| 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 |
