# Grade 11 – Functions and Applications Mathematics – Canada

### Grade 11 – Functions and Applications Mathematics

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

1 | Study Plan | Study plan – Grade 11 – Functions and Applications | |

Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. | |||

2 | Algebra – Products and factors | Squaring a Binomial (monic) | |

Objective: To expand the square of a binomial by multiplication and by inspection | |||

3 | Algebra – Products and factors | Squaring a Binomial (nonmonic) | |

Objective: To expand the square of a nonmonic binomial by inspection | |||

4 | Algebra – Products and factors | Expansions Leading to the Difference of Two Squares | |

Objective: To expand the product of conjugate binomials leading to differences of squares | |||

5 | Algebra – Products and factors | Products in Simplification of Algebraic Expressions | |

Objective: To simplify algebraic expressions containing binomial products | |||

6 | Algebra – Products and factors | Larger Expansions | |

Objective: To expand and simplify the product of a binomial and a trinomial | |||

7 | Algebra – Products and factors | Highest Common Factor | |

Objective: To factorise an expression by identifying and extracting the highest common factor | |||

8 | Algebra – Products and factors | Factors by Grouping | |

Objective: To factorise a four-term expression by grouping | |||

9 | Algebra – Products and factors | Difference of Two Squares | |

Objective: To factorise differences of two squares | |||

10 | Algebra – Products and factors | Common factor and the difference of two squares | |

Objective: On completion of the lesson the student will be aware of common factors and recognize the difference of two squares. | |||

11 | Algebra – Products and factors | Quadratic Trinomials (monic): Case 1 | |

Objective: On completion of the lesson the student will understand the factorization of quadratic trinomial equations with all terms positive. | |||

12 | Algebra – Products and factors | Quadratic Trinomials (monic): Case 2 | |

Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative. | |||

13 | Algebra – Products and factors | Quadratic Trinomials (monic): Case 3 | |

Objective: On completion of the lesson the student will have an increased knowledge on factorizing quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative. | |||

14 | Algebra – Products and factors | Quadratic Trinomials (monic): Case 4 | |

Objective: On completion of the lesson the student will understand how to factorize all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative. | |||

15 | Algebra – Products and factors | Factorisation of nonmonic quadratic trinomials | |

Objective: To factorise nonmonic quadratic trinomials using the ‘X’ method | |||

16 | Algebra – Products and factors | Factorisation of nonmonic quadratic trinomials: Moon method | |

Objective: To factorise nonmonic quadratic trinomials using the ‘Moon’ method | |||

17 | Graphs part 1 | The parabola: to describe properties of a parabola from its equation | |

Objective: To describe properties of a parabola from its equation and sketch the parabola | |||

18 | Graphs part 1 | Quadratic Polynomials of the form y = ax^2 + bx + c | |

Objective: To describe and sketch parabolas of the form y = x^2 + bx + c | |||

19 | Graphs part 1 | Graphing perfect squares: y=(a-x) squared | |

Objective: To describe and sketch parabolas of the form y = (x – a)^2 | |||

20 | Graphs part 1 | Graphing irrational roots | |

Objective: To determine the vertex (using -b/2a), and other derived properties, to sketch a parabola | |||

21 | Graphs part 1 | Solving Simultaneous Equations graphically | |

Objective: To solve simultaneous equations graphically | |||

22 | Algebra – Quadratic equations | Introduction to Quadratic Equations | |

Objective: To find the solutions of quadratic equations presented as a product of factors | |||

23 | Algebra – Quadratic equations | Solving Quadratic Equations with Factorisation | |

Objective: To solve quadratic equations requiring factorisation | |||

24 | Algebra – Quadratic equations | Solving Quadratic Equations | |

Objective: To solve quadratic equations that need to be changed into the form ax^2 + bx + c = 0 | |||

25 | Algebra – Quadratic equations | Completing the square | |

Objective: To complete an incomplete square | |||

26 | Algebra – Quadratic equations | Solving Quadratic Equations by Completing the Square | |

Objective: To solve quadratic equations by completing the square | |||

27 | Algebra – Quadratic equations | The Quadratic Formula | |

Objective: To find the roots of a quadratic equation by using the quadratic formula | |||

28 | Algebra – Quadratic equations | Problem solving with quadratic equations | |

Objective: To solve problems which require finding the roots of a quadratic equation | |||

29 | Algebra – Quadratic equations | Solving Simultaneous Quadratic Equations Graphically | |

Objective: To determine points of intersection of quadratic and linear equations | |||

30 | Uniform motion | The Speed Formula | |

Objective: To calculate speed, distance or time using speed = distance/time | |||

31 | Uniform motion | Using Subscripted Variables | |

Objective: To use subscripted variables to solve motion problems | |||

32 | Uniform motion | Uniform Motion With Equal Distances | |

Objective: To solve motion problems where distances are equal | |||

33 | Uniform motion | Uniform Motion Adding the Distances | |

Objective: To solve motion problems where total distance travelled is given | |||

34 | Uniform motion | Uniform Motion With Unequal Distances or Time | |

Objective: To solve motion problems where either distance or time are different | |||

35 | Uniform motion | Uniform Motion Problems Where the Rate is Constant | |

Objective: To solve miscellaneous motion problems where the rate is constant | |||

36 | Uniform motion | Vertical Motion under gravity: Object Dropped from Rest | |

Objective: To calculate velocity, time and distance for vertically falling objects dropped from rest | |||

37 | 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 | |||

38 | Indices/Exponents | Adding indices when multiplying terms with the same base | |

Objective: To add indices when multiplying powers that have the same base | |||

39 | Indices/Exponents | Subtracting indices when dividing terms with the same base | |

Objective: To subtract indices when dividing powers of the same base | |||

40 | Indices/Exponents | Multiplying indices when raising a power to a power | |

Objective: To multiply indices when raising a power to a power | |||

41 | Indices/Exponents | Multiplying indices when raising to more than one term | |

Objective: To raise power products to a power | |||

42 | Indices/Exponents | Terms raised to the power of zero | |

Objective: To evaluate expressions where quantities are raised to the power 0 | |||

43 | Indices/Exponents | Negative Indices | |

Objective: To evaluate or simplify expressions containing negative indices | |||

44 | Indices/Exponents | Fractional Indices | |

Objective: To evaluate or simplify expressions containing fractional indices | |||

45 | Indices/Exponents | Complex fractions as indices | |

Objective: To evaluate or simplify expressions containing complex fractional indices and radicals | |||

46 | Algebra – Basic | Simplifying easy algebraic fractions | |

Objective: To simplify simple algebraic fractions using cancellation of common factors | |||

47 | Algebra – Basic | Simplifying algebraic fractions using the Index Laws | |

Objective: To use the index laws for division to simplify algebraic fractions | |||

48 | Algebra – Basic | Algebraic fractions resulting in negative Indices | |

Objective: To simplify algebraic fractions using negative indices (as required) in the answer | |||

49 | Algebra – Basic | Factorisation of algebraic fractions including binomials | |

Objective: To simplify algebraic fractions requiring the factorisation of binomial expressions | |||

50 | Algebra – Basic | Cancelling binomial factors in algebraic fractions | |

Objective: To simplify algebraic fractions with binomials in both the numerator and denominator | |||

51 | 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 | |||

52 | 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) | |||

53 | 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 | |||

54 | Graphs part 2 | Absolute Value Equations | |

Objective: To graph equations involving absolute values | |||

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 | Graphs part 2 | The Exponential Function | |

Objective: To graph exponential curves whose exponents are either positive or negative | |||

57 | Graphs part 2 | Logarithmic Functions | |

Objective: To graph and describe log curves whose equations are of the form y = log (ax + b) | |||

58 | Conic sections | Introduction to Conic Sections and Their General Equation | |

Objective: To identify the conic from its equation by examining the coefficients of x^2 and y^2 | |||

59 | Conic sections | The Parabola | |

Objective: To examine the properties of parabolas of the forms x^2 = 4py and y^2 = 4px | |||

60 | Conic sections | Circles | |

Objective: To graph circles of the form x^2 + y^2 = r^2 and to form the equation of the given circles | |||

61 | Conic sections | The Ellipsis | |

Objective: To identify ellipses of the form x^2/a^2 + y^2/b^2 = 1 and to find the equation of ellipses | |||

62 | Conic sections | The Hyperbola | |

Objective: To find the equation of a hyperbola and to derive properties (e.g. vertex) from its equation | |||

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

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

64 | Function | Function Notation | |

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

65 | Function | Selecting Appropriate Domain and Range | |

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

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

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

67 | Function | Evaluating and Graphing Piecewise Functions | |

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

68 | Function | Combining Functions | |

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

69 | Function | Simplifying Composite Functions | |

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

70 | Function | Inverse Functions | |

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

71 | Function | Graphing Rational Functions Part 1 | |

Objective: To determine asymptotes and graph rational functions using intercepts and asymptotes | |||

72 | Function | Graphing Rational Functions Part 2 | |

Objective: To determine asymptotes and graph rational functions | |||

73 | Function | Parametric Equations | |

Objective: To interchange parametric and Cartesian equations and to identify graphs | |||

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

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

75 | Function | Parametric Functions | |

Objective: To change Cartesian and parametric equations and to graph parametric functions | |||

76 | Logarithms | Powers of 2 | |

Objective: To convert between logarithm statements and indice statements | |||

77 | 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 | |||

78 | Logarithms | Equations of type log 32 to the base x = 5 | |

Objective: To solve Logrithmic Equation where the variable is the base x = 5 | |||

79 | Series and sequences part 2 | Compound Interest | |

Objective: To calculate the compound interest of an investment using A=P(1+r/100)^n | |||

80 | Series and sequences part 2 | Superannuation | |

Objective: To calculate the end value of adding a regular amount to a fund with stable interest paid over time | |||

81 | Series and sequences part 2 | Time Payments | |

Objective: To calculate the payments required to pay off a loan | |||

82 | 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 | |||

83 | 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 | |||

84 | 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 | |||

85 | 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 | |||

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

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

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

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

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

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

89 | 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 | |||

90 | 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 | |||

91 | 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 | |||

92 | 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 | |||

93 | 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 | |||

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

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

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

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

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

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

97 | Exam | Exam – Grade 11 – Functions and Applications | |

Objective: Exam |