# Grade 11 – Functions Mathematics – Canada

### Grade 11 – Functions Mathematics

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

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

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

2 | Surds/Radicals | Introducing surds | |

Objective: To recognise and simplify numerical expressions involving surds | |||

3 | Surds/Radicals | Some rules for the operations with surds | |

Objective: To learn rules for the division and multiplication of surds | |||

4 | Surds/Radicals | Simplifying Surds | |

Objective: To simplify numerical expressions and solve equations involving surds | |||

5 | Surds/Radicals | Creating entire surds | |

Objective: To write numbers as entire surds and compare numbers by writing as entire surds | |||

6 | Surds/Radicals | Adding and subtracting like surds | |

Objective: To add and subtract surds and simplify expressions by collecting like surds | |||

7 | Surds/Radicals | Expanding surds | |

Objective: To expand and simplify binomial expressions involving surds | |||

8 | Surds/Radicals | Binomial expansions | |

Objective: To expand and simplify the squares of binomial sums and differences involving surds | |||

9 | Surds/Radicals | Conjugate binomials with surds | |

Objective: To expand and simplify products of conjugate binomial expressions | |||

10 | Surds/Radicals | Rationalising the denominator | |

Objective: To rationalise the denominator of a fraction where the denominator is a monomial surd | |||

11 | Surds/Radicals | Rationalising binomial denominators | |

Objective: To rationalise the denominator of a fraction when the denominator is a binomial with surds | |||

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

22 | Indices/Exponents | Negative Indices | |

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

23 | Indices/Exponents | Fractional Indices | |

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

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

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

25 | 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 | |||

26 | 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 | |||

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

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

28 | Graphs part 1 | Graphing irrational roots | |

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

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

Objective: To solve simultaneous equations graphically | |||

30 | Algebra – Quadratic equations | Solving Quadratic Equations | |

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

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

Objective: To complete an incomplete square | |||

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

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

33 | Algebra – Quadratic equations | The Quadratic Formula | |

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

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

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

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

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

36 | Logarithms | Powers of 2 | |

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

37 | 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 | |||

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

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

39 | 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 | |||

40 | 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) | |||

41 | 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 | |||

42 | Graphs part 2 | Absolute Value Equations | |

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

43 | Graphs part 2 | The Rectangular Hyperbola | |

Objective: To graph rectangular hyperbolae whose equations are of the form xy = a and y = a/x | |||

44 | Graphs part 2 | The Exponential Function | |

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

45 | Graphs part 2 | Logarithmic Functions | |

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

46 | 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 | |||

47 | Conic sections | The Parabola | |

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

48 | 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 | |||

49 | 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 | |||

50 | Conic sections | The Hyperbola | |

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

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

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

52 | Function | Function Notation | |

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

53 | Function | Selecting Appropriate Domain and Range | |

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

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

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

55 | Function | Evaluating and Graphing Piecewise Functions | |

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

56 | Function | Combining Functions | |

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

57 | Function | Simplifying Composite Functions | |

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

58 | Function | Inverse Functions | |

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

59 | Function | Graphing Rational Functions Part 1 | |

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

60 | Function | Graphing Rational Functions Part 2 | |

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

61 | Function | Parametric Equations | |

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

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

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

63 | Function | Parametric Functions | |

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

64 | Polynomials | Introduction to polynomials | |

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

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

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

66 | Series and sequences part 1 | General Sequences | |

Objective: To use the general form of the n’th term of a sequence to find the first 3 terms | |||

67 | Series and sequences part 1 | Finding Tn Given Sn | |

Objective: To find the value of the n’th term in a sequence given the sum of the first n terms | |||

68 | Series and sequences part 1 | The Arithmetic Progression | |

Objective: To find the common difference of a given arithmetic progression | |||

69 | Series and sequences part 1 | Finding the position of a term in an A.P. | |

Objective: To find the position of a term in a sequence, given an arithmetic progression and a value term | |||

70 | Series and sequences part 1 | Given two terms of A.P. find the sequence | |

Objective: To find the first term and the common difference in an A.P. given the values and positions of two terms | |||

71 | Series and sequences part 1 | Arithmetic Means | |

Objective: To find the arithmetic mean of two values | |||

72 | Series and sequences part 1 | The sum to n terms of an A.P. | |

Objective: To find the sum of n terms of an arithmetic progression given the first three terms | |||

73 | Series and sequences part 1 | The Geometric Progression | |

Objective: To find the common ratio of a given geometric progression | |||

74 | Series and sequences part 1 | Finding the position of a term in a G.P. | |

Objective: To find the place of a term in a given geometric progression | |||

75 | Series and sequences part 1 | Given two terms of G.P. find the sequence | |

Objective: To find the first term given two terms of a geometric progression | |||

76 | Series and sequences part 2 | Geometric Means | |

Objective: To find geometric means of a and b and insert geometric means between 2 endpoints | |||

77 | Series and sequences part 2 | The sum to n terms of a G.P. | |

Objective: To find the sum of n terms of a sequence | |||

78 | Series and sequences part 2 | Sigma notation | |

Objective: To evaluate progressions using sigma notation | |||

79 | Series and sequences part 2 | Limiting Sum or Sum to Infinity | |

Objective: To find the limiting sum of a sequence | |||

80 | Series and sequences part 2 | Recurring Decimals and the Infinite G.P. | |

Objective: To express recurring decimals as a G.P. and to express the limiting sum as a fraction | |||

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

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

82 | 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 | |||

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

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

84 | Series and sequences part 2 | Applications of arithmetic sequences | |

Objective: To learn about practical situations with arithmetic series | |||

85 | Probability | The Binomial Theorem and Binomial Coefficients | |

Objective: To calculate binomial coefficients and expand binomial powers. | |||

86 | Probability | Binomial probabilities using the Binomial Theorem | |

Objective: To calculate the binomial probability of a given number of successful trials | |||

87 | Trigonometry part 1 | Trigonometric Ratios | |

Objective: To name the sides of a right-angled triangle and to determine the trig ratios of an angle | |||

88 | Trigonometry part 1 | Using the Calculator | |

Objective: To determine trigonometric ratios using a calculator | |||

89 | 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 | |||

90 | 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 | |||

91 | 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 | |||

92 | 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 | |||

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

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

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

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

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

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

96 | 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 | |||

97 | 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 | |||

98 | 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 | |||

99 | 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 | |||

100 | 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 | |||

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

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

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

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

103 | Trigonometry part 2 | Reciprocal Ratios | |

Objective: To find the trigonometric ratios for a given right-angled triangle | |||

104 | Trigonometry part 2 | Complementary Angle Results | |

Objective: To use complementary angle ratios to find an unknown angle given a trigonometric equality | |||

105 | Trigonometry part 2 | Trigonometric Identities | |

Objective: To simplify expressions using trigonometric equalities | |||

106 | Trigonometry part 2 | Angles of Any Magnitude | |

Objective: To assign angles to quadrants and to find trigonometric values for angles | |||

107 | 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 | |||

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

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

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

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

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

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

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

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

112 | 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. | |||

113 | Exam | Exam – Grade 11 – Functions | |

Objective: Exam |