| # | TOPIC | TITLE | +/- | |
|---|---|---|---|---|
| 1 | Study Plan | Study plan - Grade 12 - Mathematics of College Technology | Info | Go |
|
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. |
||||
| 2 | Indices/Exponents | Adding indices when multiplying terms with the same base | Info | Go |
|
Objective: To add indices when multiplying powers that have the same base |
||||
| 3 | Indices/Exponents | Subtracting indices when dividing terms with the same base | Info | Go |
|
Objective: To subtract indices when dividing powers of the same base |
||||
| 4 | Indices/Exponents | Multiplying indices when raising a power to a power | Info | Go |
|
Objective: To multiply indices when raising a power to a power |
||||
| 5 | Indices/Exponents | Multiplying indices when raising to more than one term | Info | Go |
|
Objective: To raise power products to a power |
||||
| 6 | Indices/Exponents | Terms raised to the power of zero | Info | Go |
|
Objective: To evaluate expressions where quantities are raised to the power 0 |
||||
| 7 | Indices/Exponents | Negative Indices | Info | Go |
|
Objective: To evaluate or simplify expressions containing negative indices |
||||
| 8 | Indices/Exponents | Fractional Indices | Info | Go |
|
Objective: To evaluate or simplify expressions containing fractional indices |
||||
| 9 | Indices/Exponents | Complex fractions as indices | Info | Go |
|
Objective: To evaluate or simplify expressions containing complex fractional indices and radicals |
||||
| 10 | Logarithms | Powers of 2 | Info | Go |
|
Objective: To convert between logarithm statements and indice statements |
||||
| 11 | Logarithms | Equations of type log x to the base 3 = 4 | Info | Go |
|
Objective: To find the value of x in a statement of type log x to the base 3 = 4 |
||||
| 12 | Logarithms | Equations of type log 32 to the base x = 5 | Info | Go |
|
Objective: To solve Logrithmic Equation where the variable is the base x = 5 |
||||
| 13 | Logarithms | Laws of Logarithms | Info | Go |
|
Objective: To review the logarithm laws |
||||
| 14 | Logarithms | Using the Log Laws to Expand Logarithmic Expressions | Info | Go |
|
Objective: To expand expressions using the logarithm laws |
||||
| 15 | Logarithms | Using the Log Laws to Simplify Expressions Involving Logarithms | Info | Go |
|
Objective: To simplify expressions using the logarithm laws |
||||
| 16 | Logarithms | Using the Log Laws to Find the Logarithms of Numbers | Info | Go |
|
Objective: To find the logarithm of a number, with an unknown base, using the logarithm laws |
||||
| 17 | Logarithms | Equations Involving Logarithms | Info | Go |
|
Objective: To solve equations involving logarithms using the logarithm laws |
||||
| 18 | Logarithms | Using Logarithms to Solve Equations | Info | Go |
|
Objective: To use logarithms to solve exponential equations |
||||
| 19 | Logarithms | Change of Base Formula | Info | Go |
|
Objective: To evaluate log expressions using logarithms |
||||
| 20 | Logarithms | The Graph of the Logarithmic Curve | Info | Go |
|
Objective: To learn the properties of the logarithmic curve |
||||
| 21 | Logarithms | The Graph of the Logarithmic Curve | Info | Go |
|
Objective: To solve problems involving logarithmic curves |
||||
| 22 | Graphs part 2 | The Exponential Function | Info | Go |
|
Objective: To graph exponential curves whose exponents are either positive or negative |
||||
| 23 | Graphs part 2 | Logarithmic Functions | Info | Go |
|
Objective: To graph and describe log curves whose equations are of the form y = log (ax + b) |
||||
| 24 | Polynomials | Introduction to polynomials | Info | Go |
|
Objective: To define polynomials by degree, leading term, leading coefficient, constant term and monic |
||||
| 25 | Polynomials | The Sum, Difference and Product of Two Polynomials | Info | Go |
|
Objective: To add, subtract and multiply polynomials |
||||
| 26 | Polynomials | Polynomials and Long Division | Info | Go |
|
Objective: To perform long division of polynomials, finding quotient and remainder |
||||
| 27 | Polynomials | The Remainder Theorem | Info | Go |
|
Objective: To determine a remainder when a first polynomial is divided by a second |
||||
| 28 | Polynomials | More on Remainder Theorem | Info | Go |
|
Objective: To determine polynomial coefficients given a divisor and remainder |
||||
| 29 | Polynomials | The factor theorem | Info | Go |
|
Objective: To use the factor theorem to show that (x-a) is a factor of P(x) |
||||
| 30 | Polynomials | More on the factor theorem | Info | Go |
|
Objective: To use the factor theorem to find algebraic variables in polynomials |
||||
| 31 | Polynomials | Complete factorisations using the factor theorem | Info | Go |
|
Objective: To use the factor theorem to derive factors of a polynomial |
||||
| 32 | Polynomials | Polynomial equations | Info | Go |
|
Objective: To practise solving polynomial equations |
||||
| 33 | Polynomials | Graphs of polynomials | Info | Go |
|
Objective: To derive graphs of polynomials by factorising |
||||
| 34 | Graphs part 2 | Graphing complex polynomials: quadratics with no real roots | Info | Go |
|
Objective: To graph quadratics that have no real roots, hence don't cut the x-axis |
||||
| 35 | Graphs part 2 | General equation of a circle: determine and graph the equation | Info | Go |
|
Objective: To determine and graph the equation of a circle with radius a and centre (h,k) |
||||
| 36 | Graphs part 2 | Graphing cubic curves | Info | Go |
|
Objective: To graph cubic curves whose equation is of the form y = (x - a)^3 + b or y = (a - x)^3 + b |
||||
| 37 | Function | Functions and Relations: domain and range | Info | Go |
|
Objective: To identify and represent functions and relations |
||||
| 38 | Function | Function Notation | Info | Go |
|
Objective: To write and evaluate functions using function notation |
||||
| 39 | Function | Selecting Appropriate Domain and Range | Info | Go |
|
Objective: To determine appropriate domains for functions |
||||
| 40 | Function | Domain and Range from Graphical Representations | Info | Go |
|
Objective: To determine the range of a function from its graphical representation |
||||
| 41 | Function | Evaluating and Graphing Piecewise Functions | Info | Go |
|
Objective: To evaluate and graph piecewise functions |
||||
| 42 | Function | Combining Functions | Info | Go |
|
Objective: To determine the resultant function after functions have been combined by plus, minus, times and divide |
||||
| 43 | Function | Simplifying Composite Functions | Info | Go |
|
Objective: To simplify, evaluate and determine the domain of composite functions |
||||
| 44 | Function | Inverse Functions | Info | Go |
|
Objective: To find the inverse of a function and determine whether this inverse is itself a function |
||||
| 45 | Function | Polynomial Addition: in Combining and Simplifying Functions | Info | Go |
|
Objective: To evaluate, simplify and graph rational functions |
||||
| 46 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 1 Sin] | Info | Go |
|
Objective: To use the sine ratio to calculate the opposite side of a right-angled triangle |
||||
| 47 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 2 Cosine] | Info | Go |
|
Objective: To use the cosine ratio to calculate the adjacent side of a right-angle triangle |
||||
| 48 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 3 Tangent Ratio] | Info | Go |
|
Objective: To use the tangent ratio to calculate the opposite side of a right-angled triangle |
||||
| 49 | Trigonometry part 1 | Unknown in the Denominator [Case 4] | Info | Go |
|
Objective: To use trigonometry to find sides of a right-angled triangle and the Unknown in denominator |
||||
| 50 | Trigonometry part 1 | Bearings: The Compass | Info | Go |
|
Objective: To change from true bearings to compass bearings and vice versa |
||||
| 51 | Trigonometry part 1 | Angles of Elevation and Depression | Info | Go |
|
Objective: To identify and distinguish between angles of depression and elevation |
||||
| 52 | Trigonometry part 1 | Trigonometric Ratios in Practical Situations | Info | Go |
|
Objective: To solve problems involving bearings and angles of elevation and depression |
||||
| 53 | Trigonometry part 1 | The Cosine Rule to find an unknown side [Case 1 SAS] | Info | Go |
|
Objective: To complete the cosine rule to find a subject side for given triangles |
||||
| 54 | Trigonometry part 1 | The Sine Rule to find an unknown side: Case 1 | Info | Go |
|
Objective: To complete the cosine rule to find a subject angle for given triangles |
||||
| 55 | Trigonometry part 1 | The Sine Rule: Finding a Side | Info | Go |
|
Objective: To find an unknown side of a triangle using the sine rule |
||||
| 56 | Trigonometry part 1 | The Sine Rule: Finding an Angle | Info | Go |
|
Objective: To find an unknown angle of a triangle using the sine rule |
||||
| 57 | Trigonometry part 2 | Trigonometric ratios of 0°, 90°, 180°, 270° and 360° | Info | Go |
|
Objective: To find trigonometric ratios of 0, 90, 180, 270 and 360 degrees |
||||
| 58 | Trigonometry part 2 | Graphing the Trigonometric Ratios I: Sine Curve | Info | Go |
|
Objective: To recognise the sine curve and explore shifts of phase and amplitude |
||||
| 59 | Trigonometry part 2 | Graphing the Trigonometric Ratios II: Cosine Curve | Info | Go |
|
Objective: To recognise the cosine curve and explore shifts of phase and amplitude |
||||
| 60 | Trigonometry part 2 | Graphing the Trigonometric Ratios III: Tangent Curve | Info | Go |
|
Objective: To recognise the tangent curve and explore shifts of phase and amplitude |
||||
| 61 | Trigonometry part 2 | Graphing the Trigonometric Ratios IV: Reciprocal Ratios | Info | Go |
|
Objective: To graph the primary trigonometric functions and their inverses |
||||
| 62 | Trigonometry part 2 | Using One Trig. Ratio to Find Another | Info | Go |
|
Objective: To derive trig ratios complement from one given trig ratio + some other quadrant identifier. |
||||
| 63 | Trigonometry part 2 | Solving Trigonometric Equations - Type I | Info | Go |
|
Objective: To Solve trigonometric equations for angles from 0 to 360 degrees. |
||||
| 64 | Trigonometry part 2 | Solving Trigonometric Equations - Type II | Info | Go |
|
Objective: To solve trigonometric equations for angles from 0 to 360 degrees. |
||||
| 65 | Trigonometry part 2 | Solving Trigonometric Equations - Type III | Info | Go |
|
Objective: To solve trigonometric equations using tan? = sin?/cos?. |
||||
| 66 | Matrices | Vectors | Info | Go |
|
Objective: To use vectors to find resultant speeds and displacements |
||||
| 67 | Matrices - Linear systems | Number of Solutions | Info | Go |
|
Objective: To determine solutions to systems of equations |
||||
| 68 | Matrices - Linear systems | Vector Addition in 2 and 3D | Info | Go |
|
Objective: To represent, add, subtract and determine the direction of vectors |
||||
| 69 | Polar coordinates | Polar Coordinates - Plotting and Converting | Info | Go |
|
Objective: To plot polar points and convert polar coordinates to rectangular coordinates |
||||
| 70 | Polar coordinates | Converting Rectangular Coordinates to Polar Form | Info | Go |
|
Objective: To convert rectangular to polar coordinates |
||||
| 71 | Polar coordinates | Graphing Polar Functions | Info | Go |
|
Objective: To write the polar coordinates of a point for selected argument ranges |
||||
| 72 | Measurement - Advanced area | Area of a Trapezium | Info | Go |
|
Objective: To calculate the area of trapezia using A=(h/2)(a+b) |
||||
| 73 | Measurement - Advanced area | Area of a Rhombus | Info | Go |
|
Objective: To calculate the area of a rhombus using diagonal products |
||||
| 74 | Measurement - Advanced area | Area of a Circle | Info | Go |
|
Objective: To calculate the area of circles and sectors and to solve circle problems |
||||
| 75 | Measurement - Advanced area | Area of Regular Polygons and Composite Figures | Info | Go |
|
Objective: To calculate area of composite figures and solve problems using correct formulae |
||||
| 76 | Measurement - Advanced volume | Finding the volume of prisms | Info | Go |
|
Objective: To calculate the volume of prisms using V=Ah and solve volume problems |
||||
| 77 | Measurement - Advanced volume | Volume of a Cylinder and Sphere | Info | Go |
|
Objective: To solve problems and calculate volumes of cylinders and spheres and parts of each |
||||
| 78 | Measurement - Advanced volume | Volume of Pyramids and Cones | Info | Go |
|
Objective: To calculate the volumes of pyramids and cones |
||||
| 79 | Measurement - Advanced volume | Composite Solids | Info | Go |
|
Objective: To calculate the volume of composite figures using appropriate formulae |
||||
| 80 | Surface area | Surface Area of a Cube/Rectangular Prism | Info | Go |
|
Objective: To calculate the surface area of cubes and rectangular prisms |
||||
| 81 | Surface area | Surface Area of a Triangular/Trapezoidal Prism | Info | Go |
|
Objective: To calculate the surface area of triangular and trapezoidal prisms |
||||
| 82 | Surface area | Surface Area of a Cylinder and Sphere | Info | Go |
|
Objective: To calculate the surface area of cylinders and spheres |
||||
| 83 | Surface area | Surface Area of Pyramids | Info | Go |
|
Objective: To calculate the surface area of pyramids |
||||
| 84 | Surface area | Surface Area of Composite Solids | Info | Go |
|
Objective: To calculate the surface area of composite solids |
||||
| 85 | Surface area | Surface area of composite solids | Info | Go |
|
Objective: On completion of the lesson the student will be able to find the surface areas of Composite solids. |
||||
| 86 | Geometry part 2 | Similar Triangles | Info | Go |
|
Objective: To use similarity tests for triangles and determine unknown sides and angles in triangles |
||||
| 87 | Geometry part 2 | Using Similar Triangles to Calculate Lengths | Info | Go |
|
Objective: To determine unknown sides and angles of similar triangles |
||||
| 88 | Geometry part 2 | Examples involving overlapping triangles | Info | Go |
|
Objective: To determine the lengths of unknown sides in overlapping or adjacent similar triangles |
||||
| 89 | Geometry part 3 | The Triangle Inequality Theorem | Info | Go |
|
Objective: To use the triangle inequality theorem to determine constructability of triangles |
||||
| 90 | Circle geometry part 1 | Theorem - Equal arcs subtend equal angles at the centre | Info | Go |
|
Objective: To know that equal arcs on circles of equal radii subtend equal angles at the centre |
||||
| 91 | Circle geometry part 1 | Theorem - The perpendicular from the centre to a chord bisects the chord | Info | Go |
|
Objective: To know that the perpendicular from the centre of a circle to a chord bisects the chord and to know that the line from the centre of a circle to the mid-point of a chord is perpendicular to the chord |
||||
| 92 | Circle geometry part 1 | Theorem - Equal chords in a circle are equidistant from the centre | Info | Go |
|
Objective: To know that equal chords in equal circles are equidistant from the centres |
||||
| 93 | Circle geometry part 1 | Theorem - At the point of contact a tangent is perpendicular to the radius | Info | Go |
|
Objective: To know that the tangent to a circle is perpendicular to the radius drawn to it |
||||
| 94 | Circle geometry part 1 | Theorem: Tangents to a circle from an external point are equal | Info | Go |
|
Objective: To know that the tangents to a circle from an external point are equal |
||||
| 95 | Exam | Exam - Grade 12 - Mathematics of College Technology | Info | Go |
|
Objective: Exam |
||||
Join today and have your whole family enjoy the benefits that only a great educational product can deliver. With a 14-day Money Back Guarantee you can't afford not to join!Enquiry form
Simply fill out our enquiry form with any questions or suggestions you may have. Our friendly staff is more
than keen to answer any question you have regarding
our learning system or general questions. Enquiry form