You have selected TAS Maths Applied 5 Grade 12

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1 Study Plan Study plan - Grade 12 - Mathematics Applied 5 Info Go

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

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2 Surface area Surface area of a triangular/trapezoidal prism. Info Go

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.

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3 Surface area Surface area of a cylinder and sphere. Info Go

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.

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4 Surface area Surface area of pyramids Info Go

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

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5 Surface area Surface area of cones Info Go

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

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6 Algebraic expressions Simplifying Algebraic expressions: combining addition and subtraction. Info Go

Objective: On completion of the lesson the student will understand how to approach algebraic expressions questions and avoid the most common mistakes.

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7 Algebraic expressions Expanding algebraic expressions: multiplication Info Go

Objective: On completion of the lesson the student will be able mentally to multiply and remove parentheses from simple algebraic expressions in one step.

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8 Algebraic expressions Expanding algebraic expressions: negative multiplier Info Go

Objective: On completion of the lesson the student will be able to expand expressions using a negative multiplier.

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9 Algebraic expressions Expanding and simplifying algebraic expressions Info Go

Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions.

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10 Algebraic equations Solving equations containing binomial expressions Info Go

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

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11 Algebraic equations Equations involving grouping symbols. Info Go

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

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12 Algebraic equations Equations involving fractions. Info Go

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

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13 Algebra- formulae Equations resulting from substitution into formulae. Info Go

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

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14 Algebra- formulae Changing the subject of the formula. Info Go

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.

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15 Algebra-inequalities Solving Inequalities. Info Go

Objective: On completion of the lesson the student will understand the 'greater than' and 'less than' signs, and be able to perform simple inequalities.

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16 Algebra-factorising Simplifying easy algebraic fractions. Info Go

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

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17 Algebraic fractions Simplifying algebraic fractions using the index laws. Info Go

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

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18 Algebra-negative indices Algebraic fractions resulting in negative indices. Info Go

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.

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19 Factorisation Factorisation of algebraic fractions including binomials. Info Go

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

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20 Algebraic fractions-binomial Cancelling binomial factors in algebraic fractions. Info Go

Objective: On completion of the lesson the student should be able to factorise binomials to simplify fractions.

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21 Absolute value or modulus Simplifying absolute values Info Go

Objective: On completion of the lesson the student will be able to simplify expressions involving absolute values or the modulus of real numbers.

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22 Absolute value or modulus Solving for the variable Info Go

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

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23 Absolute value or modulus Solving and graphing inequalities Info Go

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

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24 Rules for indices/exponents Adding indices when multiplying terms with the same base Info Go

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.

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25 Rules for indices/exponents Subtracting indices when dividing terms with the same base Info Go

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.

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26 Rules for indices/exponents Multiplying indices when raising a power to a power Info Go

Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power.

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27 Rules for indices/exponents Multiplying indices when raising to more than one term Info Go

Objective: On completion of the lesson the student will be able to use the law of multiplication of indices when raising more than one term to the same power.

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28 Rules for indices/exponents Terms raised to the power of zero Info Go

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

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29 Rules for indices/exponents Negative Indices Info Go

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

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30 Fractional indices/exponents Fractional indices Info Go

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

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31 Fractional indices/exponents Complex fractions as indices Info Go

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

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32 Significant figures Significant figures Info Go

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.

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33 Number theory - sets Number sets and their members Info Go

Objective: On completion of the lesson the student will understand the notation used with sets and the subsets of the real number system.

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34 Number theory - operations Properties of real numbers using addition and multiplication Info Go

Objective: On completion of the lesson the student will know and use the closure, identity, commutative, associative, identity and distributive properties for addition and multiplication.

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35 Number theory - equations Transformations that produce equivalent equations Info Go

Objective: On completion of the lesson the student will know and use the correct terms to describe the processes in solving equations.

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36 Geometry-angles Measuring angles Info Go

Objective: On completion of the lesson the student will be able to measure any angle between 0 and 360 degrees using a protractor, and identify what type of angle it is.

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37 Geometry-angles Adjacent angles Info Go

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.

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38 Geometry-angles Complementary and supplementary angles Info Go

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

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39 Geometry-angles Vertically opposite angles Info Go

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.

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40 Geometry-angles Angles at a Point. Info Go

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.

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41 Geometry-angles Parallel Lines. Info Go

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

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42 Geometry-problems Additional questions involving parallel lines Info Go

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

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43 Geometry-triangles Angle sum of a triangle Info Go

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.

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44 Geometry-triangles Exterior angle theorem Info Go

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.

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45 Special triangles Special triangles Info Go

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.

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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.

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47 Geometry-constructions Geometric constructions Info Go

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

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48 Geometry To identify collinear points, coplanar lines and points in 2 and 3 dimensions Info Go

Objective: On completion of the lesson the student will use correct terms to describe points, lines, intervals and rays.

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49 Geometry - angles To determine angle labelling rules, naming angles according to size, angle bisector properties and related algebra Info Go

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

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50 Geometry-constructions Angle bisector construction and its properties (Stage 2) Info Go

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

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51 Geometry-constructions Circumcentre and incentre (Stage 2) Info Go

Objective: On completion of the lesson the student will be able geometrically construct the circumcentre and incentre for a triangle and to use Pythagoras' Theorem to calculate values.

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52 Geometry-constructions Orthocentre and centroids (Stage 2) Info Go

Objective: On completion of the lesson the student will be able geometrically construct the orthocentre and centroid for a triangle and to use algebra to calculate values.

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53 Geometry-quadrilaterals Midsegments of Triangles Info Go

Objective: On completion of the lesson the student will be able to use coordinate geometry to apply the midsegment properties of a triangle.

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

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55 Geometry-quadrilaterals Using the Properties of a Parallelogram Info Go

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

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56 Geometry-quadrilaterals Proving a Shape is a Parallelogram Info Go

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

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57 Geometry-quadrilaterals Properties of the Rectangle, Square and Rhombus Info Go

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.

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58 Geometry-quadrilaterals Properties of the Trapezium and Kite Info Go

Objective: On completion of this lesson students will be able to use the properties of the trapezium and kite for formal proofs and to find values.

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59 Geometry-quadrilaterals The quadrilateral family and coordinate methods in geometry Info Go

Objective: On completion of this lesson the student will know the relationships between quadrilaterals and use coordinate methods to prove some of the properties.

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60 Geometry-locus Constructions and loci - single condition Info Go

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

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61 Geometry-locus Constructions and loci - multiple conditions Info Go

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

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62 Geometry problems More difficult exercises involving parallel lines Info Go

Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out log

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63 Geometry-reasoning Further difficult exercises involving formal reasoning Info Go

Objective: On completion of the lesson the student will be able to identify which geometric properties are needed to complete a question and be able to use formal reasoning to write out this information.

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64 Geometry-polygons Angles of regular polygons Info Go

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.

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65 Geometry-congruence Congruent triangles, Test 1 and 2 Info Go

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

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66 Geometry-congruence Congruent triangles, Test 3 and 4 Info Go

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

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67 Geometry-congruence Proofs and congruent triangles. Info Go

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

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68 Overlapping triangles Examples involving overlapping triangles Info Go

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

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69 Geometry - triangles Triangle inequality theorem Info Go

Objective: On completion of the lesson the student will understand and use the triangle inequality theorem.

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70 Surds Introducing surds Info Go

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.

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71 Surds Some rules for the operations with surds Info Go

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

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72 Surds Simplifying surds Info Go

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

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73 Surds Creating entire surds Info Go

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

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74 Surds Adding and subtracting like surds Info Go

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

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75 Surds Expanding surds Info Go

Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds.

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76 Surds Binomial expansions Info Go

Objective: On completion of the lesson the student will be able to expand and simplify the squares of binomial sums and differences involving surds.

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77 Surds Conjugate binomials with surds Info Go

Objective: On completion of the lesson the student will be able to expand and simplify conjugate binomial expressions involving surds.

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78 Surds Rationalising the denominator Info Go

Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves surds.

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79 Surds Rationalising binomial denominators Info Go

Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves binomial expressions.

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80 Simultaneous equns Simultaneous equations Info Go

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

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81 Simultaneous equns Elimination method Info Go

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

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82 Simultaneous equns Elimination method part 2 Info Go

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.

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83 Simultaneous equns Applications of simultaneous equations Info Go

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.

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84 Pythagoras Proofs of Pythagoras theorem Info Go

Objective: On completion of this lesson the student will have geometric proofs for Pythagoras' Theorem

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85 Coordinate Geometry-equation of line General form of a line and the x and y Intercepts. Info Go

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.

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86 Coordinate Geometry-intercept Slope intercept form of a line. Info Go

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.

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87 Geometry-circles The circle: to find radii of circles Info Go

Objective: On completion of the lesson the student will be able to describe a circle mathematically given its equation or its graph. Additionally, the student will be able to work out the equation of a circle given its centre and radius.

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88 Geometry-circles The semicircle: to select the equation given the semi circle and vice versa Info Go

Objective: On completion of the lesson the student will be able to sketch a semicircle given its equation and derive the equation of a given semicircle.

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89 Geometry-parabola The parabola: to describe properties of a parabola from its equation Info Go

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.

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90 Functions and graphs Quadratic polynomials of the form y = ax. + bx + c. Info Go

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.

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91 Functions and graphs Graphing perfect squares: y=(a-x) squared Info Go

Objective: On completion of the lesson the student will be able to analyse a curve and then check their work by graphing the curve.

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92 Graphing roots Graphing irrational roots Info Go

Objective: On completion of the lesson the student will be able to solve any polynomial which has real roots, whether they are rational or irrational.

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93 Coordinate geometry Solve by graphing Info Go

Objective: On completion of the lesson students will use the slope intercept form of a line to create graphs and find points of intersection.

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94 Uniform motion Average speed Info Go

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

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95 Uniform motion Using subscripted variables Info Go

Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, distance and time.

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96 Uniform motion Uniform motion with equal distances Info Go

Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, equal distances and time.

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97 Uniform motion Uniform motion adding the distances Info Go

Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, adding distances for total distance and time.

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98 Uniform motion Uniform motion with unequal distances Info Go

Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, unequal distances and time.

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99 Uniform motion Uniform motion of all types Info Go

Objective: On completion of the lesson the student will use all types of subscripted variables for calculations to determine speed, distance and time.

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100 Motion under acceleration Motion under gravity - objects in vertical motion Info Go

Objective: On completion of the lesson the student will convert rates and use equations of motion that include uniform acceleration.

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101 Motion under acceleration Introducing initial velocity Info Go

Objective: On completion of the lesson the student will use equations of motion that include uniform acceleration and an initial velocity.

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102 Graphing binomials Binomial products. Info Go

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

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103 Graphing binomials Binomial products with negative multiplier Info Go

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

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104 Graphing binomials Binomial products [non-monic]. Info Go

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

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105 Squaring binomial Squaring a binomial. [monic] Info Go

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

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106 Squaring binomial Squaring a binomial [non-monic]. Info Go

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

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107 Factorising Expansions leading to the difference of two squares Info Go

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

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108 Algebraic expressions-products Products in simplification of algebraic expressions Info Go

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

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109 Algebraic expressions-larger expansions Algebraic Expressions - Larger expansions. Info Go

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

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110 Algebra-highest common factor Highest common factor. Info Go

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.

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111 Factors by grouping Factors by grouping. Info Go

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

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112 Difference of 2 squares Difference of two squares Info Go

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

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113 Common fact and diff Common factor and the difference of two squares Info Go

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

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

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115 Factorising quads Factorising quadratic trinomials [monic] - Case 2. Info Go

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

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116 Factorising quads Factorising quadratic trinomials [monic] - Case 3. Info Go

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.

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117 Factorising quads Factorising quadratic trinomials [monic] - Case 4. Info Go

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.

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Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial.

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119 Factorising quads Factorisation of non-monic quadratic trinomials - moon method Info Go

Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method.

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120 Sum/diff 2 cubes Sum and difference of two cubes. Info Go

Objective: On completion of the lesson the student will be cognisant of the sum and difference of 2 cubes and be capable of factorising them.

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121 Algebraic fractions Simplifying algebraic fractions. Info Go

Objective: On completion of the lesson the student should be familiar with all of the factorisation methods presented to this point.

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122 Trigonometry-compass Bearings - the compass. Info Go

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.

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123 Trigonometry-elevation Angles of elevation and depression. Info Go

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.

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124 Trigonometry-practical Trigonometric ratios in practical situations. Info Go

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.

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125 Trigonometry-ratios Using the calculator to find an angle given a trigonometric ratio. Info Go

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.

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126 Trigonometry- ratios Using the trigonometric ratios to find an angle in a right-angled triangle. Info Go

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.

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127 Trigonometry-exact ratios Trigonometric ratios of 30., 45. and 60. - exact ratios. Info Go

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.

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128 Trigonometry-cosine rule The cosine rule to find an unknown side. [Case 1 SAS]. Info Go

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.

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129 Trigonometry-cosine rule The cosine rule to find an unknown angle. [Case 2 SSS]. Info Go

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.

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130 Trigonometry-sine rule The sine rule to find an unknown side. Case 1. Info Go

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.

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131 Trigonometry-sine rule The sine rule to find an unknown angle. Case 2. Info Go

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.

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132 Trigonometry-areas The area formula Info Go

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.

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

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

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

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136 Quadratic equations Completing the square Info Go

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

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137 Quadratic equations Solving quadratic equations by completing the square Info Go

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

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

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

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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..

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141 Coordinate Geometry-the plane Distance formula. Info Go

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.

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142 Coordinate Geometry-midpoint, slope Mid-point formula Info Go

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

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143 Coordinate Geometry-point slope Point slope form of a line Info Go

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.

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144 Statistic-probability Cumulative frequency Info Go

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

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145 Statistic-probability Calculating the median from a frequency distribution Info Go

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

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146 Statistic-probability Rolling a pair of dice Info Go

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

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147 Statistic-probability Experimental probability Info Go

Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial.

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148 Statistic-probability Tree diagrams - not depending on previous outcomes Info Go

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.

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149 Statistic-probability Tree diagrams - depending on previous outcomes Info Go

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.

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150 Statistic-probability The complementary result .. Info Go

Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results where the complementary event is involved.

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151 Statistic-probability P[A or B] When A and B are NOT mutually exclusive Info Go

Objective: On completion of this lesson the student will be able to distinguish between mutually exclusive and non mutually exclusive events and be able to find the probabilities of both.

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152 Statistic-probability Binomial Theorem. Info Go

Objective: On completion of this lesson the student will use Pascal's triangle and the binomial theorem to write the expansion of binomial expressions raised to integer powers.

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153 Statistic-probability Binomial probabilities using the Binomial Theorem Info Go

Objective: On completion of the lesson the student will be able to solve certain types of probability questions using the binomial theorem

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154 Simultaneous equations Number of solutions (Stage 2) Info Go

Objective: On completion of the lesson of the lesson the student will identify simultaneous equations that are consistent, inconsistent or the same.

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155 Vectors Vectors Info Go

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.

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156 Linear systems Optimal solutions (Stage 2) Info Go

Objective: On completion of the lesson the student will understand the process of linear programming to find optimal solutions.

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157 Linear systems Linear systems with matrices (Stage 2) Info Go

Objective: On completion of the lesson the student will process matrices formed from linear systems of equations.

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158 Linear systems Row-echelon form (Stage 2) Info Go

Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the row-echelon form.

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159 Linear systems Gauss Jordan elimination method (Stage 2) Info Go

Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the Gauss Jordan elimination method.

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160 Graphing-polynomials Graphing complex polynomials: quadratics with no real roots Info Go

Objective: On completion of the lesson the student will be able to determine whether a quadratic has real or complex roots and then graph it.

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161 Graphing-cubic curves Graphing cubic curves Info Go

Objective: On completion of this lesson the student will be able to graph a cubic given its equation or derive the equation of a cubic given its graph or other relevant information.

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162 Absolute value equations Absolute value equations Info Go

Objective: On completion of this lesson the student will be able to relate to graphs involving the absolute value function. The student will be capable of graphing the function given its equation and be able to solve for the intersection of an absolute value functio

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163 Rect.hyperbola The rectangular hyperbola. Info Go

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

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164 Exponential function The exponential function. Info Go

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.

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165 Log functions Logarithmic functions. Info Go

Objective: On completion of this lesson the student will be able to define basic logarithmic functions and describe the relationship between logarithms and exponents including graph logarithmic functions. The student will understand the relationship between logarit

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166 Conic sections Introduction to conic sections and their general equation Info Go

Objective: On completion of the lesson the student will identify the conic section from the coefficients of the equation.

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167 Conic sections The parabola x. = 4ay Info Go

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

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168 Graphing-polynomials General equation of a circle: determine and graph the equation Info Go

Objective: On completion of the lesson the student will be able to solve these types of problems. Working with circles will also help the student in the topic of circle geometry, which tests the student's skills in logic and reasoning.

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169 Conic sections Ellipses Info Go

Objective: On completion of the lesson the student will identify focus, vertices and axes of an ellipse.

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170 Conic sections Hyperbola Info Go

Objective: On completion of the lesson the student will identify focus, vertices, axes and asymptotes of a hyperbola.

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171 Functions Definition, domain and range Info Go

Objective: On completion of this lesson the student will be able to select functions from relations by referring to the domain and range.

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172 Functions Notation and evaluations Info Go

Objective: On completion of the lesson the student will be understand different notations for functions.

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173 Functions More on domain and range Info Go

Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation.

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174 Functions Domain and range from graphical representations Info Go

Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation from graphical representations.

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175 Functions Evaluating and graphing piecewise functions Info Go

Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions.

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176 Functions Functions combinations Info Go

Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains.

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177 Functions Composition of functions Info Go

Objective: On completion of the lesson the student will understand composition of functions or a function of a function.

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178 Statistics - grouped data Calculating mean, mode and median from grouped data Info Go

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.

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179 Statistics using a calculator Statistics and the student calculator Info Go

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.

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180 Statistics - Range and dispersion Range as a measure of dispersion Info Go

Objective: On completion of the lesson the student will be able to determine the range and using it in decision making.

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Objective: On completion of the lesson the student will be able to find the standard deviation, using a data set or a frequency distribution table and calculator.

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182 Statistics - Standard deviation Standard deviation applications Info Go

Objective: On completion of the lesson the student will be able to use standard deviation as a measure of deviation from a mean.

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183 Statistics - Standard deviation Normal distribution Info Go

Objective: On completion of the lesson the student will be able to use the standard deviation of a normal distribution to find the percentage of scores within ranges.

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184 Statistics - Interquartile range Measures of spread: the interquartile range Info Go

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

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185 Co-ordinate Geometry-Two point formula Two point formula: equation of a line which joins a pair of points. Info Go

Objective: On completion of the lesson the student will be able to calculate the equation of a line given any two named points on the line.

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186 Co-ordinate Geometry-Intercept form Intercept form of a straight line: find the equation when given x and y Info Go

Objective: On completion of the lesson the student will have an effective and efficient method for calculating the equation of a straight line.

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187 Co-ordinate Geometry-Parallel lines equations Parallel lines: identify equation of a line parallel to another Info Go

Objective: On completion of the lesson the student will be able to decide if two or more lines are parallel or not and to solve problems involving parallel lines.

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188 Co-ordinate Geometry-Perpendicular lines Perpendicular lines. Info Go

Objective: On completion of the lesson the student will be able to derive the equation of a line, given that it is perpendicular to another stated line.

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189 Co-ordinate Geometry-Inequalities Inequalities on the number plane. Info Go

Objective: On completion of the lesson the student will be able to derive the expression for an inequality given its graph. The student will also be able to solve some problems using inequalities.

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190 Co-ordinate Geometry-Theorems Perpendicular distance Info Go

Objective: On completion of the lesson the student will be able to derive the formula to calculate the distance between a given point and a given line. The student will also be able to calculate the distance between parallel lines.

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191 Co-ordinate Geometry-Theorems Line through intersection of two given lines Info Go

Objective: On completion of the lesson the student will be able to calculate the equation of a line which goes through the intersection of two given lines and also through another named point or satisfies some other specified condition.

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192 Co-ordinate Geometry-Theorems Internal and external division of an interval Info Go

Objective: On completion of the lesson the student will be able to divide an interval according to a given ratio and to calculate what point divides an interval in a given ratio for both internal and external divisions.

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193 Trig-reciprocal ratios Reciprocal ratios. Info Go

Objective: On completion of the lesson the student will be able to identify and use the reciprocal trigonometric ratios of sine, cosine and tan, that is, the cosecant, secant and cotangent ratios.

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194 Trig complementary angles Complementary angle results. Info Go

Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations.

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195 Trig identities Trigonometric identities Info Go

Objective: On completion of the lesson the student will be able to simplify trigonometrical expressions and solve trigonometry equations using the knowledge of trig identities.

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196 Trig larger angles Angles of any magnitude Info Go

Objective: On completion of the lesson the student will be able to find the trigonometric values of angles of any magnitude by assigning angles to the four quadrants of the circle.

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197 Trig larger angles Trigonometric ratios of 0Â°, 90Â°, 180Â°, 270Â° and 360Â° Info Go

Objective: On completion of the lesson the student will learn how to find the Trigonometric Ratios of 0, 90, 180, 270 and 360 degrees.

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198 Graph sine Graphing the trigonometric ratios - I Sine curve. Info Go

Objective: On completion of the lesson the student will recognise and draw the sine curve exploring changes in amplitude and period.

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199 Graph cosine Graphing the trigonometric ratios - II Cosine curve. Info Go

Objective: On completion of the lesson the student will know how to recognise and draw the cosine curve exploring changes in amplitude and period.

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200 Graphs tan curve Graphing the trigonometric ratios - III Tangent curve. Info Go

Objective: On completion of the lesson the student will know how to recognise and draw the tan curve.

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201 Graph reciprocals Graphing the trigonometric ratios - IV Reciprocal ratios. Info Go

Objective: On completion of the lesson the student will know how to recognise and draw the curves of the reciprocal ratios: cosec, sec and cot.

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202 Trig larger angles Using one ratio to find another. Info Go

Objective: On completion of the lesson the student will find other trig ratios given one trig ratio and to work with angles of any magnitude.

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203 Trig equations Solving trigonometric equations - Type I. Info Go

Objective: On completion of the lesson the student will solve simple trig equations with restricted domains.

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204 Trig equations Solving trigonometric equations - Type II. Info Go

Objective: On completion of the lesson the student will solve trig equations with multiples of theta and restricted domains.

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205 Trig equations Solving trigonometric equations - Type III. Info Go

Objective: On completion of the lesson the student will solve trig equations with two trig ratios and restricted domains.

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206 Polar coordinates Plotting polar coordinates and converting polar to rectangular Info Go

Objective: On completion of the lesson the student will understand the polar coordinate system and relate this to the rectangular coordinate system.

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207 Polar coordinates Converting rectangular coordinates to polar form Info Go

Objective: On completion of the lesson the student will understand the polar coordinate system and report these from rectangular coordinates.

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208 Polar coordinates Write and graph points in polar form with negative vectors (Stage 2) Info Go

Objective: On completion of the lesson the student will be using negative angles and negative vector lengths.

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209 Trigonometry Sin(A+B) etc sum and difference identities (Stage 2) Info Go

Objective: On completion of the lesson the student will be using the reference triangles for 30, 45 and 60 degrees with the sum and difference of angles to find additional exact values of trigonometric ratios.

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210 Logarithms-Power of 2 Powers of 2. Info Go

Objective: On completion of the lesson the student should be able to convert between logarithmic statements and index statements to the power of 2.

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211 Logarithms-Equations and logs Equations of type log x to the base 3 = 4. Info Go

Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the number from which the logarithm evolves.

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212 Logarithms-Equations and logs Equations of type log 32 to the base x = 5. Info Go

Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the base from which the number came.

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213 Logarithms-Log laws Laws of logarithms. Info Go

Objective: On completion of the lesson the student will be familiar with 5 logarithm laws.

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214 Logarithms-Log laws expansion Using the log laws to expand logarithmic expressions. Info Go

Objective: On completion of the lesson the student will be able to use the log laws to expand logarithmic expressions.

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215 Logarithms-Log laws simplifying Using the log laws to simplify expressions involving logarithms. Info Go

Objective: On completion of the lesson the student will be able to simplify logarithmic expressions using the log laws.

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216 Logarithms-Log laws numbers Using the log laws to find the logarithms of numbers. Info Go

Objective: On completion of the lesson the student will have an enhanced understanding of the use of the log laws and be able to do more applications with numerical examples.

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217 Logarithms-Equations and logs Equations involving logarithms. Info Go

Objective: On completion of the lesson the student will be able to solve equations with log terms.

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218 Logarithms-Logs to solve equations Using logarithms to solve equations. Info Go

Objective: On completion of the lesson the student will be able to use logarithms to solve index equations with the assistance of a calculator.

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219 Logarithms-Change base formula Change of base formula Info Go

Objective: On completion of the lesson the student will have seen the change of base formula for logarithms and be capable of using it to change the logarithm of one base to another base.

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220 Logarithms-Graph-log curve The graph of the logarithmic curve Info Go

Objective: On completion of the lesson the student will be able to draw a logarithmic curve to a given base and know the general properties of log curves.

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221 Logarithms-Log curves Working with log curves. Info Go

Objective: On completion of the lesson the student will be able to solve problems with log curves

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222 Logarithms-Complex numbers Fundamental theorem of algebra (Stage 2) Info Go

Objective: On completion of the lesson the student will recognise and use the fundamental theorem of algebra to find factors for polynomials with real coefficients over the complex number field.

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223 Algebra-polynomials Introduction to polynomials Info Go

Objective: On completion of the lesson the student will understand all the terminology associated with polynomials and be able to judge if any algebraic expression is a polynomial or not.

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224 Algebra-polynomials The sum, difference and product of two polynomials. Info Go

Objective: On completion of the lesson the student will be able to add subtract and multiply polynomials and find the degrees of the answers.

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225 Algebra-polynomials Polynomials and long division. Info Go

Objective: On completion of the lesson the student will understand the long division process with polynomials.

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226 Remainder theorem The remainder theorem. Info Go

Objective: On completion of the lesson the student will understand how the remainder theorem works and how it can be applied.

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227 Remainder theorem More on remainder theorem Info Go

Objective: On completion of the lesson the student will understand the remainder theorem and how it can be applied to solve some interesting questions on finding unknown coefficients of polynomials.

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228 Factor theorem The factor theorem Info Go

Objective: On completion of the lesson the student will be able to use the factor theorem and determine if a term in the form of x minus a is a factor of a given polynomial.

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229 Factor theorem More on the factor theorem Info Go

Objective: On completion of the lesson the student will fully understand the factor theorem and how it can be applied to solve some questions on finding unknown coefficients of polynomials.

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230 Factor theorem Complete factorisations using the factor theorem Info Go

Objective: On completion of the lesson the student will be able to factorise polynomials of a higher degree than 2 and to find their zeros.

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231 Polynomial equations Polynomial equations Info Go

Objective: On completion of the lesson the student will be capable of solving polynomial equations given in different forms.

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232 Graphs, polynomials Graphs of polynomials Info Go

Objective: On completion of the lesson the student will understand how to graph polynomials using the zeros of polynomials, the y intercepts and the direction of the curves.

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233 Roots quad equations Sum and product of roots of quadratic equations Info Go

Objective: On completion of the lesson the student will understand the formulas for the sum and product of roots of quadratic polynomials and how to use them. The student will understand how to form a quadratic equation given its roots.

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234 Roots quad equations Sum and product of roots of cubic and quartic equations Info Go

Objective: On completion of the lesson the student will be able to do problems on the sum and products of roots of cubic and quartic equations.

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235 Approx roots Methods of approximating roots Info Go

Objective: On completion of the lesson the student will be capable of finding approximate roots of polynomial equations using half the interval method. The student will be able to make a number of applications of this rule within the one question.

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236 Circle Geometry Theorem - Equal arcs on circles of equal radii subtend equal angles at the centre. Theorem - Equal angles at the centre of a circle on equal arcs. Info Go

Objective: On completion of the lesson the student will be able to prove that 'Equal arcs on circles of equal radii, subtend equal angles at the centre', and that 'Equal angles at the centre of a circle stand on equal arcs.' They should then be able to use these pro

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237 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. Info Go

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'

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238 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. Info Go

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

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239 Circle Geometry Theorem - The angle at the centre of a circle is double the angle at the circumference standing on the same arc. Info Go

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.

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240 Circle Geometry Theorem - Angles in the same segment of a circle are equal. Info Go

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

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241 Circle Geometry Theorem - The angle of a semi-circle is a right angle. Info Go

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

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242 Circle Geometry Theorem - The opposite angles of a cyclic quadrilateral are supplementary. Info Go

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

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243 Circle Geometry Theorem - The exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite angle. Info Go

Objective: On completion of the lesson the student will be able to prove that the exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite.

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244 Circle Geometry Theorem - The tangent to a circle is perpendicular to the radius drawn to it at the point of contact. Info Go

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.

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245 Circle Geometry Theorem - Tangents to a circle from an external point are equal. Info Go

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

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246 Circle Geometry Theorem - The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. Info Go

Objective: On completion of the lesson the student will be able to prove that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.

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247 Sequences and Series General sequences. Info Go

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.

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248 Sequences and Series Finding Tn given Sn. Info Go

Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term.

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249 Arithmetic Progression The arithmetic progression Info Go

Objective: On completion of the lesson the student will be able to test if a given sequence is an Arithmetic Progression or not and be capable of finding a formula for the nth term, find any term in the A.P. and to solve problems involving these concepts.

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250 Arithmetic Progression Finding the position of a term in an A.P. Info Go

Objective: On completion of the lesson the student will be able to solve many problems involving finding terms of an Arithmetic Progression.

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251 Arithmetic Progression Given two terms of A.P., find the sequence. Info Go

Objective: On completion of the lesson the student will be able to find any term of an Arithmetic Progression when given two terms

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252 Arithmetic Progression Arithmetic means Info Go

Objective: On completion of the lesson the student will be able to make an arithmetic progression between two given terms. This could involve finding one, two, or even larger number of arithmetic means.

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253 Arithmetic Progression The sum to n terms of an A.P. Info Go

Objective: On completion of the lesson the student will understand the formulas for the sum of an Arithmetic Progression and how to use them in solving problems.

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254 Geometric Progression The geometric progression. Info Go

Objective: On completion of the lesson the student will be able to test if a given sequence is a Geometric Progression or not and be capable of finding a formula for the nth term, find any term in the G.P. and to solve problems involving these concepts.

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255 Geometric Progression Finding the position of a term in a G.P. Info Go

Objective: On completion of the lesson the student will understand how to find terms in a geometric progression and how to apply it different types of problems.

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256 Geometric Progression Given two terms of G.P., find the sequence. Info Go

Objective: On completion of this lesson the student will be able to solve all problems involving finding the common ratio of a Geometric Progression.

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257 Calculus Limits Info Go

Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule.

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258 Calculus=1st prin Differentiation from first principles. Info Go

Objective: On completion of the lesson the student will be able apply the first principles (calculus) formula to find the gradient of a tangent at any point on a continuous curve.

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259 Calculus=1st prin Differentiation of y = x to the power of n. Info Go

Objective: On completion of the Calculus lesson the student will be able to differentiate a number of expressions involving x raised to the power of n.

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260 Calculus-differential, integ Meaning of dy over dx - equations of tangents and normals. Info Go

Objective: On completion of the Calculus lesson the student will be able to apply differentiation and algebra skills to find the equation of the tangent and the normal to a point on a curve.

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261 Calculus-differential, integ Function of a function rule, product rule, quotient rule. Info Go

Objective: On completion of the Calculus lesson the student will understand how to use the chain rule, the product rule and the quotient rule.

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262 Calculus-differential, integ Increasing, decreasing and stationary functions. Info Go

Objective: On completion of the lesson the student will understand how to find the first derivative of various functions, and use it in various situations to identify increasing, decreasing and stationary functions.

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263 Calculus Turning points and the first derivative. Info Go

Objective: On completion of the Calculus lesson the student will be able to use the first derivative to find and identify the nature of stationary points on a curve.

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264 Calculus-2nd derivative The second derivative - concavity. Info Go

Objective: On completion of the Calculus lesson the student will be able to find a second derivative, and use it to find the domain over which a curve is concave up or concave down, as well as any points of inflexion.

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265 Sequences and Series-Geometric means Geometric means. Info Go

Objective: On completion of the lesson the student will be able to make a geometric progression between two given terms. This could involve finding one, two, or even larger number of geometric means.

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266 Sequences and Series-Sum of gp The sum to n terms of a G.P. Info Go

Objective: On completion of the lesson the student will understand the formulas and how to use them to solve problems in summing terms of a Geometric Progression (G.P).

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267 Sequences and Series-Sigma notation Sigma notation Info Go

Objective: On completion of the G.P. lesson the student will be familiar with the sigma notation and how it operates.

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268 Sequences and Series-Sum-infinity Limiting sum or sum to infinity. Info Go

Objective: On completion of the lesson the student will have learnt the formula for the limiting sum of a G.P., the conditions for it to exist and how to apply it to particular problems.

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269 Sequences and Series-Recurring decimal infinity Recurring decimals and the infinite G.P. Info Go

Objective: On completion of the G.P. lesson the student will have understood how to convert any recurring decimal to a rational number.

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270 Sequences and Series-Compound interest Compound interest Info Go

Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods.

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271 Sequences and Series-Superannuation Superannuation. Info Go

Objective: On completion of the lesson the student will understand the method of finding the accumulated amount of a superannuation investment using the sum formula for a G.P.

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272 Sequences and Series-Time payments Time payments. Info Go

Objective: On completion of the lesson the student will have examined examples carefully and be capable of setting out the long method of calculating a regular payment for a reducible interest loan.

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273 Calculus - Curve sketching Curve sketching Info Go

Objective: On completion of the Calculus lesson the student will be able to use the first and second derivatives to find turning points of a curve, identify maxima and minima, and concavity, then use this information to sketch a curve.

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274 Calculus - Maxima minima Practical applications of maxima and minima Info Go

Objective: On completion of the lesson the student will be able to apply calculus to a suite of simple maxima or minima problems.

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275 Calculus - Integration Integration - anti-differentiation, primitive function Info Go

Objective: On completion of the Calculus lesson the student will be able to use rules of integration to find primitives of some simple functions.

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276 Calculus - Computation area Computation of an area Info Go

Objective: On completion of the Calculus lesson the student will be able to select an appropriate formula to calculate an area, re-arrange an expression to suit the formula, and use correct limits in the formula to evaluate an area.

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277 Calculus - Computation volumes Computation of volumes of revolution Info Go

Objective: On completion of the Calculus lesson the student will know how to choose an appropriate volume formula, re-arrange an expression to suit the formula, and then calculate a result to a prescribed accuracy.

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278 Calculus - Trapezoidal and Simpson's rules The Trapezoidal rule and Simpson's rule Info Go

Objective: On completion of the Calculus lesson the student will know how to calculate sub-intervals, set up a table of values, then apply the Trapezoidal Rule, or Simpson's Rule to approximate an area beneath a curve.

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279 Exam Exam - Grade 12 - Mathematics Applied 5 Info Go

Objective: Exam

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