| 1 |
Study Plan |
Study plan – Grade 12 – Mathematics of College Technology |
| 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 |
| Objective: To add indices when multiplying powers that have the same base |
| 3 |
Indices/Exponents |
Subtracting indices when dividing terms with the same base |
| Objective: To subtract indices when dividing powers of the same base |
| 4 |
Indices/Exponents |
Multiplying indices when raising a power to a power |
| Objective: To multiply indices when raising a power to a power |
| 5 |
Indices/Exponents |
Multiplying indices when raising to more than one term |
| Objective: To raise power products to a power |
| 6 |
Indices/Exponents |
Terms raised to the power of zero |
| Objective: To evaluate expressions where quantities are raised to the power 0 |
| 7 |
Indices/Exponents |
Negative Indices |
| Objective: To evaluate or simplify expressions containing negative indices |
| 8 |
Indices/Exponents |
Fractional Indices |
| Objective: To evaluate or simplify expressions containing fractional indices |
| 9 |
Indices/Exponents |
Complex fractions as indices |
| Objective: To evaluate or simplify expressions containing complex fractional indices and radicals |
| 10 |
Logarithms |
Powers of 2 |
| Objective: To convert between logarithm statements and indice statements |
| 11 |
Logarithms |
Equations of type log x to the base 3 = 4 |
| 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 |
| Objective: To solve Logrithmic Equation where the variable is the base x = 5 |
| 13 |
Logarithms |
Laws of Logarithms |
| Objective: To review the logarithm laws |
| 14 |
Logarithms |
Using the Log Laws to Expand Logarithmic Expressions |
| Objective: To expand expressions using the logarithm laws |
| 15 |
Logarithms |
Using the Log Laws to Simplify Expressions Involving Logarithms |
| Objective: To simplify expressions using the logarithm laws |
| 16 |
Logarithms |
Using the Log Laws to Find the Logarithms of Numbers |
| Objective: To find the logarithm of a number, with an unknown base, using the logarithm laws |
| 17 |
Logarithms |
Equations Involving Logarithms |
| Objective: To solve equations involving logarithms using the logarithm laws |
| 18 |
Logarithms |
Using Logarithms to Solve Equations |
| Objective: To use logarithms to solve exponential equations |
| 19 |
Logarithms |
Change of Base Formula |
| Objective: To evaluate log expressions using logarithms |
| 20 |
Logarithms |
The Graph of the Logarithmic Curve |
| Objective: To learn the properties of the logarithmic curve |
| 21 |
Logarithms |
The Graph of the Logarithmic Curve |
| Objective: To solve problems involving logarithmic curves |
| 22 |
Graphs part 2 |
The Exponential Function |
| Objective: To graph exponential curves whose exponents are either positive or negative |
| 23 |
Graphs part 2 |
Logarithmic Functions |
| Objective: To graph and describe log curves whose equations are of the form y = log (ax + b) |
| 24 |
Polynomials |
Introduction to polynomials |
| Objective: To define polynomials by degree, leading term, leading coefficient, constant term and monic |
| 25 |
Polynomials |
The Sum, Difference and Product of Two Polynomials |
| Objective: To add, subtract and multiply polynomials |
| 26 |
Polynomials |
Polynomials and Long Division |
| Objective: To perform long division of polynomials, finding quotient and remainder |
| 27 |
Polynomials |
The Remainder Theorem |
| Objective: To determine a remainder when a first polynomial is divided by a second |
| 28 |
Polynomials |
More on Remainder Theorem |
| Objective: To determine polynomial coefficients given a divisor and remainder |
| 29 |
Polynomials |
The factor theorem |
| Objective: To use the factor theorem to show that (x-a) is a factor of P(x) |
| 30 |
Polynomials |
More on the factor theorem |
| Objective: To use the factor theorem to find algebraic variables in polynomials |
| 31 |
Polynomials |
Complete factorisations using the factor theorem |
| Objective: To use the factor theorem to derive factors of a polynomial |
| 32 |
Polynomials |
Polynomial equations |
| Objective: To practise solving polynomial equations |
| 33 |
Polynomials |
Graphs of polynomials |
| Objective: To derive graphs of polynomials by factorising |
| 34 |
Graphs part 2 |
Graphing complex polynomials: quadratics with no real roots |
| 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 |
| Objective: To determine and graph the equation of a circle with radius a and centre (h,k) |
| 36 |
Graphs part 2 |
Graphing cubic curves |
| 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 |
| Objective: To identify and represent functions and relations |
| 38 |
Function |
Function Notation |
| Objective: To write and evaluate functions using function notation |
| 39 |
Function |
Selecting Appropriate Domain and Range |
| Objective: To determine appropriate domains for functions |
| 40 |
Function |
Domain and Range from Graphical Representations |
| Objective: To determine the range of a function from its graphical representation |
| 41 |
Function |
Evaluating and Graphing Piecewise Functions |
| Objective: To evaluate and graph piecewise functions |
| 42 |
Function |
Combining Functions |
| Objective: To determine the resultant function after functions have been combined by plus, minus, times and divide |
| 43 |
Function |
Simplifying Composite Functions |
| Objective: To simplify, evaluate and determine the domain of composite functions |
| 44 |
Function |
Inverse Functions |
| 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 |
| Objective: To evaluate, simplify and graph rational functions |
| 46 |
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 |
| 47 |
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 |
| 48 |
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 |
| 49 |
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 |
| 50 |
Trigonometry part 1 |
Bearings: The Compass |
| Objective: To change from true bearings to compass bearings and vice versa |
| 51 |
Trigonometry part 1 |
Angles of Elevation and Depression |
| Objective: To identify and distinguish between angles of depression and elevation |
| 52 |
Trigonometry part 1 |
Trigonometric Ratios in Practical Situations |
| 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] |
| 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 |
| Objective: To complete the cosine rule to find a subject angle for given triangles |
| 55 |
Trigonometry part 1 |
The Sine Rule: Finding a Side |
| Objective: To find an unknown side of a triangle using the sine rule |
| 56 |
Trigonometry part 1 |
The Sine Rule: Finding an Angle |
| 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° |
| Objective: To find trigonometric ratios of 0, 90, 180, 270 and 360 degrees |
| 58 |
Trigonometry part 2 |
Graphing the Trigonometric Ratios I: Sine Curve |
| Objective: To recognise the sine curve and explore shifts of phase and amplitude |
| 59 |
Trigonometry part 2 |
Graphing the Trigonometric Ratios II: Cosine Curve |
| Objective: To recognise the cosine curve and explore shifts of phase and amplitude |
| 60 |
Trigonometry part 2 |
Graphing the Trigonometric Ratios III: Tangent Curve |
| Objective: To recognise the tangent curve and explore shifts of phase and amplitude |
| 61 |
Trigonometry part 2 |
Graphing the Trigonometric Ratios IV: Reciprocal Ratios |
| Objective: To graph the primary trigonometric functions and their inverses |
| 62 |
Trigonometry part 2 |
Using One Trig. Ratio to Find Another |
| Objective: To derive trig ratios complement from one given trig ratio + some other quadrant identifier. |
| 63 |
Trigonometry part 2 |
Solving Trigonometric Equations – Type I |
| Objective: To Solve trigonometric equations for angles from 0 to 360 degrees. |
| 64 |
Trigonometry part 2 |
Solving Trigonometric Equations – Type II |
| Objective: To solve trigonometric equations for angles from 0 to 360 degrees. |
| 65 |
Trigonometry part 2 |
Solving Trigonometric Equations – Type III |
| Objective: To solve trigonometric equations using tan? = sin?/cos?. |
| 66 |
Matrices |
Vectors |
| Objective: To use vectors to find resultant speeds and displacements |
| 67 |
Matrices – Linear systems |
Number of Solutions |
| Objective: To determine solutions to systems of equations |
| 68 |
Matrices – Linear systems |
Vector Addition in 2 and 3D |
| Objective: To represent, add, subtract and determine the direction of vectors |
| 69 |
Polar coordinates |
Polar Coordinates – Plotting and Converting |
| Objective: To plot polar points and convert polar coordinates to rectangular coordinates |
| 70 |
Polar coordinates |
Converting Rectangular Coordinates to Polar Form |
| Objective: To convert rectangular to polar coordinates |
| 71 |
Polar coordinates |
Graphing Polar Functions |
| Objective: To write the polar coordinates of a point for selected argument ranges |
| 72 |
Measurement – Advanced area |
Area of a Trapezium |
| Objective: To calculate the area of trapezia using A=(h/2)(a+b) |
| 73 |
Measurement – Advanced area |
Area of a Rhombus |
| Objective: To calculate the area of a rhombus using diagonal products |
| 74 |
Measurement – Advanced area |
Area of a Circle |
| 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 |
| Objective: To calculate area of composite figures and solve problems using correct formulae |
| 76 |
Measurement – Advanced volume |
Finding the volume of prisms |
| Objective: To calculate the volume of prisms using V=Ah and solve volume problems |
| 77 |
Measurement – Advanced volume |
Volume of a Cylinder and Sphere |
| Objective: To solve problems and calculate volumes of cylinders and spheres and parts of each |
| 78 |
Measurement – Advanced volume |
Volume of Pyramids and Cones |
| Objective: To calculate the volumes of pyramids and cones |
| 79 |
Measurement – Advanced volume |
Composite Solids |
| Objective: To calculate the volume of composite figures using appropriate formulae |
| 80 |
Surface area |
Surface Area of a Cube/Rectangular Prism |
| Objective: To calculate the surface area of cubes and rectangular prisms |
| 81 |
Surface area |
Surface Area of a Triangular/Trapezoidal Prism |
| Objective: To calculate the surface area of triangular and trapezoidal prisms |
| 82 |
Surface area |
Surface Area of a Cylinder and Sphere |
| Objective: To calculate the surface area of cylinders and spheres |
| 83 |
Surface area |
Surface Area of Pyramids |
| Objective: To calculate the surface area of pyramids |
| 84 |
Surface area |
Surface Area of Composite Solids |
| Objective: To calculate the surface area of composite solids |
| 85 |
Surface area |
Surface area of composite solids |
| 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 |
| 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 |
| Objective: To determine unknown sides and angles of similar triangles |
| 88 |
Geometry part 2 |
Examples involving overlapping triangles |
| Objective: To determine the lengths of unknown sides in overlapping or adjacent similar triangles |
| 89 |
Geometry part 3 |
The Triangle Inequality Theorem |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| Objective: To know that the tangents to a circle from an external point are equal |
| 95 |
Exam |
Exam – Grade 12 – Mathematics of College Technology |
| Objective: Exam |
