivalent fractions, and reduce a fraction to its lowest equivalent form.

3. Reducing fractions to lowest equivalent form

• Objective: Reduce a fraction to its lowest equivalent form by dividing the numerator and denominator by a common factor.

4. Comparing and ordering fractions greater than (>) 1

• Objective: Use diagrams, number lines and equivalent fractions to compare and order fractions greater than one.

5. Subtracting fractions from whole numbers

• Objective: Use a diagram to subtract fractions from a whole number, develop mental strategies for subtracting fractions from whole numbers, and recognise and use the written form for subtracting fractions from whole numbers.

6. Adding and subtracting fractions with the same denominator

• Objective: Add and subtract fractions with the same denominator.

7. Adding and subtracting fractions with different denominators

• Objective: Add and subtract fractions where one denominator is a multiple of the other.

8. Multiplying fractions by whole numbers

• Objective: Multiply simple fractions by whole numbers.

9. Multiplying fractions

• Objective: Multiply fractions and reduce the answer to its lowest form.

10. Multiplying mixed numbers (mixed numerals)

• Objective: Multiply mixed numbers and reduce the answer to its lowest form.

11. Finding reciprocals of fractions and mixed numbers (mixed numerals)

• Objective: Find the reciprocals of fractions and mixed numbers.

12. Dividing fractions

• Objective: Divide fractions.

13. Dividing mixed numbers (mixed numerals)

• Objective: Divide mixed numbers.

14. Using Order of Operation procedures (BIDMAS) with Fractions

• Objective: Apply the order of operations rules to simplify expressions with integers and fractions.

15. Calculating Percentages and Fractions of Quantities

• Objective: Find percentages and fractions of quantities and solve problems with percentages.

16. Solving equations containing binomial expressions

• Objective: Move terms in binomial equations.

17. Adding decimals to two decimal places

• Objective: Add decimals with the same number of decimal places (to two decimal places).

18. Subtracting decimals to two decimal places

• Objective: Subtract decimals with the same number of decimal places (to two decimal places).

19. Using decimals – shopping problems

• Objective: Read and interpret problems involving money, interpret the everyday use of decimals, and perform calculations with money.

20. Using decimals to record length

• Objective: Interpret the everyday use of fractions and decimals and use knowledge of decimals to record measurements.

21. Decimals to three decimal places

• Objective: Express thousandths as a decimal and interpret decimal notation for thousandths.

22. Adding decimals with a different number of decimal places

• Objective: Add decimal numbers with different numbers of decimal places.

23. Subtracting decimals with a different number of places

• Objective: Subtract decimals with different numbers of decimal places.

24. Multiplication of decimals by decimals to two decimal places

• Objective: Multiply decimals to two digits.

25. Dividing decimals by 10, 100 and 1000

• Objective: Divide decimal numbers by one hundred and recognise the pattern formed when decimals are divided by ten, one hundred and one thousand.

26. Dividing decimal fractions by whole numbers

• Objective: Divide decimal fractions by whole numbers.

27. Dividing numbers by a decimal fraction

• Objective: Divide numbers by a decimal fraction.

28. Introduction to percentages, including relating common fractions to percentages

• Objective: Recognise that the symbol % means ‘per cent’ and relate common fractions to a percentage.

29. Changing fractions and decimals to percentages using tenths and hundredths

• Objective: Change simple fractions to percentages and decimals to percentages by using place value conversion.

30. Changing percentages to fractions and decimals

• Objective: Change percentages to fractions and know how to change percentages to decimals.

31. One quantity as a percentage of another

• Objective: Find a percentage of an amount and how to express one quantity as a percentage of another.

32. Equations involving grouping symbols

• Objective: Solve equations using grouping symbols.

33. Equations involving fractions

• Objective: Solve equations using fractions.

34. Solving Inequalities

• Objective: Understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities.

35. Simplifying easy algebraic fractions

• Objective: Understand how to simplify algebraic fractions by factorising.

36. Adding indices when multiplying terms with the same base

• Objective: Use the index law of addition of powers when multiplying terms with the same base.

37. Subtracting indices when dividing terms with the same base

• Objective: Use the index law of subtraction of powers when dividing terms with the same base.

38. Multiplying indices when raising a power to a power

• Objective: Use the law of multiplication of indices when raising a power to a power.

39. Multiplying indices when raising to more than one term

• Objective: Use the law of multiplication of indices when raising more than one term to the same power.

40. Terms raised to the power of zero

• Objective: Evaluate or simplify terms that are raised to the power of zero.

41. Negative Indices

• Objective: Evaluate or simplify expressions containing negative indices.

42. Simplifying algebraic fractions using the index laws

• Objective: Simplify most algebraic fractions using different methodologies.

43. Fractional indices

• Objective: Evaluate or simplify expressions containing fractional indices.

44. Scientific notation with larger numbers

• Objective: Change numbers greater than 1 to scientific notation.

45. Scientific notation with small numbers

• Objective: Change numbers between zero and 1 to scientific notation.

46. Changing scientific notation to numerals

• Objective: Change numbers written in scientific notation to basic numerals and be capable of solving problems on the calculator in scientific notation.

47. Significant figures

• Objective: Observe how many significant figures are in a number and how to express a number to a certain level of significant figures.

48. Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio]

• Objective: Use the tangent ratio to calculate the length of the opposite side in a right angle triangle.

49. Unknown in the denominator. [Case 4]

• Objective: Use the trig ratios to calculate lengths and distances when the denominator is unknown.

50. Bearings – the compass

• Objective: Identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north.

51. Angles of elevation and depression

• Objective: Identify angles of depression and angles of elevation, and the relationship between them.

52. Trigonometric ratios in practical situations

• Objective: Use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation.

53. Using the trigonometric ratios to find an angle in a right-angled triangle

• Objective: Find the value of an unknown angle in a right angle triangle given the lengths of two of the sides.

54. Using the calculator to find an angle given a trigonometric ratio

• Objective: Use a calculator to find the value of an unknown angle when given a trigonometric ratio.

55. Additional questions involving parallel lines

• Objective: Complete two-step parallel line questions, and identify other ways to solve them.

56. Quadrilaterals

• Objective: Find missing angles by using the fact that a quadrilateral’s angle sum is 360 degrees.

57. Geometric constructions

• Objective: Complete constructions with a ruler and a pair of compasses.

58. Further difficult exercises involving formal reasoning

• Objective: Identify which geometric properties are needed to complete a question and be able to use formal reasoning to write out this information.

59. Congruent triangles, Test 1 and 2

• Objective: Identify which test to use to show two triangles are congruent.

60. Congruent triangles, Test 3 and 4

• Objective: Identify other tests to use to show two triangles are congruent.

61. Proofs and congruent triangles

• Objective: Set out a formal proof to show that two triangles are congruent.

62. Using similar triangles to calculate lengths

• Objective: Calculate lengths using similar triangles.

63. Examples involving overlapping triangles

• Objective: Calculate unknown sides in overlapping or adjacent similar triangles.

64. Triangle inequality theorem

• Objective: Understand and use the triangle inequality theorem.

65. Area of a trapezium

• Objective: Calculate the area of all types of different shaped trapeziums using a given formula.

66. Area of a rhombus

• Objective: Identify a rhombus, learn how to find the formula for the area of a rhombus, and use it in solving problems.

67. Area of a circle

• Objective: Calculate the area of a circle, and also calculate the radius and diameter of a circle.

68. Area of regular polygons and composite figures

• Objective: Calculate the area of a number of different shapes by applying the appropriate formula.

69. Surface area of a cube/rectangular prism

• Objective: Calculate the surface area of a number of different shapes by applying the appropriate formula.

70. Surface area of a triangular/trapezoidal prism

• Objective: Calculate the surface area of a number of triangular and trapezoidal shapes by applying the appropriate formula.

71. Surface area of a cylinder and sphere

• Objective: Calculate the surface area of different cylindrical and spherical shapes by applying the appropriate formula.

72. Surface area of pyramids

• Objective: Find the surface areas of pyramids.

73. Surface area of cones

• Objective: Find the surface areas of cones by finding the area of the base ‘πr²’ and the area of the curved surface ‘πrl’. Also be able to find the slant height ‘l’ given the perpendicular height.

74. Surface area of composite solids

• Objective: Find the surface areas of composite solids.

75. Volume of pyramids and cones

• Objective: Use formulae to find the volume of right pyramids and cones, and calculate the volume of a variety of pyramids and cones.

76. Composite solids

• Objective: Dissect composite solids into simpler shapes so that the volume can be calculated, calculate the volume of a variety of composite solids, and use formulae appropriately.

77. Distance formula

• Objective: Calculate the distance between any two points on the number plane and interpret the results.

78. Mid-point formula

• Objective: Understand the mid-point formula and use it practically.

79. Gradient

• Objective: Calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run.

80. Gradient formula

• Objective: Calculate the gradient of a line given any two points on the line and also be capable of checking whether three or more points lie on the same line and what an unknown point will make to parallel lines.

81. The straight line

• Objective: Draw a line which is parallel to either axis and comment on its gradient, where that gradient exists.

82. Lines through the origin

• Objective: Draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems.

83. General form of a line and the x and y intercepts

• Objective: Change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa.

84. Slope intercept form of a line

• Objective: Find the slope and intercept given the equation and given the slope and intercept, derive the equation.

85. Point slope form of a line

• Objective: Understand how to derive the equation of a straight line given the gradient and a point on the line.

86. Frequency distribution table

• Objective: Construct a frequency distribution table for raw data and interpret the table.

87. Cumulative frequency

• Objective: Construct cumulative frequency columns, histograms and polygons.

88. Calculating the median from a frequency distribution

• Objective: Determine the median from a cumulative frequency polygon.

89. Tree diagrams – not depending on previous outcomes

• Objective: Be confident in drawing tree diagrams to list outcomes of a multi-stage probability problem and then finding probabilities of certain events not depending on previous outcomes.

90. Tree diagrams – depending on previous outcomes

• Objective: Be confident in drawing tree diagrams to list outcomes of other multi-stage probability problems and then finding probabilities of certain events depending on previous outcomes.

91. Exam – Year 10

• Objective: Exam