### 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.
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
Objective: To simplify numerical expressions and solve equations involving surds
Objective: To write numbers as entire surds and compare numbers by writing as entire surds
Objective: To add and subtract surds and simplify expressions by collecting like surds
Objective: To expand and simplify binomial expressions involving surds
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
Objective: To rationalise the denominator of a fraction where the denominator is a monomial surd
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
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
Objective: To find the roots of a quadratic equation by using the quadratic formula
Objective: To solve problems which require finding the roots of a quadratic equation
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