| 1 |
Study Plan |
Study plan – Class IX |
| Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. |
| 2 |
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. |
| 3 |
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. |
| 4 |
Rules for indices/exponents |
Multiplying indices when raising a power to a power |
| Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power. |
| 5 |
Rules for indices/exponents |
Multiplying indices when raising to more than one term |
| 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. |
| 6 |
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. |
| 7 |
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. |
| 8 |
Fractional indices/exponents |
Fractional indices |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices. |
| 9 |
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. |
| 10 |
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. |
| 11 |
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. |
| 12 |
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. |
| 13 |
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. |
| 14 |
Number theory – sets |
Number sets and their members |
| Objective: On completion of the lesson the student will understand the notation used with sets and the subsets of the real number system. |
| 15 |
Number theory – operations |
Properties of real numbers using addition and multiplication |
| 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. |
| 16 |
Number theory – equations |
Transformations that produce equivalent equations |
| Objective: On completion of the lesson the student will know and use the correct terms to describe the processes in solving equations. |
| 17 |
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. |
| 18 |
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. |
| 19 |
Graphing binomials |
Binomial products [non-monic]. |
| Objective: On completion of the lesson, the student will have examined more complex examples with binomial products. |
| 20 |
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. |
| 21 |
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. |
| 22 |
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. |
| 23 |
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. |
| 24 |
Algebraic expressions-larger expansions |
Algebraic Expressions – Larger expansions. |
| Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions. |
| 25 |
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. |
| 26 |
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. |
| 27 |
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. |
| 28 |
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. |
| 29 |
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. |
| 30 |
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. |
| 31 |
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. |
| 32 |
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. |
| 33 |
Factorising quads |
Factorisation of non-monic quadratic trinomials |
| Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial. |
| 34 |
Factorising quads |
Factorisation of non-monic quadratic trinomials – moon method |
| Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method. |
| 35 |
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. |
| 36 |
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. |
| 37 |
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. |
| 38 |
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. |
| 39 |
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. |
| 40 |
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. |
| 41 |
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. |
| 42 |
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. |
| 43 |
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. |
| 44 |
Algebra-polynomials |
Introduction to polynomials |
| 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. |
| 45 |
Algebra-polynomials |
The sum, difference and product of two polynomials. |
| Objective: On completion of the lesson the student will be able to add subtract and multiply polynomials and find the degrees of the answers. |
| 46 |
Algebra-polynomials |
Polynomials and long division. |
| Objective: On completion of the lesson the student will understand the long division process with polynomials. |
| 47 |
Remainder theorem |
The remainder theorem. |
| Objective: On completion of the lesson the student will understand how the remainder theorem works and how it can be applied. |
| 48 |
Remainder theorem |
More on remainder theorem |
| 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. |
| 49 |
Factor theorem |
The factor theorem |
| 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. |
| 50 |
Coordinate geometry |
Solve by graphing |
| Objective: On completion of the lesson students will use the slope intercept form of a line to create graphs and find points of intersection. |
| 51 |
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. |
| 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 |
| 52 |
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’ |
| 53 |
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. |
| 54 |
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. |
| 55 |
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. |
| 56 |
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.’ |
| 57 |
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. |
| 58 |
Pythagoras |
Proofs of Pythagoras theorem |
| Objective: On completion of this lesson the student will have geometric proofs for Pythagoras’ Theorem |
| 59 |
Pythagoras |
Pythagorean triples |
| Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple. |
| 60 |
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. |
| 61 |
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. |
| 62 |
Area |
Area of a rhombus. |
| Objective: On completion of the lesson the student will be able to: identify a rhombus, learn how to find the formula for the area of a rhombus, and use it in solving problems. |
| 63 |
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. |
| 64 |
Geometry-constructions |
Geometric constructions |
| Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses. |
| 65 |
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. |
| 66 |
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. |
| 67 |
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. |
| 68 |
Surface area |
Surface area of pyramids |
| Objective: On completion of the lesson the student will be able to find the surface areas of pyramids. |
| 69 |
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 |
| 70 |
Geometry problems |
More difficult exercises involving parallel lines |
| 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 |
| 71 |
Geometry-reasoning |
Further difficult exercises involving formal reasoning |
| 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. |
| 72 |
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. |
| 73 |
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. |
| 74 |
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. |
| 75 |
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. |
| 76 |
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. |
| 77 |
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. |
| 78 |
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. |
| 79 |
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. |
| 80 |
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 |
| 81 |
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. |
| 82 |
Surds |
Expanding surds |
| Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds. |
| 83 |
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. |
| 84 |
Statistics |
Frequency histograms and polygons |
| Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons. |
| 85 |
Statistics |
Relative frequency |
| Objective: On completion of the lesson the student will be able to collect, display and make judgements about data. |
| 86 |
Statistics |
The range. |
| Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table. |
| 87 |
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. |
| 88 |
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. |
| 89 |
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 |
| 90 |
Statistic-probability |
Cumulative frequency |
| Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons. |
| 91 |
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. |
| 92 |
Logic |
Inductive and deductive reasoning |
| Objective: On completion of this lesson the student will understand and use the terms hypothesis, conclusion, inductive and deductive. |
| 93 |
Logic |
Definition and use of counter examples |
| Objective: On completion of this lesson the student will be able to create counter examples to statements. |
| 94 |
Volume/capacity |
Problems with volume/capacity. |
| Objective: Problem Solving: problems involving volume/capacity |
| 95 |
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. |
| 96 |
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. |
| 97 |
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. |
| 98 |
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. |
| 99 |
Co-ordinate Geometry-Two point formula |
Two point formula: equation of a line which joins a pair of points. |
| 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. |
| 100 |
Co-ordinate Geometry-Intercept form |
Intercept form of a straight line: find the equation when given x and y |
| Objective: On completion of the lesson the student will have an effective and efficient method for calculating the equation of a straight line. |
| 101 |
Co-ordinate Geometry-Parallel lines equations |
Parallel lines: identify equation of a line parallel to another |
| 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. |
| 102 |
Co-ordinate Geometry-Perpendicular lines |
Perpendicular lines. |
| 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. |
| 103 |
Co-ordinate Geometry-Inequalities |
Inequalities on the number plane. |
| 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. |
| 104 |
Statistic-probability |
Probability of Simple Events |
| Objective: On completion of the lesson the student will be able to understand the probability of simple events. |
| 105 |
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. |
| 106 |
Statistic-probability |
Experimental probability |
| Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial. |
| 107 |
Exam |
Exam – Class IX |
| Objective: Exam |
