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Grade 12 – Advanced Functions Mathematics

# TOPIC TITLE
1 Study Plan Study plan – Grade 12 – Advanced Functions
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 Trigonometry part 1 Angles of Elevation and Depression
Objective: To identify and distinguish between angles of depression and elevation
25 Trigonometry part 1 Trigonometric Ratios in Practical Situations
Objective: To solve problems involving bearings and angles of elevation and depression
26 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
27 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
28 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
29 Trigonometry part 2 Reciprocal Ratios
Objective: To find the trigonometric ratios for a given right-angled triangle
30 Trigonometry part 2 Complementary Angle Results
Objective: To use complementary angle ratios to find an unknown angle given a trigonometric equality
31 Trigonometry part 2 Trigonometric Identities
Objective: To simplify expressions using trigonometric equalities
32 Trigonometry part 2 Angles of Any Magnitude
Objective: To assign angles to quadrants and to find trigonometric values for angles
33 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
34 Trigonometry part 2 Graphing the Trigonometric Ratios I: Sine Curve
Objective: To recognise the sine curve and explore shifts of phase and amplitude
35 Trigonometry part 2 Graphing the Trigonometric Ratios II: Cosine Curve
Objective: To recognise the cosine curve and explore shifts of phase and amplitude
36 Trigonometry part 2 Graphing the Trigonometric Ratios III: Tangent Curve
Objective: To recognise the tangent curve and explore shifts of phase and amplitude
37 Trigonometry part 2 Graphing the Trigonometric Ratios IV: Reciprocal Ratios
Objective: To graph the primary trigonometric functions and their inverses
38 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.
39 Trigonometry part 2 Solving Trigonometric Equations – Type I
Objective: To Solve trigonometric equations for angles from 0 to 360 degrees.
40 Trigonometry part 2 Solving Trigonometric Equations – Type II
Objective: To solve trigonometric equations for angles from 0 to 360 degrees.
41 Trigonometry part 2 Solving Trigonometric Equations – Type III
Objective: To solve trigonometric equations using tan? = sin?/cos?.
42 Trigonometry part 2 Trigonometric Sum and Difference Identities
Objective: To evaluate trig functions of angles using sum and difference identities
43 Trigonometry part 2 Double Angle Identities
Objective: To use double angle identities to evaluate trig. functions and solve trig equations
44 Trigonometry part 2 Half-angle Identities
Objective: To evaluate trig. functions of angles using half-angle identities
45 Polynomials Introduction to polynomials
Objective: To define polynomials by degree, leading term, leading coefficient, constant term and monic
46 Polynomials The Sum, Difference and Product of Two Polynomials
Objective: To add, subtract and multiply polynomials
47 Polynomials Polynomials and Long Division
Objective: To perform long division of polynomials, finding quotient and remainder
48 Polynomials The Remainder Theorem
Objective: To determine a remainder when a first polynomial is divided by a second
49 Polynomials More on Remainder Theorem
Objective: To determine polynomial coefficients given a divisor and remainder
50 Polynomials The factor theorem
Objective: To use the factor theorem to show that (x-a) is a factor of P(x)
51 Polynomials More on the factor theorem
Objective: To use the factor theorem to find algebraic variables in polynomials
52 Polynomials Complete factorisations using the factor theorem
Objective: To use the factor theorem to derive factors of a polynomial
53 Polynomials Polynomial equations
Objective: To practise solving polynomial equations
54 Polynomials Graphs of polynomials
Objective: To derive graphs of polynomials by factorising
55 Graphs part 2 The Rectangular Hyperbola
Objective: To graph rectangular hyperbolae whose equations are of the form xy = a and y = a/x
56 Function Functions and Relations: domain and range
Objective: To identify and represent functions and relations
57 Function Function Notation
Objective: To write and evaluate functions using function notation
58 Function Selecting Appropriate Domain and Range
Objective: To determine appropriate domains for functions
59 Function Domain and Range from Graphical Representations
Objective: To determine the range of a function from its graphical representation
60 Function Evaluating and Graphing Piecewise Functions
Objective: To evaluate and graph piecewise functions
61 Function Combining Functions
Objective: To determine the resultant function after functions have been combined by plus, minus, times and divide
62 Function Simplifying Composite Functions
Objective: To simplify, evaluate and determine the domain of composite functions
63 Function Inverse Functions
Objective: To find the inverse of a function and determine whether this inverse is itself a function
64 Function Graphing Rational Functions Part 1
Objective: To determine asymptotes and graph rational functions using intercepts and asymptotes
65 Function Graphing Rational Functions Part 2
Objective: To determine asymptotes and graph rational functions
66 Function Parametric Equations
Objective: To interchange parametric and Cartesian equations and to identify graphs
67 Function Polynomial Addition: in Combining and Simplifying Functions
Objective: To evaluate, simplify and graph rational functions
68 Uniform motion The Speed Formula
Objective: To calculate speed, distance or time using speed = distance/time
69 Uniform motion Using Subscripted Variables
Objective: To use subscripted variables to solve motion problems
70 Uniform motion Uniform Motion With Equal Distances
Objective: To solve motion problems where distances are equal
71 Uniform motion Uniform Motion Adding the Distances
Objective: To solve motion problems where total distance travelled is given
72 Uniform motion Uniform Motion With Unequal Distances or Time
Objective: To solve motion problems where either distance or time are different
73 Uniform motion Uniform Motion Problems Where the Rate is Constant
Objective: To solve miscellaneous motion problems where the rate is constant
74 Uniform motion Vertical Motion under gravity: Object Dropped from Rest
Objective: To calculate velocity, time and distance for vertically falling objects dropped from rest
75 Uniform motion Vertical Motion under gravity: Initial Velocity not Zero
Objective: To calculate velocity, time and distance for vertical motion with initial velocity not zero
76 Exam Exam – Grade 12 – Advanced Functions
Objective: Exam