# Grade 12 – Mathematics of College Technology Mathematics – Canada

### Grade 12 – Mathematics of College Technology Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Study Plan | Study plan – Grade 12 – Mathematics of College Technology | |

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 | Polynomials | Introduction to polynomials | |

Objective: To define polynomials by degree, leading term, leading coefficient, constant term and monic | |||

25 | Polynomials | The Sum, Difference and Product of Two Polynomials | |

Objective: To add, subtract and multiply polynomials | |||

26 | Polynomials | Polynomials and Long Division | |

Objective: To perform long division of polynomials, finding quotient and remainder | |||

27 | Polynomials | The Remainder Theorem | |

Objective: To determine a remainder when a first polynomial is divided by a second | |||

28 | Polynomials | More on Remainder Theorem | |

Objective: To determine polynomial coefficients given a divisor and remainder | |||

29 | Polynomials | The factor theorem | |

Objective: To use the factor theorem to show that (x-a) is a factor of P(x) | |||

30 | Polynomials | More on the factor theorem | |

Objective: To use the factor theorem to find algebraic variables in polynomials | |||

31 | Polynomials | Complete factorisations using the factor theorem | |

Objective: To use the factor theorem to derive factors of a polynomial | |||

32 | Polynomials | Polynomial equations | |

Objective: To practise solving polynomial equations | |||

33 | Polynomials | Graphs of polynomials | |

Objective: To derive graphs of polynomials by factorising | |||

34 | Graphs part 2 | Graphing complex polynomials: quadratics with no real roots | |

Objective: To graph quadratics that have no real roots, hence don’t cut the x-axis | |||

35 | Graphs part 2 | General equation of a circle: determine and graph the equation | |

Objective: To determine and graph the equation of a circle with radius a and centre (h,k) | |||

36 | Graphs part 2 | Graphing cubic curves | |

Objective: To graph cubic curves whose equation is of the form y = (x – a)^3 + b or y = (a – x)^3 + b | |||

37 | Function | Functions and Relations: domain and range | |

Objective: To identify and represent functions and relations | |||

38 | Function | Function Notation | |

Objective: To write and evaluate functions using function notation | |||

39 | Function | Selecting Appropriate Domain and Range | |

Objective: To determine appropriate domains for functions | |||

40 | Function | Domain and Range from Graphical Representations | |

Objective: To determine the range of a function from its graphical representation | |||

41 | Function | Evaluating and Graphing Piecewise Functions | |

Objective: To evaluate and graph piecewise functions | |||

42 | Function | Combining Functions | |

Objective: To determine the resultant function after functions have been combined by plus, minus, times and divide | |||

43 | Function | Simplifying Composite Functions | |

Objective: To simplify, evaluate and determine the domain of composite functions | |||

44 | Function | Inverse Functions | |

Objective: To find the inverse of a function and determine whether this inverse is itself a function | |||

45 | Function | Polynomial Addition: in Combining and Simplifying Functions | |

Objective: To evaluate, simplify and graph rational functions | |||

46 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 1 Sin] | |

Objective: To use the sine ratio to calculate the opposite side of a right-angled triangle | |||

47 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 2 Cosine] | |

Objective: To use the cosine ratio to calculate the adjacent side of a right-angle triangle | |||

48 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 3 Tangent Ratio] | |

Objective: To use the tangent ratio to calculate the opposite side of a right-angled triangle | |||

49 | Trigonometry part 1 | Unknown in the Denominator [Case 4] | |

Objective: To use trigonometry to find sides of a right-angled triangle and the Unknown in denominator | |||

50 | Trigonometry part 1 | Bearings: The Compass | |

Objective: To change from true bearings to compass bearings and vice versa | |||

51 | Trigonometry part 1 | Angles of Elevation and Depression | |

Objective: To identify and distinguish between angles of depression and elevation | |||

52 | Trigonometry part 1 | Trigonometric Ratios in Practical Situations | |

Objective: To solve problems involving bearings and angles of elevation and depression | |||

53 | Trigonometry part 1 | The Cosine Rule to find an unknown side [Case 1 SAS] | |

Objective: To complete the cosine rule to find a subject side for given triangles | |||

54 | Trigonometry part 1 | The Sine Rule to find an unknown side: Case 1 | |

Objective: To complete the cosine rule to find a subject angle for given triangles | |||

55 | Trigonometry part 1 | The Sine Rule: Finding a Side | |

Objective: To find an unknown side of a triangle using the sine rule | |||

56 | Trigonometry part 1 | The Sine Rule: Finding an Angle | |

Objective: To find an unknown angle of a triangle using the sine rule | |||

57 | 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 | |||

58 | Trigonometry part 2 | Graphing the Trigonometric Ratios I: Sine Curve | |

Objective: To recognise the sine curve and explore shifts of phase and amplitude | |||

59 | Trigonometry part 2 | Graphing the Trigonometric Ratios II: Cosine Curve | |

Objective: To recognise the cosine curve and explore shifts of phase and amplitude | |||

60 | Trigonometry part 2 | Graphing the Trigonometric Ratios III: Tangent Curve | |

Objective: To recognise the tangent curve and explore shifts of phase and amplitude | |||

61 | Trigonometry part 2 | Graphing the Trigonometric Ratios IV: Reciprocal Ratios | |

Objective: To graph the primary trigonometric functions and their inverses | |||

62 | 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. | |||

63 | Trigonometry part 2 | Solving Trigonometric Equations – Type I | |

Objective: To Solve trigonometric equations for angles from 0 to 360 degrees. | |||

64 | Trigonometry part 2 | Solving Trigonometric Equations – Type II | |

Objective: To solve trigonometric equations for angles from 0 to 360 degrees. | |||

65 | Trigonometry part 2 | Solving Trigonometric Equations – Type III | |

Objective: To solve trigonometric equations using tan? = sin?/cos?. | |||

66 | Matrices | Vectors | |

Objective: To use vectors to find resultant speeds and displacements | |||

67 | Matrices – Linear systems | Number of Solutions | |

Objective: To determine solutions to systems of equations | |||

68 | Matrices – Linear systems | Vector Addition in 2 and 3D | |

Objective: To represent, add, subtract and determine the direction of vectors | |||

69 | Polar coordinates | Polar Coordinates – Plotting and Converting | |

Objective: To plot polar points and convert polar coordinates to rectangular coordinates | |||

70 | Polar coordinates | Converting Rectangular Coordinates to Polar Form | |

Objective: To convert rectangular to polar coordinates | |||

71 | Polar coordinates | Graphing Polar Functions | |

Objective: To write the polar coordinates of a point for selected argument ranges | |||

72 | Measurement – Advanced area | Area of a Trapezium | |

Objective: To calculate the area of trapezia using A=(h/2)(a+b) | |||

73 | Measurement – Advanced area | Area of a Rhombus | |

Objective: To calculate the area of a rhombus using diagonal products | |||

74 | Measurement – Advanced area | Area of a Circle | |

Objective: To calculate the area of circles and sectors and to solve circle problems | |||

75 | Measurement – Advanced area | Area of Regular Polygons and Composite Figures | |

Objective: To calculate area of composite figures and solve problems using correct formulae | |||

76 | Measurement – Advanced volume | Finding the volume of prisms | |

Objective: To calculate the volume of prisms using V=Ah and solve volume problems | |||

77 | Measurement – Advanced volume | Volume of a Cylinder and Sphere | |

Objective: To solve problems and calculate volumes of cylinders and spheres and parts of each | |||

78 | Measurement – Advanced volume | Volume of Pyramids and Cones | |

Objective: To calculate the volumes of pyramids and cones | |||

79 | Measurement – Advanced volume | Composite Solids | |

Objective: To calculate the volume of composite figures using appropriate formulae | |||

80 | Surface area | Surface Area of a Cube/Rectangular Prism | |

Objective: To calculate the surface area of cubes and rectangular prisms | |||

81 | Surface area | Surface Area of a Triangular/Trapezoidal Prism | |

Objective: To calculate the surface area of triangular and trapezoidal prisms | |||

82 | Surface area | Surface Area of a Cylinder and Sphere | |

Objective: To calculate the surface area of cylinders and spheres | |||

83 | Surface area | Surface Area of Pyramids | |

Objective: To calculate the surface area of pyramids | |||

84 | Surface area | Surface Area of Composite Solids | |

Objective: To calculate the surface area of composite solids | |||

85 | Surface area | Surface area of composite solids | |

Objective: On completion of the lesson the student will be able to find the surface areas of Composite solids. | |||

86 | Geometry part 2 | Similar Triangles | |

Objective: To use similarity tests for triangles and determine unknown sides and angles in triangles | |||

87 | Geometry part 2 | Using Similar Triangles to Calculate Lengths | |

Objective: To determine unknown sides and angles of similar triangles | |||

88 | Geometry part 2 | Examples involving overlapping triangles | |

Objective: To determine the lengths of unknown sides in overlapping or adjacent similar triangles | |||

89 | Geometry part 3 | The Triangle Inequality Theorem | |

Objective: To use the triangle inequality theorem to determine constructability of triangles | |||

90 | Circle geometry part 1 | Theorem – Equal arcs subtend equal angles at the centre | |

Objective: To know that equal arcs on circles of equal radii subtend equal angles at the centre | |||

91 | Circle geometry part 1 | Theorem – The perpendicular from the centre to a chord bisects the chord | |

Objective: To know that the perpendicular from the centre of a circle to a chord bisects the chord and to know that the line from the centre of a circle to the mid-point of a chord is perpendicular to the chord | |||

92 | Circle geometry part 1 | Theorem – Equal chords in a circle are equidistant from the centre | |

Objective: To know that equal chords in equal circles are equidistant from the centres | |||

93 | Circle geometry part 1 | Theorem – At the point of contact a tangent is perpendicular to the radius | |

Objective: To know that the tangent to a circle is perpendicular to the radius drawn to it | |||

94 | Circle geometry part 1 | Theorem: Tangents to a circle from an external point are equal | |

Objective: To know that the tangents to a circle from an external point are equal | |||

95 | Exam | Exam – Grade 12 – Mathematics of College Technology | |

Objective: Exam |