# Grade 12 – Advanced Functions Mathematics – Canada

### 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 |