| 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 |
| 83 |
Algebra – Quadratic equations |
Introduction to Quadratic Equations |
| Objective: To find the solutions of quadratic equations presented as a product of factors |
| 84 |
Algebra – Quadratic equations |
Solving Quadratic Equations with Factorisation |
| Objective: To solve quadratic equations requiring factorisation |
| 85 |
Algebra – Quadratic equations |
Solving Quadratic Equations |
| 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 |
| 88 |
Algebra – Quadratic equations |
The Quadratic Formula |
| Objective: To find the roots of a quadratic equation by using the quadratic formula |
| 89 |
Algebra – Quadratic equations |
Problem solving with quadratic equations |
| Objective: To solve problems which require finding the roots of a quadratic equation |
| 90 |
Algebra – Quadratic equations |
Solving Simultaneous Quadratic Equations Graphically |
| Objective: To determine points of intersection of quadratic and linear equations |
| 91 |
Conic sections |
The Parabola |
| Objective: To examine the properties of parabolas of the forms x^2 = 4py and y^2 = 4px |
| 92 |
Exam |
Exam – Grade 10 – Foundation of Mathematics (Applied) |
| Objective: Exam |
