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Grade 12 – Mathematics of College Technology Mathematics

# TOPIC TITLE
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