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1 Study Plan Study plan – Grade 10 – Principles of Mathematics (Academic)
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2 Algebra – Products and factors Binomial Products
Objective: To expand and simplify monic binomial products of the form (x + a)(x +/- b)
3 Algebra – Products and factors Binomial products with negative multiplier
Objective: To expand and simplify monic binomial products of the form (x – a)(x +/- b)
4 Algebra – Products and factors Binomial Products (nonmonic)
Objective: To expand and simplify nonmonic binomial products
5 Algebra – Products and factors Squaring a Binomial (monic)
Objective: To expand the square of a binomial by multiplication and by inspection
6 Algebra – Products and factors Squaring a Binomial (nonmonic)
Objective: To expand the square of a nonmonic binomial by inspection
7 Algebra – Products and factors Expansions Leading to the Difference of Two Squares
Objective: To expand the product of conjugate binomials leading to differences of squares
8 Algebra – Products and factors Products in Simplification of Algebraic Expressions
Objective: To simplify algebraic expressions containing binomial products
9 Algebra – Products and factors Larger Expansions
Objective: To expand and simplify the product of a binomial and a trinomial
10 Algebra – Products and factors Highest Common Factor
Objective: To factorise an expression by identifying and extracting the highest common factor
11 Algebra – Products and factors Factors by Grouping
Objective: To factorise a four-term expression by grouping
12 Algebra – Products and factors Difference of Two Squares
Objective: To factorise differences of two squares
13 Algebra – Products and factors Common factor and the difference of two squares
Objective: On completion of the lesson the student will be aware of common factors and recognize the difference of two squares.
14 Algebra – Products and factors Quadratic Trinomials (monic): Case 1
Objective: On completion of the lesson the student will understand the factorization of quadratic trinomial equations with all terms positive.
15 Algebra – Products and factors 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.
16 Algebra – Products and factors Quadratic Trinomials (monic): Case 3
Objective: On completion of the lesson the student will have an increased knowledge on factorizing quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative.
17 Algebra – Products and factors Quadratic Trinomials (monic): Case 4
Objective: On completion of the lesson the student will understand how to factorize all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative.
18 Algebra – Products and factors Factorisation of nonmonic quadratic trinomials
Objective: To factorise nonmonic quadratic trinomials using the ‘X’ method
19 Graphs part 1 The parabola: to describe properties of a parabola from its equation
Objective: To describe properties of a parabola from its equation and sketch the parabola
20 Graphs part 1 Quadratic Polynomials of the form y = ax^2 + bx + c
Objective: To describe and sketch parabolas of the form y = x^2 + bx + c
21 Graphs part 1 Graphing perfect squares: y=(a-x) squared
Objective: To describe and sketch parabolas of the form y = (x – a)^2
22 Graphs part 1 Graphing irrational roots
Objective: To determine the vertex (using -b/2a), and other derived properties, to sketch a parabola
23 Graphs part 1 Solving Simultaneous Equations graphically
Objective: To solve simultaneous equations graphically
Objective: To find the solutions of quadratic equations presented as a product of factors
Objective: To solve quadratic equations requiring factorisation
Objective: To solve quadratic equations that need to be changed into the form ax^2 + bx + c = 0
27 Algebra – Quadratic equations Completing the square
Objective: To complete an incomplete square
28 Algebra – Quadratic equations Solving Quadratic Equations by Completing the Square
Objective: To solve quadratic equations by completing the square
Objective: To find the roots of a quadratic equation by using the quadratic formula
Objective: To solve problems which require finding the roots of a quadratic equation
Objective: To determine points of intersection of quadratic and linear equations
32 Conic sections The Parabola
Objective: To examine the properties of parabolas of the forms x^2 = 4py and y^2 = 4px
33 Graphs part 2 The Rectangular Hyperbola
Objective: To graph rectangular hyperbolae whose equations are of the form xy = a and y = a/x
34 Graphs part 2 The Exponential Function
Objective: To graph exponential curves whose exponents are either positive or negative
35 Co-ordinate geometry part 1 The Distance Formula
Objective: To use the distance formula to calculate the lengths of lines and distances
36 Co-ordinate geometry part 1 The Mid-Point Formula
Objective: To determine the mid-point of an interval using the mid-point formula
37 Co-ordinate geometry part 1 The Gradient
Objective: To find the gradient of a line given its angle of inclination or given rise and run
38 Co-ordinate geometry part 1 The Gradient Formula
Objective: To use the gradient formula to find the gradient of straight lines
39 Co-ordinate geometry part 1 The Straight Line
Objective: To state the equation of lines parallel to the axes and to graph equations x = a and y = b
40 Co-ordinate geometry part 1 Lines Through the Origin
Objective: To state the equation of lines passing through the origin and to graph y = mx
41 Co-ordinate geometry part 1 General Form of a Line and the x and y Intercepts
Objective: To write linear equations in general form, to find the x and y intercepts and to calculate area
42 Co-ordinate geometry part 1 Slope Intercept Form of a Line
Objective: To change equation to slope intercept form and graph it and to find equation given graph
43 Co-ordinate geometry part 1 Point Slope Form of a Line
Objective: To find the equation of a line given its slope and a point on the line (y-y1) = m(x-x1)
44 Graphs part 1 The Circle: to find radii of circles
Objective: To find radii of circles, centre (0, 0) using x^2 + y^2 = a^2 and write equations of circles
45 Graphs part 1 The semicircle: to select the equation given the semicircle and vice versa
Objective: To select the equation given a semicircle and vice versa
46 Conic sections Circles
Objective: To graph circles of the form x^2 + y^2 = r^2 and to form the equation of the given circles
47 Co-ordinate geometry part 2 Two Point Formula: equation of a line which joins a pair of points
Objective: To find the equation of the line which joins a pair of points
48 Co-ordinate geometry part 2 Intercept form of a straight line: find the equation when given x and y
Objective: To find the equation of a line given the x-axis and y-axis intercepts
49 Co-ordinate geometry part 2 Parallel Lines: identify equation of a line parallel to another
Objective: To change the standard form of a straight line equation to the y = mx + b form
50 Co-ordinate geometry part 2 Perpendicular Lines
Objective: To identify the equation of a line that is perpendicular to a given linear equation
51 Co-ordinate geometry part 2 Perpendicular Distance
Objective: To calculate the perpendicular distance from a point to a line and between lines
52 Geometry part 2 Congruent triangles: Tests 1 and 2
Objective: To recognise congruent triangles and matching sides and angles using SSS and SAS
53 Geometry part 2 Congruent triangles: Tests 3 and 4
Objective: To recognise congruent triangles and matching sides and angles using AAS and RHS
54 Geometry part 2 Proofs and Congruent Triangles
Objective: To use congruency in formal proofs in order to determine unknown angles and sides
55 Geometry part 2 Similar Triangles
Objective: To use similarity tests for triangles and determine unknown sides and angles in triangles
56 Geometry part 2 Using Similar Triangles to Calculate Lengths
Objective: To determine unknown sides and angles of similar triangles
57 Geometry part 2 Examples involving overlapping triangles
Objective: To determine the lengths of unknown sides in overlapping or adjacent similar triangles
58 Pythagoras Pythagoras’ Theorem: Finding the Hypotenuse
Objective: To calculate the length of a hypotenuse using Pythagoras’ Theorem
59 Pythagoras Using Pythagorean Triples to Identify Right Triangles
Objective: To identify right triangles by using Pythagorean Triples or Pythagoras’ Theorem
60 Pythagoras Calculating the Hypotenuse of a right-angled Triangle
Objective: To calculate the length of a hypotenuse where lengths are given as surds or decimals
61 Pythagoras Calculating a Leg of a right-angled Triangle
Objective: To calculate the length of sides other than the hypotenuse using Pythagoras’ Theorem
62 Trigonometry part 1 Trigonometric Ratios
Objective: To name the sides of a right-angled triangle and to determine the trig ratios of an angle
63 Trigonometry part 1 Using the Calculator
Objective: To determine trigonometric ratios using a calculator
64 Trigonometry part 1 Using the Trigonometric Ratios to find unknown length [Case 1 Sin]
Objective: To use the sine ratio to calculate the opposite side of a right-angled triangle
65 Trigonometry part 1 Using the Trigonometric Ratios to find unknown length [Case 2 Cosine]
Objective: To use the cosine ratio to calculate the adjacent side of a right-angle triangle
66 Trigonometry part 1 Using the Trigonometric Ratios to find unknown length [Case 3 Tangent Ratio]
Objective: To use the tangent ratio to calculate the opposite side of a right-angled triangle
67 Trigonometry part 1 Unknown in the Denominator [Case 4]
Objective: To use trigonometry to find sides of a right-angled triangle and the Unknown in denominator
68 Trigonometry part 1 Bearings: The Compass
Objective: To change from true bearings to compass bearings and vice versa
69 Trigonometry part 1 Angles of Elevation and Depression
Objective: To identify and distinguish between angles of depression and elevation
70 Trigonometry part 1 Trigonometric Ratios in Practical Situations
Objective: To solve problems involving bearings and angles of elevation and depression
71 Trigonometry part 1 Using the Calculator to Find an Angle Given a Trigonometric Ratio
Objective: To find angles in right-angled triangles given trigonometric ratios
72 Trigonometry part 1 Using the Trigonometric Ratios to Find an Angle in a Right-Angled Triangle
Objective: To use trigonometric ratios to determine angles in right-angled triangles and in problems
73 Trigonometry part 1 Trigonometric Ratios of 30, 45 and 60 Degrees: Exact Ratios
Objective: To determine the exact values of sin, cos and tan of 30, 45 and 60 degrees
74 Trigonometry part 1 The Cosine Rule to find an unknown side [Case 1 SAS]
Objective: To complete the cosine rule to find a subject side for given triangles
75 Trigonometry part 1 The Sine Rule to find an unknown side: Case 1
Objective: To complete the cosine rule to find a subject angle for given triangles
76 Trigonometry part 1 The Sine Rule: Finding a Side
Objective: To find an unknown side of a triangle using the sine rule
77 Trigonometry part 1 The Sine Rule: Finding an Angle
Objective: To find an unknown angle of a triangle using the sine rule