| 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 |
| 24 |
Algebra – Quadratic equations |
Introduction to Quadratic Equations |
| Objective: To find the solutions of quadratic equations presented as a product of factors |
| 25 |
Algebra – Quadratic equations |
Solving Quadratic Equations with Factorisation |
| Objective: To solve quadratic equations requiring factorisation |
| 26 |
Algebra – Quadratic equations |
Solving Quadratic Equations |
| 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 |
| 29 |
Algebra – Quadratic equations |
The Quadratic Formula |
| Objective: To find the roots of a quadratic equation by using the quadratic formula |
| 30 |
Algebra – Quadratic equations |
Problem solving with quadratic equations |
| Objective: To solve problems which require finding the roots of a quadratic equation |
| 31 |
Algebra – Quadratic equations |
Solving Simultaneous Quadratic Equations Graphically |
| 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 |
| 78 |
Exam |
Exam – Grade 10 – Principles of Mathematics (Academic) |
| Objective: Exam |
