# Grade 12 – Calculus and Vectors Mathematics – Canada

### 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 |