### 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
Objective: To find the solutions of quadratic equations presented as a product of factors
Objective: To solve quadratic equations requiring factorisation
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
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
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