### Grade 12 – Calculus and Vectors Mathematics

# TOPIC TITLE
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