| 1 |
Study Plan |
Study plan – Grade 12 – Calculus and Vectors |
| Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. |
| 2 |
Co-ordinate geometry part 2 |
Two Point Formula: equation of a line which joins a pair of points |
| Objective: To find the equation of the line which joins a pair of points |
| 3 |
Co-ordinate geometry part 2 |
Intercept form of a straight line: find the equation when given x and y |
| Objective: To find the equation of a line given the x-axis and y-axis intercepts |
| 4 |
Co-ordinate geometry part 2 |
Parallel Lines: identify equation of a line parallel to another |
| Objective: To change the standard form of a straight line equation to the y = mx + b form |
| 5 |
Co-ordinate geometry part 2 |
Perpendicular Lines |
| Objective: To identify the equation of a line that is perpendicular to a given linear equation |
| 6 |
Co-ordinate geometry part 2 |
Inequalities on the Number Plane |
| Objective: To identify the graph which matches a given inequality |
| 7 |
Co-ordinate geometry part 2 |
Perpendicular Distance |
| Objective: To calculate the perpendicular distance from a point to a line and between lines |
| 8 |
Co-ordinate geometry part 2 |
Line through the intersection of two given lines |
| Objective: To determine the equation of a line passing through the intersection of two lines |
| 9 |
Co-ordinate geometry part 2 |
Angles between two lines |
| Objective: To find the angle between two given straight lines |
| 10 |
Co-ordinate geometry part 2 |
Transformations: Reflections |
| Objective: To identify reflections and to use isometric properties of reflections |
| 11 |
Geometry transformations |
Geometry Transformations without Matrices: Translation |
| Objective: To find the image of a point or object after a translation |
| 12 |
Geometry transformations |
Geometry Transformations without Matrices: Rotation |
| Objective: To determine rotation angle and to perform prescribed rotations |
| 13 |
Geometry transformations |
Geometry Transformations without Matrices: Dilation or Enlargement |
| Objective: To describe dilations and to calculate lengths and scale factors of dilated figures |
| 14 |
Geometry transformations |
Geometry Transformations without Matrices: Mixed and Combined Transformations |
| Objective: To identify images produced by a given sequence of transformations |
| 15 |
Graphs part 2 |
The Exponential Function |
| Objective: To graph exponential curves whose exponents are either positive or negative |
| 16 |
Calculus part 1 |
Limits |
| Objective: To find the limit value of a function as x approaches n |
| 17 |
Calculus part 1 |
Differentiation from First Principles |
| Objective: To differentiate functions from first principles |
| 18 |
Calculus part 1 |
Differentiation of y = x to the power of n |
| Objective: To differentiate algebraic functions using the laws of differentiation |
| 19 |
Calculus part 1 |
Meaning of dy over dx – Equations of Tangents and Normals |
| Objective: To find and use the slope of tangents and normals |
| 20 |
Calculus part 1 |
Function of a Function Rule, Product Rule, Quotient Rule. |
| Objective: To differentiate functions using the product, quotient and chain rules. |
| 21 |
Calculus part 1 |
Increasing, Decreasing and Stationary Functions. |
| Objective: To determine values of x for which f(x) is increasing, decreasing or stationary. |
| 22 |
Calculus part 1 |
The Second Derivative – Concavity. |
| Objective: To determine concavity of a curve at a point using the second derivative. |
| 23 |
Calculus part 1 |
Classification of Stationary Points. |
| Objective: To Locate and describe stationary points and points of inflection using differention. |
| 24 |
Calculus part 2 |
Curve Sketching. |
| Objective: To practice curve sketching of polynomials using calculus techniques. |
| 25 |
Calculus part 2 |
Practical Applications of Maxima and Minima. |
| Objective: To use maxima and minima to solve practical problems. |
| 26 |
Polar coordinates |
Polar Coordinates – Plotting and Converting |
| Objective: To plot polar points and convert polar coordinates to rectangular coordinates |
| 27 |
Polar coordinates |
Converting Rectangular Coordinates to Polar Form |
| Objective: To convert rectangular to polar coordinates |
| 28 |
Matrices |
Vectors |
| Objective: To use vectors to find resultant speeds and displacements |
| 29 |
Matrices – Linear systems |
Number of Solutions |
| Objective: To determine solutions to systems of equations |
| 30 |
Matrices – Linear systems |
Vector Addition in 2 and 3D |
| Objective: To represent, add, subtract and determine the direction of vectors |
| 31 |
Matrices – Linear systems |
Optimal Solutions |
| Objective: To use linear programming to maximise or minimise an objective function |
| 32 |
Function |
Functions and Relations: domain and range |
| Objective: To identify and represent functions and relations |
| 33 |
Function |
Function Notation |
| Objective: To write and evaluate functions using function notation |
| 34 |
Function |
Selecting Appropriate Domain and Range |
| Objective: To determine appropriate domains for functions |
| 35 |
Function |
Domain and Range from Graphical Representations |
| Objective: To determine the range of a function from its graphical representation |
| 36 |
Function |
Evaluating and Graphing Piecewise Functions |
| Objective: To evaluate and graph piecewise functions |
| 37 |
Function |
Combining Functions |
| Objective: To determine the resultant function after functions have been combined by plus, minus, times and divide |
| 38 |
Function |
Simplifying Composite Functions |
| Objective: To simplify, evaluate and determine the domain of composite functions |
| 39 |
Function |
Inverse Functions |
| Objective: To find the inverse of a function and determine whether this inverse is itself a function |
| 40 |
Function |
Graphing Rational Functions Part 1 |
| Objective: To determine asymptotes and graph rational functions using intercepts and asymptotes |
| 41 |
Function |
Graphing Rational Functions Part 2 |
| Objective: To determine asymptotes and graph rational functions |
| 42 |
Function |
Parametric Equations |
| Objective: To interchange parametric and Cartesian equations and to identify graphs |
| 43 |
Function |
Polynomial Addition: in Combining and Simplifying Functions |
| Objective: To evaluate, simplify and graph rational functions |
| 44 |
Function |
Parametric Functions |
| Objective: To change Cartesian and parametric equations and to graph parametric functions |
| 45 |
Exam |
Exam – Grade 12 – Calculus and Vectors |
| Objective: Exam |
