# Grade 9 – 10 Mathematics – Singapore

### Grade 9 – 10 Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Study Plan | Study plan – Grade 9 – 10 | |

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

2 | Percentages | Changing percentages to fractions and decimals | |

Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals. | |||

3 | Percentages | One quantity as a percentage of another | |

Objective: On completion of the lesson the student will be able to find a percentage of an amount and how to express one quantity as a percentage of another. | |||

4 | Percentages | Calculating Percentages and Fractions of Quantities | |

Objective: To find percentages and fractions of quantities and solve problems with percentages | |||

5 | Time, 24-hour | 24 hour time | |

Objective: On completion of the lesson the student will be able to: tell the time accurately using twenty-four hour time, change the time from am and pm time to twenty-four hour time, and change the time from twenty-four hour time to am and pm time. | |||

6 | Uniform motion | Average speed | |

Objective: On completion of the lesson the student will be able to convert units for speed, distance and time. | |||

7 | Rules properties | Using Order of Operation procedures (BIDMAS) with Fractions | |

Objective: On completion of the lesson the student will know how to apply the order of operations rules to simplify expressions with integers and fractions. | |||

8 | Decimals | Rounding decimals | |

Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number. | |||

9 | Scientific notation | Scientific notation with larger numbers | |

Objective: On completion of the lesson the student will be able to change numbers greater than 1 to scientific notation. | |||

10 | Scientific notation | Scientific notation with small numbers | |

Objective: On completion of the lesson the student will be able to change numbers between zero and 1 to scientific notation. | |||

11 | Scientific notation | Changing scientific notation to numerals | |

Objective: On completion of the lesson the student will be able to change numbers written in scientific notation to basic numerals and be capable of solving problems on the calculator in scientific notation. | |||

12 | Significant figures | Significant figures | |

Objective: On completion of the lesson the student will be able to observe how many significant figures are in a number and how to express a number to a certain level of significant figures. | |||

13 | Capacity | Converting between volume and capacity using millilitres and litres | |

Objective: On completion of the lesson the student will be able to convert between units of capacity. | |||

14 | Capacity | Estimate, measure and compare the capacity of containers | |

Objective: On completion of the lesson the student will know why and when we might need to estimate and a way to go about it. | |||

15 | Area | Larger areas: square metre, hectare, square kilometre. | |

Objective: On completion of the lesson the student will be able to calculate larger areas using the correct square unit. | |||

16 | Data | Bar Charts | |

Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs. | |||

17 | Data | Line graphs. | |

Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs. | |||

18 | Data | Pie and bar graphs. | |

Objective: On completion of the lesson the student will be able to organise, read and summarise information in pie and bar graphs. | |||

19 | Surds | Introducing surds | |

Objective: On completion of the lesson the student will be able to identify and know the properties of surds as irrational numbers and be able to distinguish them from rational numbers. | |||

20 | Surds | Some rules for the operations with surds | |

Objective: On completion of the lesson the student will know how to use the rules for division and multiplication of surds. | |||

21 | Surds | Simplifying surds | |

Objective: On completion of the lesson the student will know how to use the rules for simplifying surds using division and multiplication. | |||

22 | Surds | Creating entire surds | |

Objective: On completion of the lesson the student will be able to write numbers as entire surds and compare numbers by writing as entire surds | |||

23 | Surds | Adding and subtracting like surds | |

Objective: On completion of the lesson the student will be able to add and subtract surds and simplify expressions by collecting like surds. | |||

24 | Quadratic equations | Solving simultaneous quadratic equations graphically | |

Objective: On completion of the lesson the student will better understand why quadratic equations have two solutions and will be capable of solving quadratic equations and problems graphically.. | |||

25 | Coordinate Geometry-the plane | Distance formula. | |

Objective: On completion of the lesson the student will be able to calculate the distance between any two points on the number plane and interpret the results. | |||

26 | Coordinate Geometry-midpoint, slope | Mid-point formula | |

Objective: On completion of the lesson the student will be able to understand the mid point formula and use it practically. | |||

27 | Coordinate Geometry-gradient | Gradient | |

Objective: On completion of the lesson the student will be able to calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run. | |||

28 | Coordinate Geometry-gradient | Gradient formula. | |

Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines. | |||

29 | Coordinate Geometry-straight line | The straight line. | |

Objective: On completion of the lesson the student will be able to draw a line which is parallel to either axis and comment on its gradient, where that gradient exists. | |||

30 | Coordinate Geometry-slope, etc. | Lines through the origin. | |

Objective: On completion of the lesson the student will be able to 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. | |||

31 | Coordinate Geometry-equation of line | General form of a line and the x and y Intercepts. | |

Objective: On completion of the lesson the student will be able to change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa. | |||

32 | Coordinate Geometry-intercept | Slope intercept form of a line. | |

Objective: On completion of the lesson the student will be able to find the slope and intercept given the equation and given the slope and intercept, derive the equation. | |||

33 | Coordinate Geometry-point slope | Point slope form of a line | |

Objective: On completion of the lesson the student will understand how to derive the equation of a straight line given the gradient and a point on the line. | |||

34 | Geometry-parabola | The parabola: to describe properties of a parabola from its equation | |

Objective: On completion of the lesson the student will be able to predict the general shape and important features of a parabola and then graph the parabola to check the predictions. | |||

35 | Functions and graphs | Quadratic polynomials of the form y = ax. + bx + c. | |

Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis. | |||

36 | Rect.hyperbola | The rectangular hyperbola. | |

Objective: On completion of the lesson the student will be able to analyse and graph a rectangular hyperbola and describe its important features. | |||

37 | Exponential function | The exponential function. | |

Objective: On completion of the lesson the student will be able to graph any equation in the form y equals a to the power x, where a is any positive real number apart from 1. | |||

38 | Conic sections | The parabola x. = 4ay | |

Objective: On completion of the lesson the student will identify the focus and directrix for a parabola given in standard form. | |||

39 | Geometry-locus | Constructions and loci – single condition | |

Objective: On completion of the lesson the student will understand the term locus and describe several using a single condition. | |||

40 | Geometry-locus | Constructions and loci – multiple conditions | |

Objective: On completion of the lesson the student will describe a locus that satisfies multiple conditions on a number plane. | |||

41 | Algebraic equations | Solving two step equations | |

Objective: On completion of the lesson the student will be able to solve two step equations. | |||

42 | Algebraic equations | Solving equations containing binomial expressions | |

Objective: On completion of the lesson the student will be able to move terms in binomial equations. | |||

43 | Algebraic equations | Equations involving grouping symbols. | |

Objective: On completion of the lesson the student will be able to solve equations using grouping symbols | |||

44 | Algebraic equations | Equations involving fractions. | |

Objective: On completion of the lesson the student will know how to solve equations using fractions. | |||

45 | Algebra- formulae | Equations resulting from substitution into formulae. | |

Objective: On completion of the lesson the student will be able to substitute into formulae and then solve the resulting equations. | |||

46 | Algebra- formulae | Changing the subject of the formula. | |

Objective: On completion of the lesson the student will be able to move pronumerals around an equation using all the rules and operations covered previously. | |||

47 | Algebra-factorising | Simplifying easy algebraic fractions. | |

Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising. | |||

48 | Algebraic fractions | Simplifying algebraic fractions using the index laws. | |

Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies. | |||

49 | Algebra-negative indices | Algebraic fractions resulting in negative indices. | |

Objective: On completion of the lesson the student will be able to understand how to simplify an algebraic fractional expression with a negative index, and also how to write such an expression without a negative index. | |||

50 | Factorisation | Factorisation of algebraic fractions including binomials. | |

Objective: On completion of the lesson the student should be able to simplify more complex algebraic fractions using a variety of methods. | |||

51 | Absolute value or modulus | Solving for the variable | |

Objective: On completion of the lesson the student will be able to solve equations involving a single absolute value. | |||

52 | Absolute value or modulus | Solving and graphing inequalities | |

Objective: On completion of the lesson the student will be able to solve inequalities involving one absolute value. | |||

53 | Graphing binomials | Binomial products. | |

Objective: On completion of the lesson the student will understand the term binomial product and be capable of expanding and simplifying an expression. | |||

54 | Graphing binomials | Binomial products with negative multiplier | |

Objective: On completion of the lesson the student will understand specific terms and be prepared to expand and simplify different monic binomial products. | |||

55 | Graphing binomials | Binomial products [non-monic]. | |

Objective: On completion of the lesson, the student will have examined more complex examples with binomial products. | |||

56 | Squaring binomial | Squaring a binomial. [monic] | |

Objective: On completion of the lesson the student should understand the simple one-step process of squaring a monic binomial. | |||

57 | Squaring binomial | Squaring a binomial [non-monic]. | |

Objective: On completion of the lesson the student will apply the same rule that is used with monic binomials. | |||

58 | Factorising | Expansions leading to the difference of two squares | |

Objective: On completion of the lesson the student will understand expansions leading to differences of 2 squares. | |||

59 | Algebraic expressions-products | Products in simplification of algebraic expressions | |

Objective: On completion of the lesson the student will understand simplification of algebraic expressions in step-by-step processing. | |||

60 | Algebraic expressions-larger expansions | Algebraic Expressions – Larger expansions. | |

Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions. | |||

61 | Algebra-highest common factor | Highest common factor. | |

Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression. | |||

62 | Factors by grouping | Factors by grouping. | |

Objective: On completion of the lesson the student will be able to complete the process given just two factors for the whole expression. | |||

63 | Difference of 2 squares | Difference of two squares | |

Objective: On completion of the lesson the student understand the difference of two squares and be capable of recognising the factors. | |||

64 | Common fact and diff | Common factor and the difference of two squares | |

Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares. | |||

65 | Quadratic trinomials | Quadratic trinomials [monic] – Case 1. | |

Objective: On completion of the lesson the student will understand the factorisation of quadratic trinomial equations with all terms positive. | |||

66 | Factorising quads | Factorising quadratic trinomials [monic] – Case 2. | |

Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative. | |||

67 | Factorising quads | Factorising quadratic trinomials [monic] – Case 3. | |

Objective: On completion of the lesson the student will have an increased knowledge on factorising quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative. | |||

68 | Factorising quads | Factorising quadratic trinomials [monic] – Case 4. | |

Objective: On completion of the lesson the student will understand how to factorise all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative. | |||

69 | Quadratic equations | Introduction to quadratic equations. | |

Objective: On completion of the lesson the student will understand simple quadratic equations. | |||

70 | Quadratic equations | Quadratic equations with factorisation. | |

Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising. | |||

71 | Quadratic equations | Solving quadratic equations. | |

Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations. | |||

72 | Quadratic equations | Completing the square | |

Objective: On completion of the lesson the student will understand the process of completing the square. | |||

73 | Quadratic equations | Solving quadratic equations by completing the square | |

Objective: On completion of the lesson the student will understand the reasoning behind completing the square. | |||

74 | Quadratic equations | The quadratic formula | |

Objective: On completion of the lesson the student will be familiar with the quadratic formula. | |||

75 | Quadratic equations | Problem solving with quadratic equations | |

Objective: On completion of the lesson the student will be able to express a problem as a quadratic equation and then solve it. | |||

76 | Rules for indices/exponents | Adding indices when multiplying terms with the same base | |

Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base. | |||

77 | Rules for indices/exponents | Subtracting indices when dividing terms with the same base | |

Objective: On completion of the lesson the student will know how to use the index law of subtraction of powers when dividing terms with the same base. | |||

78 | Rules for indices/exponents | Terms raised to the power of zero | |

Objective: On completion of the lesson the student will learn how to evaluate or simplify terms that are raised to the power of zero. | |||

79 | Rules for indices/exponents | Negative Indices | |

Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing negative indices. | |||

80 | Fractional indices/exponents | Fractional indices | |

Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices. | |||

81 | Fractional indices/exponents | Complex fractions as indices | |

Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing complex fractional indices. | |||

82 | Simultaneous equns | Simultaneous equations | |

Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the substitution method. | |||

83 | Simultaneous equns | Elimination method | |

Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the elimination method. | |||

84 | Simultaneous equns | Elimination method part 2 | |

Objective: On completion of the lesson the student will be able to solve all types of simultaneous equations with 2 unknown variables by the elimination method. | |||

85 | Simultaneous equns | Applications of simultaneous equations | |

Objective: On completion of this lesson the student will be able to derive simultaneous equations from a given problem and then solve those simultaneous equations. | |||

86 | 2-D shapes | Using the prefix to determine polygons | |

Objective: On completion of the lesson the student will be able to recognise and name two-dimensional shapes such as pentagons and hexagons, using the prefix of the shapes name to determine number of angles and sides. | |||

87 | 2-D shapes | Spatial properties of quadrilaterals | |

Objective: On completion of the lesson the student will know how to analyse and explain the spatial properties of quadrilaterals. | |||

88 | Geometry-angles | Adjacent angles | |

Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems. | |||

89 | Geometry-angles | Vertically opposite angles | |

Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems. | |||

90 | Geometry-angles | Angles at a Point. | |

Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems. | |||

91 | Geometry-angles | Parallel Lines. | |

Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles. | |||

92 | Geometry-problems | Additional questions involving parallel lines | |

Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them. | |||

93 | Geometry-triangles | Angle sum of a triangle | |

Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems. | |||

94 | Geometry-triangles | Exterior angle theorem | |

Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions. | |||

95 | Special triangles | Special triangles | |

Objective: On completion of the lesson the student will able to identify an equilateral and an isosceles triangle and solve geometry questions involving these triangles. | |||

96 | Geometry-quadrilaterals | Quadrilaterals | |

Objective: On completion of the lesson the student will able to find missing angles by using the fact that a quadrilateral’s angle sum is 360 degrees. | |||

97 | Geometry-constructions | Geometric constructions | |

Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses. | |||

98 | Geometry – angles | To determine angle labelling rules, naming angles according to size, angle bisector properties and related algebra | |

Objective: On completion of the lesson the student will label angles, use a protractor and perform calculations using algebra involving angles. | |||

99 | Geometry-constructions | Angle bisector construction and its properties (Stage 2) | |

Objective: On completion of the lesson the student will be able to bisect an angle using a pair of compasses and a straight edge. | |||

100 | Geometry-quadrilaterals | Classifying Quadrilaterals | |

Objective: On completion of this lesson the student will understand the properties that classify quadrilaterals. | |||

101 | Geometry-quadrilaterals | Using the Properties of a Parallelogram | |

Objective: On completion of this lesson the student will be able to use and prove the properties of a parallelogram. | |||

102 | Geometry-quadrilaterals | Proving a Shape is a Parallelogram | |

Objective: On completion of this lesson the student will be able to use properties to prove a given quadrilateral is a parallelogram. | |||

103 | Geometry-quadrilaterals | Properties of the Rectangle, Square and Rhombus | |

Objective: On completion of this lesson students will be able to use the properties of the rectangle, square and rhombus for formal proofs and to find values. | |||

104 | Geometry-polygons | Angles of regular polygons | |

Objective: On completion of the lesson the student will be able to identify and use the angle sum of a polygon formula, and understand that the external angles of a polygon add up to 360 degrees. | |||

105 | Geometry-congruence | Congruent triangles, Test 1 and 2 | |

Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are congruent. | |||

106 | Geometry-congruence | Congruent triangles, Test 3 and 4 | |

Objective: On completion of the lesson the student will be able to identify other tests to use to show two triangles are congruent. | |||

107 | Geometry-congruence | Proofs and congruent triangles. | |

Objective: On completion of the lesson the student will be able to set out a formal proof to show that two triangles are congruent. | |||

108 | Similar triangles | Similar triangles | |

Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are similar. | |||

109 | Similar triangles | Using similar triangles to calculate lengths | |

Objective: On completion of the lesson the student will be able to calculate lengths using similar triangles. | |||

110 | Overlapping triangles | Examples involving overlapping triangles | |

Objective: On completion of the lesson the student will be able to calculate unknown sides in overlapping or adjacent similar triangles. | |||

111 | Circle Geometry | Theorem – Equal chords in equal circles are equidistant from the centres. Theorem – Chords in a circle which are equidistant from the centre are equal. | |

Objective: On completion of the lesson the student will be able to prove that equal chords in equal circles are equidistant from the centre. | |||

112 | Circle Geometry | Theorem – The perpendicular from the centre of a circle to a chord bisects the chord. Theorem – The line from the centre of a circle to the mid-point of the chord is perpendicular to the chord. | |

Objective: On completion of the lesson the student will be able to prove that ‘The perpendicular from the centre of a circle to a chord bisects the chord.’ and its converse theorem ‘The line from the centre of a circle to the mid-point of the chord is perpendicular’ | |||

113 | Circle Geometry | Theorem – Tangents to a circle from an external point are equal. | |

Objective: On completion of the lesson the student will be able to prove that tangents to a circle from an external point are equal. | |||

114 | Circle Geometry | Theorem – The angle at the centre of a circle is double the angle at the circumference standing on the same arc. | |

Objective: On completion of the lesson the student will be able to prove that the angle at the centre of a circle is double the angle at the circumference standing on the same arc. | |||

115 | Circle Geometry | Theorem – Angles in the same segment of a circle are equal. | |

Objective: On completion of the lesson the student will be able to prove that the angles in the same segment are equal. | |||

116 | Circle Geometry | Theorem – The opposite angles of a cyclic quadrilateral are supplementary. | |

Objective: On completion of the lesson the student will be able to prove that the opposite angles of a cyclic quadrilateral are supplementary. | |||

117 | Circle Geometry | Theorem – The angle of a semi-circle is a right angle. | |

Objective: On completion of the lesson the student will be able to prove that ‘The angle of a semi-circle is a right-angle.’ | |||

118 | Circle Geometry | Theorem – The tangent to a circle is perpendicular to the radius drawn to it at the point of contact. | |

Objective: On completion of the lesson the student will be able to prove that the tangent and the radius of a circle are perpendicular at the point of contact. | |||

119 | Trigonometry-compass | Bearings – the compass. | |

Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north. | |||

120 | Pythagoras | Find the hypotenuse | |

Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse. | |||

121 | Pythagoras | Pythagorean triples | |

Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple. | |||

122 | Pythagoras | Find the hypotenuse Part 2 | |

Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse using decimals and surds. | |||

123 | Pythagoras | Calculating a leg of a right-angled triangle | |

Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle. | |||

124 | Area | Introducing the rules for finding the area of a rectangle and a parallelogram. | |

Objective: On completion of the lesson the student will be able to investigate areas of rectangles and parallelograms using a given formula of multiplying measurements of sides. | |||

125 | Area | Finding the area of a triangle and other composite shapes. | |

Objective: On completion of the lesson the student will be able calculate areas of triangles and shapes based on triangles, rectangles and parallelograms using given formulas. | |||

126 | Area | Area of a trapezium. | |

Objective: On completion of the lesson the student will be able calculate the area of all types of different shaped trapeziums using a given formula. | |||

127 | Area | Area of a circle. | |

Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle. | |||

128 | Volume | Finding the volume of prisms | |

Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume. | |||

129 | Volume | Volume of a cylinder and sphere. | |

Objective: On completion of the lesson the student will be able to: calculate the volume of cylinders, spheres and hemispheres using the appropriate formulae, and use the relationship between litres and other measures of volume. | |||

130 | Volume | Volume of pyramids and cones. | |

Objective: On completion of the lesson the student will be able to: use formulae to find the volume of right pyramids and cones, and calculate the volume of a variety of pyramids and cones. | |||

131 | Volume | Composite solids. | |

Objective: On completion of the lesson the student will be able to: 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. | |||

132 | Surface area | Surface area of a cube/rectangular prism. | |

Objective: On completion of the lesson the student will be able calculate the surface area of a number of different shapes by applying the appropriate formula. | |||

133 | Surface area | Surface area of a triangular/trapezoidal prism. | |

Objective: On completion of the lesson the student will be able calculate the surface area of a number of triangular and trapezoidal shapes by applying the appropriate formula. | |||

134 | Surface area | Surface area of a cylinder and sphere. | |

Objective: On completion of the lesson the student will be able calculate the surface area of different cylindrical and spherical shapes by applying the appropriate formula. | |||

135 | Surface area | Surface area of pyramids | |

Objective: On completion of the lesson the student will be able to find the surface areas of pyramids. | |||

136 | Surface area | Surface area of cones | |

Objective: On completion of the lesson the student will be able to find the surface areas of cones by finding the area or the base ‘p r . ‘and the area of the curved surface ‘ p r l’. The student will also be able to find the slant height ‘l’ given the perpendicul | |||

137 | Trigonometry-ratios | Trigonometric ratios. | |

Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op | |||

138 | Trigonometry-ratios | Using the calculator. | |

Objective: On completion of the lesson the student will be able to use the calculator to find values for the sine, cosine and tangent ratios of acute angles. | |||

139 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 1 Sine]. | |

Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances. | |||

140 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 2 Cosine]. | |

Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle. | |||

141 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio]. | |

Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle. | |||

142 | Trigonometry-ratios | Unknown in the denominator. [Case 4]. | |

Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown. | |||

143 | Trigonometry-elevation | Angles of elevation and depression. | |

Objective: On completion of the lesson the student will be able to identify angles of depression and angles of elevation, and the relationship between them. | |||

144 | Trigonometry-practical | Trigonometric ratios in practical situations. | |

Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation. | |||

145 | Trigonometry-ratios | Using the calculator to find an angle given a trigonometric ratio. | |

Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio. | |||

146 | Trigonometry- ratios | Using the trigonometric ratios to find an angle in a right-angled triangle. | |

Objective: On completion of the lesson the student will be able to find the value of an unknown angle in a right angle triangle given the lengths of 2 of the sides. | |||

147 | Trigonometry-exact ratios | Trigonometric ratios of 30., 45. and 60. – exact ratios. | |

Objective: On completion of the lesson the student will be able to find the exact sine, cosine and tangent ratios for the angles 30., 45.and 60. | |||

148 | Trigonometry-cosine rule | The cosine rule to find an unknown side. [Case 1 SAS]. | |

Objective: On completion of the lesson the student will be able to use the cosine rule to find the length of an unknown side of a triangle knowing 2 sides and the included angle. | |||

149 | Trigonometry-cosine rule | The cosine rule to find an unknown angle. [Case 2 SSS]. | |

Objective: On completion of the lesson the student will be able to find the size of an unknown angle of a triangle using the cosine rule given the lengths of the 3 sides. | |||

150 | Trigonometry-sine rule | The sine rule to find an unknown side. Case 1. | |

Objective: On completion of the lesson the student will be able to use the Sine rule to find the length of a particular side when the student is given the sizes of 2 of the angles and one of the sides. | |||

151 | Trigonometry-sine rule | The sine rule to find an unknown angle. Case 2. | |

Objective: On completion of the lesson the student will be able to use the sine rule to find an unknown angle when given 2 sides and a non-included angle. | |||

152 | Trigonometry-areas | The area formula | |

Objective: On completion of the lesson the student will be able to use the sine formula for finding the area of a triangle given 2 sides and the included angle. | |||

153 | Statistics | Frequency distribution table | |

Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table. | |||

154 | Statistics | Frequency histograms and polygons | |

Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons. | |||

155 | Statistic-probability | The mode | |

Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon. | |||

156 | Statistic-probability | The mean | |

Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column. | |||

157 | Statistic-probability | The median | |

Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores | |||

158 | Statistic-probability | Cumulative frequency | |

Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons. | |||

159 | Statistic-probability | Calculating the median from a frequency distribution | |

Objective: On completion of the lesson the student will be able to determine the median from a cumulative frequency polygon. | |||

160 | Statistics – grouped data | Calculating mean, mode and median from grouped data | |

Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values. | |||

161 | Statistics using a calculator | Statistics and the student calculator | |

Objective: On completion of the lesson the student will be capable of using a scientific calculator in statistics mode to calculate answers to statistical problems. | |||

162 | Statistics – Interquartile range | Measures of spread: the interquartile range | |

Objective: On completion of the lesson the student will be able to find the upper and lower quartiles and the interquartile range | |||

163 | Statistic-probability | Probability of Simple Events | |

Objective: On completion of the lesson the student will be able to understand the probability of simple events. | |||

164 | Statistic-probability | Rolling a pair of dice | |

Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously. | |||

165 | Statistic-probability | Tree diagrams – not depending on previous outcomes | |

Objective: On completion of the lesson the student will 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. | |||

166 | Statistic-probability | Tree diagrams – depending on previous outcomes | |

Objective: On completion of the lesson the student will 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. | |||

167 | Translations | Transformations – reflections | |

Objective: On completion of the lesson the student will be able to take a pre-image and using the appropriate techniques, accurately show its image after reflection. | |||

168 | Geometric transformations | Geometry transformations without matrices: reflection (Stage 2) | |

Objective: On completion of this lesson the student will use and understand the language used in geometric transformations and perform reflections in a number plane. | |||

169 | Geometric transformations | Geometry transformations without matrices: translation (Stage 2) | |

Objective: On completion of this lesson the student will perform translations in a number plane. | |||

170 | Geometric transformations | Geometry transformations without matrices: rotation (Stage 2) | |

Objective: On completion of this lesson the student will perform and construct rotations. | |||

171 | Geometric transformations | Geometry transformations without matrices: dilation or enlargement (Stage 2) | |

Objective: On completion of this lesson the student will perform the non-congruent transformation of dilation or emlargement and calculate scale factor. | |||

172 | Vectors | Vectors | |

Objective: On completion of the lesson the student will be able to represent a vector in matrix and diagrammatic form, as well as add two vectors using matrices and/or a diagram. | |||

173 | Vectors | 2 vector addition in 2 and 3D (stage 2) | |

Objective: On completion of the lesson the student will understand and use component forms for vector resolution. | |||

174 | Sequences and Series | General sequences. | |

Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula. | |||

175 | Exam | Exam – Grade 9 – 10 | |

Objective: Exam |