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### Grade 10 – Foundation of Mathematics (Applied) Mathematics

# TOPIC TITLE
1 Study Plan Study plan – Grade 10 – Foundation of Mathematics (Applied)
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2 Geometry part 2 Congruent triangles: Tests 1 and 2
Objective: To recognise congruent triangles and matching sides and angles using SSS and SAS
3 Geometry part 2 Congruent triangles: Tests 3 and 4
Objective: To recognise congruent triangles and matching sides and angles using AAS and RHS
4 Geometry part 2 Proofs and Congruent Triangles
Objective: To use congruency in formal proofs in order to determine unknown angles and sides
5 Geometry part 2 Similar Triangles
Objective: To use similarity tests for triangles and determine unknown sides and angles in triangles
6 Geometry part 2 Using Similar Triangles to Calculate Lengths
Objective: To determine unknown sides and angles of similar triangles
7 Geometry part 2 Examples involving overlapping triangles
Objective: To determine the lengths of unknown sides in overlapping or adjacent similar triangles
8 Pythagoras Pythagoras’ Theorem: Finding the Hypotenuse
Objective: To calculate the length of a hypotenuse using Pythagoras’ Theorem
9 Pythagoras Using Pythagorean Triples to Identify Right Triangles
Objective: To identify right triangles by using Pythagorean Triples or Pythagoras’ Theorem
10 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
11 Pythagoras Calculating a Leg of a right-angled Triangle
Objective: To calculate the length of sides other than the hypotenuse using Pythagoras’ Theorem
12 Trigonometry part 1 Trigonometric Ratios
Objective: To name the sides of a right-angled triangle and to determine the trig ratios of an angle
13 Trigonometry part 1 Using the Calculator
Objective: To determine trigonometric ratios using a calculator
14 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
15 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
16 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
17 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
18 Trigonometry part 1 Bearings: The Compass
Objective: To change from true bearings to compass bearings and vice versa
19 Trigonometry part 1 Angles of Elevation and Depression
Objective: To identify and distinguish between angles of depression and elevation
20 Trigonometry part 1 Trigonometric Ratios in Practical Situations
Objective: To solve problems involving bearings and angles of elevation and depression
21 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
22 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
23 Measurement – Length Compare and convert formal units of measurement
Objective: To change cm to mm and then convert mm, cm, m and km from one to another
24 Measurement – Area Introducing the Rules for Finding the Area of a Rectangle and a Parallelogram
Objective: To calculate the areas of rectangles and parallelograms using Area of Rectangle = Length x Height and Area of Parallelogram = Base x Height
25 Measurement – Area Finding the Area of a Triangle and Other Composite Shapes
Objective: To calculate the area of triangles and measure and calculate composite shape area
26 Measurement – Capacity Converting between volume and capacity using milliliters and liters
Objective: To solve capacity problems involving mixed dimensional units
27 Measurement – Capacity Estimate, measure and compare the capacity of containers
Objective: To understand estimation and a way to go about it
28 Measurement – Advanced area Area of a Trapezium
Objective: To calculate the area of trapezia using A=(h/2)(a+b)
29 Measurement – Advanced area Area of a Rhombus
Objective: To calculate the area of a rhombus using diagonal products
30 Measurement – Advanced area Area of a Circle
Objective: To calculate the area of circles and sectors and to solve circle problems
31 Measurement – Advanced area Area of Regular Polygons and Composite Figures
Objective: To calculate area of composite figures and solve problems using correct formulae
32 Problem solving Word Problems with Area
Objective: To solve area word problems using + – x and /
33 Measurement – Advanced volume Finding the volume of prisms
Objective: To calculate the volume of prisms using V=Ah and solve volume problems
34 Measurement – Advanced volume Volume of a Cylinder and Sphere
Objective: To solve problems and calculate volumes of cylinders and spheres and parts of each
35 Measurement – Advanced volume Volume of Pyramids and Cones
Objective: To calculate the volumes of pyramids and cones
36 Measurement – Advanced volume Composite Solids
Objective: To calculate the volume of composite figures using appropriate formulae
37 Problem solving Word Problems with Volume/Capacity
Objective: To solve volume and capacity word problems using + – x and /
38 Surface area Surface Area of a Cube/Rectangular Prism
Objective: To calculate the surface area of cubes and rectangular prisms
39 Surface area Surface Area of a Triangular/Trapezoidal Prism
Objective: To calculate the surface area of triangular and trapezoidal prisms
40 Surface area Surface Area of a Cylinder and Sphere
Objective: To calculate the surface area of cylinders and spheres
41 Surface area Surface Area of Pyramids
Objective: To calculate the surface area of pyramids
42 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
43 Co-ordinate geometry part 1 The Gradient Formula
Objective: To use the gradient formula to find the gradient of straight lines
44 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
45 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
46 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
47 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
48 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)
49 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
50 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
51 Algebra – Basic Solving Two-Step Equations
Objective: To solve two-step equations without division in the initial problem
52 Algebra – Basic Solving Equations Containing Binomial Expressions
Objective: To solve equations with binomial expressions on each side
53 Algebra – Basic Equations involving Grouping Symbols
Objective: To solve equations containing grouping symbols on each side
54 Algebra – Basic Equations involving fractions
Objective: To solve fraction equations with the unknown in either the numerator or denominator
55 Algebra – Basic Equations Resulting from Substitution into Formulae
Objective: To solve equations created by substituting values into formulae
56 Algebra – Basic Changing the Subject of the Formula
Objective: To change the subject of algebraic formulae using equation-solving techniques
57 Simultaneous equations Simultaneous Equations
Objective: To solve simultaneous equations by substitution
58 Simultaneous equations Elimination method
Objective: To solve simultaneous equations by elimination
59 Simultaneous equations Elimination method part 2
Objective: To solve more difficult simultaneous equations by elimination
60 Simultaneous equations Applications of simultaneous equations
Objective: To solve problems using simultaneous equations
61 Algebra – Products and factors Binomial Products
Objective: To expand and simplify monic binomial products of the form (x + a)(x +/- b)
62 Algebra – Products and factors Binomial products with negative multiplier
Objective: To expand and simplify monic binomial products of the form (x – a)(x +/- b)
63 Algebra – Products and factors Binomial Products (nonmonic)
Objective: To expand and simplify nonmonic binomial products
64 Algebra – Products and factors Squaring a Binomial (monic)
Objective: To expand the square of a binomial by multiplication and by inspection
65 Algebra – Products and factors Squaring a Binomial (nonmonic)
Objective: To expand the square of a nonmonic binomial by inspection
66 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
67 Algebra – Products and factors Products in Simplification of Algebraic Expressions
Objective: To simplify algebraic expressions containing binomial products
68 Algebra – Products and factors Larger Expansions
Objective: To expand and simplify the product of a binomial and a trinomial
69 Algebra – Products and factors Highest Common Factor
Objective: To factorise an expression by identifying and extracting the highest common factor
70 Algebra – Products and factors Factors by Grouping
Objective: To factorise a four-term expression by grouping
71 Algebra – Products and factors Difference of Two Squares
Objective: To factorise differences of two squares
72 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.
73 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.
74 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.
75 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.
76 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.
77 Algebra – Products and factors Factorisation of nonmonic quadratic trinomials
Objective: To factorise nonmonic quadratic trinomials using the ‘X’ method
78 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
79 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
80 Graphs part 1 Graphing perfect squares: y=(a-x) squared
Objective: To describe and sketch parabolas of the form y = (x – a)^2
81 Graphs part 1 Graphing irrational roots
Objective: To determine the vertex (using -b/2a), and other derived properties, to sketch a parabola
82 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
86 Algebra – Quadratic equations Completing the square
Objective: To complete an incomplete square
87 Algebra – Quadratic equations Solving Quadratic Equations by Completing the Square
Objective: To solve quadratic equations by completing the square