Grade 11 Functions
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Lesson 1: How can we represent a relation between two variables? (graphs, table of values, equtaion, etc)
Quiz: Lesson 1
Mini Challenge: Lesson 1
Worksheet: Lesson 1
Lesson 2: Review: Set notation and interval notation
Quiz: Lesson 2
Mini Challenge: Lesson 2
Worksheet: Lesson 2
Lesson 3: Review: Function vs. Relation (including one-to-one and vertical line test)
Quiz: Lesson 3
Mini Challenge: Lesson 3
Worksheet: Lesson 3
Lesson 4: Review: Linear Equations (use function notation, tables, equations)
Quiz: Lesson 4
Mini Challenge: Lesson 4
Worksheet: Lesson 4
Lesson 5: Finding the slope (Given two points AND finding the slope given a point and y intercept)
Quiz: Lesson 5
Mini Challenge: Lesson 5
Worksheet: Lesson 5
Worksheet: Lessons 1-5
Lesson 6: interpret and use any of the forms y = mx + b, y – y1 = m(x – x1), ax + by + c = 0 in solving problems
Quiz: Lesson 6
Game Time! Drag the words
Game Time! Drag and Drop
Mini Challenge: Lesson 6
Worksheet: Lesson 6
Lesson 7: Represent quadratic functions (using function notation, tables, equations)
Quiz: Lesson 7
Mini Challenge: Lesson 7
Worksheet: Lesson 7
Lesson 8: Identify the three forms of equations of quadratic functions: standard, factored, vertex
Quiz: Lesson 8
Mini Challenge: Lesson 8
Worksheet: Lesson 8
Lesson 9: Review: Converting from standard form to factored form (with and without coefficients)
Mini Challenge: Lesson 9
Worksheet: Lesson 9
Lesson 10: Review: Converting from standard form to vertex form (completing the square)
Quiz: Lesson 10
Mini Challenge: Lesson 10
Worksheet: Lesson 10
Worksheet: Lesson 6-10
Lesson 11: Describe features of quadratic functions such as degree, shape, concavity, intercepts, vertex, optimal value, and axis of symmetry, given the graph
Quiz: Lesson 11
Mini Challenge: Lesson 11
Worksheet: Lesson 11
Lesson 12: Sketching the graphs of quadratic functions: y= (x - p)^2 + q y= - (x - p)^2 + q y= (x - a) (x - b) y= - (x - a) (x - b)
Quiz: Lesson 12
Game Time! Find the right graph
Game Time! Drag and Drop
Mini Challenge: Lesson 12
Worksheet: Lesson 12
Lesson 13: Determine the number of zeros (i.e., x-intercepts) of a quadratic function, using a variety of strategies (e.g., inspecting graphs; factoring; calculating the discriminant)
Mini Challenge: Lesson 13
Worksheet: Lesson 13
Lesson 14: Find the exact coordinates of the vertex of a quadratic function (in any form) using an appropriate algebraic method or technology
Quiz: Lesson 14
Mini Challenge: Lesson 14
Worksheet: Lesson 14
Lesson 15: Determine the algebraic representation of a quadratic function, given the real roots of the corresponding quadratic equation and a point on the function
Quiz: Lesson 15
Mini Challenge: Lesson 15
Worksheet: Lesson 15
Worksheet: Lessons 11-15
Lesson 16: Find the y intercept of quadratic functions algebraically
Quiz: Lesson 16
Mini Challenge: Lesson 16
Worksheet: Lesson 16
Lesson 17: Solve quadratic inequalities
Quiz: Lesson 17
Mini Challenge: Lesson 17
Worksheet: Lesson 17
Lesson 18: Make connections between the equations and graphs of quadratic functions: use the roles played by the parameters a, c, and d in transformed quadratic functions to describe features of the graph, given the equation
Quiz: Lesson 18
Mini Challenge: Lesson 18
Worksheet: Lesson 18
Lesson 19: Solve problems involving quadratic functions arising from real-world applications and represented using function notation
Quiz: Lesson 19
Mini Challenge: Lesson 19
Worksheet: Lesson 19
Lesson 20: Solve linear and quadratic equations algebraically
Quiz: Lesson 20
Mini Challenge: Lesson 20
Worksheet: Lesson 16-20
Worksheet: Lesson 20
Lesson 21: Solve by substitution a pair of simultaneous equations of which one is linear and one is quadratic
Quiz: Lesson 21
Mini Challenge: Lesson 21
Lesson 22: Solve real-life problems involving the intersection of a linear function and a quadratic function graphically and algebraically
Quiz: Lesson 22
Mini Challenge: Lesson 22
Lesson 23: Finding the point of intersection of two quadratics
Quiz: Lesson 23
Game Time! Question set
Game Time! Drag and Drog
Mini Challenge: Lesson 23
Lesson 24: Review: graphs of f(x) = |x| , f(x) = √x, and f(x) = 1/x
Quiz: Lesson 24/25
Mini Challenge: Lesson 24/25
Worksheet: Lesson 21-24
Lesson 26: Revision of mathematical vocabulary and terms: function, domain, range, one-one function, inverse function and composition of functions
Quiz: Lesson 26
Mini Challenge: Lesson 26
Lesson 27: Understand the meaning of |x|, sketch the graph of y = |ax + b| and use relations such as |a| = |b| ⇔ a 2 = b2 and |x – a| < b ⇔ a – b < x < a + b when solving equations and inequalities
Quiz: Lesson 27
Mini Challenge: Lesson 27
Lesson 28: Find the inverse of a one-on-one function in simple cases
Quiz: Lesson 28
Mini Challenge: Lesson 28
Lesson 29: Determining numeric or graphical representations of the inverse of a linear or quadratic function and make connections (e.g., the graph of the inverse is the reflection of the graph of the function in the line y = x)
Quiz: Lesson 29
Mini Challenge: Lesson 29
Lesson 30: Comparing the domain and range of a function and its inverse function
Quiz: Lesson 30
Game Time! Flip and learn
Game Time! Image Choice
Mini Challenge: Lesson 30
Lesson 31: The roles of the parameters a, k, d, and c in functions of the form y = af(k(x – d)) + c
Quiz: Lesson 31
Mini Challenge: Lesson 31
Lesson 32: Continue on from previous lesson
Quiz: Lesson 32
Mini Challenge: Lesson 32
Lesson 33: Sketch graphs of y = af(k(x – d)) + c by applying one or more transformations to the graphs of f(x) = x, f(x) = x , f(x) = √x, and 1/x and state the domain and range of the transformed functions (continue into next lesson)
Quiz: Lesson 33
Game Time! Put the images in the correct sequence
Mini Challenge: Lesson 33
Lesson 34: Draw graphs of piecewise functions
Quiz: Lesson 34
Mini Challenge: Lesson 34
Lesson 1: Simplifying polynomial expressions by adding and subtracting
Quiz: Lesson 1
Mini Challenge: Lesson 1
Worksheet: Lesson 1
Lesson 2: Simplifying polynomial expressions by multiplying and dividing
Quiz: Lesson 2
Game Time! Drag and drop
Mini Challenge: Lesson 2
Worksheet: Lesson 2
Lesson 2A: Division of polynomials
Quiz: Lesson 2A
Game Time! Drag and drop
Mini Challenge: Lesson 2A
Worksheet: Lesson 2A
Lesson 3: Determine if two given algebraic expressions are equivalent (i.e., by simplifying; by substituting values)
Quiz: Lesson 3
Game Time! Select the equivalent expressions
Mini Challenge: Lesson 3
Worksheet: Lesson 3
Lesson 4: Exploration and understanding that √ab = √a x √b, a ≥ 0, b ≥ 0
Quiz: Lesson 4
Game Time! Find the equivalent expression
Mini Challenge: Lesson 4
Worksheet: Lesson 4
Lesson 5: Stating restrictions on rational expressions
Quiz: Lesson 5
Mini Challenge: Lesson 5
Worksheet: Lesson 5
Lesson 6: Adding and subtracting rational expressions
Quiz: Lesson 6
Mini Challenge: Lesson 6
Worksheet: Lesson 6
Lesson 7: Multiplying rational expressions
Quiz: Lesson 7
Game Time! Find the equivalent expression
Mini Challenge: Lesson 7
Worksheet: Lesson 7
Lesson 8: Partial fraction decomposition [for the trickier examples in the video, include examples where this ends up being the denominator: (ax + b)(cx + d)(ex + f) as well as this as the denominator: (ax + b)(cx + d)^2 and this: (ax + b)(cx^2 + d) ]
Quiz: Lesson 8
Game Time! Find the equivalent expression
Mini Challenge: Lesson 8
Game Time! Memory Game: Find all pairs of equivalent expressions
Worksheet: Lesson 8
Lesson 1: Graphing an exponential relation given its equation in the form y = bˣ (b > 0, b ≠ 1) (In the lesson, define this relation as the function f(x) = bˣ and explain why it is a function)
Quiz: Lesson 1/2
Mini Challenge: Lesson 1/2
Worksheet: Lesson 1/2
Lesson 3: Determining the value of a power with a rational exponent
Quiz: Lesson 3
Mini Challenge: Lesson 3
Worksheet: Lesson 3
Lesson 4: Connections between the value of the base and the shape of the graph
Quiz: Lesson 4
Mini Challenge: Lesson 4
Worksheet: Lesson 4
Lesson 5: Converting from exponent form to radical form
Quiz: Lesson 5
Mini Challenge: Lesson 5
Worksheet: Lesson 5
Lesson 6: Simplifying and evaluating expressions with negative exponents
Quiz: Lesson 6
Mini Challenge: Lesson 6
Worksheet: Lesson 6
Lesson 7: Simplifying algebraic expressions containing integer and rational exponents
Quiz: Lesson 7
Mini Challenge: Lesson 7
Worksheet: Lesson 7
Lesson 8: Evaluating numeric expressions containing integer and rational exponents and rational bases
Quiz: Lesson 8
Mini Challenge: Lesson 8
Worksheet: Lesson 8
Lesson 9: Determining and describing key properties relating to an exponential graph's domain and range, intercepts, increasing/decreasing intervals, asymptotes, end behaviour
Quiz: Lesson 9
Mini Challenge: Lesson 9
Worksheet: Lesson 9
Lesson 10: The graph of y = e^kx for both positive and negative values of k
Quiz: Lesson 10
Mini Challenge: Lesson 10
Lesson 11: Distinguishing exponential functions from linear and quadratic functions by making comparisons in a variety of ways
Quiz: Lesson 11
Mini Challenge: Lesson 11
Lesson 12: Determining (using technology, can use desmos or GDC) the roles of the parameters a, k, d, and c in functions of the form y = af(k(x – d)) + c, and describing these roles in terms of transformations on the graph of f(x) = b^x (b > 0, b ≠ 1)
Quiz: Lesson 12
Mini Challenge: Lesson 12
Lesson 13: Sketching graphs of y = af(k(x – d)) + c by applying one or more transformations to the graph of f(x) = a (a > 0, a ≠ 1), and state the domain and range of the transformed functions
Mini Challenge: Lesson 13
Lesson 14: State the domain and range of various exponential graphs (parent function and transformed functions)
Quiz: Lesson 14
Game Time! Question set
Game Time! Image Choice
Mini Challenge: Lesson 14
Lesson 15: Determining (using technology, can use desmos or GDC) that the equation of a given exponential function can be expressed using different bases
Quiz: Lesson 15
Mini Challenge: Lesson 15
Worksheet: Lesson 15
Lesson 16: Solving exponential equations by expressing both sides of the equation as single powers of the same base and then equating the exponents
Quiz: Lesson 16
Game Time! Drag and drop
Mini Challenge: Lesson 16
Worksheet: Lesson 16
Lesson 17: Solving exponential equations using a graph
Quiz: Lesson 17
Mini Challenge: Lesson 17
Worksheet: Lesson 17
Lesson 18: Representing an exponential function with an equation, given its graph or its properties
Quiz: Lesson 18
Game Time! Find the right equation
Mini Challenge: Lesson 18
Worksheet: Lesson 18
Lesson 19: Collecting and analyzing data that can be modelled as an exponential function (with and without technology) from primary sources and graph the data
Quiz: Lesson 19
Mini Challenge: Lesson 19
Worksheet: Lesson 19
Lesson 20: Identifying exponential functions, including those that arise from real-world applications involving growth and decay given various representations
Quiz: Lesson 20
Mini Challenge: Lesson 20
Worksheet: Lesson 20
Lesson 21: Solving problems using given graphs or equations of exponential functions arising from a variety of real-world applications
Quiz: Lesson 21
Game Time! Drag and drop
Mini Challenge: Lesson 21
Game Time! Flip and Learn
Worksheet: Lesson 21
Lesson 1: Review: Discrete functions vs. continuous functions
Quiz: Lesson 1
Mini Challenge: Lesson 1
Worksheet: Lesson 1
Lesson 2: Review and identify sequence as arithmetic, geometric or neither, given a numeric or algebraic representation
Quiz: Lesson 2
Mini Challenge: Lesson 2
Worksheet: Lesson 2
Lesson 3: Represent sequences using function notation
Quiz: Lesson 3
Mini Challenge: Lesson 3
Worksheet: Lesson 3
Lesson 4: Generating sequences given the intial terms
Quiz: Lesson 4
Game Time! True or false
Mini Challenge: Lesson 4
Worksheet: Lesson 4
Lesson 5: Represent a sequence algebraically using a recursion formula
Quiz: Lesson 5
Mini Challenge: Lesson 5
Worksheet: Lessonn 5
Lesson 6: Determine recursive patterns in the Fibonacci sequence and Pascal's triangle
Quiz: Lesson 6
Game Time! Find the right image
Game Time! Find the right image
Mini Challenge: Lesson 6
Worksheet: Lesson 6
Lesson 7: Explore the relationship between pascal's triangle and expansion of binomials
Quiz: Lesson 7
Mini Challenge: Lesson 7
Worksheet: Lesson 7
Lesson 8: Binomial Expansion: expansion of (1 + x) ^ n , where n is a rational number and |x| < 1
Quiz: Lesson 8
Mini Challenge: Lesson 8
Worksheet: Lesson 8
Lesson 9: Determine the formula for the general term of an arithmetic sequence or geometric sequence
Quiz: Lesson 9
Mini Challenge: Lesson 9
Worksheet: Lesson 9
Quiz: Lesson 9/10
Worksheet: Lesson 9/10
Mini Challenge: Lesson 9/10
Lesson 11: Determine the formula for the sum of an arithmetic or geometric series and apply the formula to calculate the sum of a given number of consecutive terms
Quiz: Lesson 11/12
Mini Challenge: Lesson 11/12
Worksheet: Lesson 11/12
Lesson 13: Review: Sequences vs. Series
Quiz: Lesson 13
Game Time! Question set
Mini Challenge: Lesson 13
Worksheet: Lesson 13
Lesson 14: Expand and evaluate a series written in sigma notation; Express a series using sigma notation
Lesson 15: Arithmetic and Geometric Progressions
Quiz: Lesson 14/15
Mini Challenge: Lesson 14/15
Worksheet: Lesson 14/15
Lesson 16: Use the formulae for the nth term and for the sum of the first n terms to solve problems involving arithmetic or geometric progressions
Quiz: Lesson 16
Mini Challenge: Lesson 16
Worksheet: Lesson 16
Lesson 17: Using the condition for the convergence of a geometric progression, and the formula for the sum to infinity of a convergent geometric progression.
Quiz: Lesson 17
Game Time! Drag and drop
Mini Challenge: Lesson 17
Worksheet: Lesson 17
Lesson 18: Making connections between arithmetic sequences, simple interest, and linear growth
Quiz: Lesson 18/19
Mini Challenge: Lesson 18/19
Worksheet: Lesson 18/19
Lesson 20: Introduce the calculation of the amount, A, the principal, P, or the interest rate per compounding period, i, using the compound interest formula in the form A = A = P(1 + i) [or FV = PV(1 + i)]
Quiz: Lesson 20/21
Game Time! Find the answer
Game Time! Find the answer
Mini Challenge: Lesson 20/21
Game Time! Crossword
Worksheet: Lesson 20/21
Lesson 1: Labeling sides of a right triangle hypotenuse, opposite, and adjacent
Quiz: Lesson 1
Mini Challenge: Lesson 1
Worksheet: Lesson 1
Lesson 2: Drawing angles in standard position and recognizing coterminal angles
Quiz: Lesson 2
Mini Challenge: Lesson 2
Worksheet: Lesson 2
Lesson 3: Drawing and determining the size of the principle angle and of the related acute angle
Quiz: Lesson 3
Mini Challenge: Lesson 3
Worksheet: Lesson 3
Lesson 4: Understanding the concept of the unit circle and how to use it
Quiz: Lesson 4
Mini Challenge: Lesson 4
Worksheet: Lesson 4
Lesson 5: Using the x, y, r definitions to find the principal angle, given a point on the terminal arm
Quiz: Lesson 5
Mini Challenge: Lesson 5
Worksheet: Lesson 5
Lesson 5A: Determining the measures of two angles from 0º to 360º for which the value of a given trigonometric ratio is the same
Quiz: Lesson 5A
Mini Challenge: Lesson 5A
Worksheet: Lesson 5A
Lesson 6: Calculating the primary and reciprocal trigonometric ratios given two sides of a right triangle
Quiz: Lesson 6
Mini Challenge: Lesson 6
Worksheet: Lesson 6
Lesson 7: Relating complementary trigonometric ratios
Quiz: Lesson 7
Mini Challenge: Lesson 7
Worksheet: Lesson 7
Lesson 8: Using trig ratios to find missing angles and sides in right angle triangles
Quiz: Lesson 8
Mini Challenge: Lesson 8
Worksheet: Lesson 8
Lesson 9: Using SOHCAHTOA to solve real-world problems
Quiz: Lesson 9
Game Time! Question set
Mini Challenge: Lesson 9
Worksheet: Lesson 9
Lesson 10: Radians and arc length
Quiz: Lesson 10
Mini Challenge: Lesson 10
Worksheet: Lesson 10
Lesson 11: Converting from radians to degrees and from degrees to radians
Quiz: Lesson 11
Game Time! Drag and drop
Mini Challenge: Lesson 11
Lesson 12: Using trigonometry to find: the area of a sector
Lesson 13: Using trigonometry to find: the area of a segment
Quiz: Lesson 12/13
Game Time! Find the answer
Game Time! Dialog Cards
Mini Challenge: Lesson 12/13
Lesson 18: Proving simple trigonometric identities, using the Pythagorean identity sin x + cos x = 1
Quiz: Lesson 14-18
Game Time! Drag the Words
Mini Challenge: Lesson 14-18
Lesson 19: Using the sine law to find the angles and sides in oblique triangles
Quiz: Lesson 19
Mini Challenge: Lesson 19
Lesson 20: Using the cosine law to find the angles and sides in oblique triangles
Quiz: Lesson 20
Mini Challenge: Lesson 20
Lesson 21: Problems involving right triangles and oblique triangles in two dimensional settings, and solve these problems using the primary trigonometric ratios, the cosine law, and the sine law (including the ambiguous case)
Quiz: Lesson 21
Game Time! Drag and drop
Mini Challenge: Lesson 21
Worksheet: Lesson 21
Lesson 22: Problems involving right triangles and oblique triangles in three-dimensional settings, and solve these problems using the primary trigonometric ratios, the cosine law, and the sine law
Quiz: Lesson 22
Game Time! Solve the 3D Problem
Mini Challenge: Lesson 22
Worksheet: Lesson 22
Lesson 23: Recognizing conditions of the ambiguous case of the sine law
Lesson 24: Drawing diagrams and finding missing sides and angles for the two possibilities of the ambiguous case
Quiz: Lesson 23/24
Mini Challenge: Lesson 23/24
Worksheet: Lesson 23/24
Lesson 25: Describing key properties (e.g., cycle, amplitude, period) of periodic functions arising from real-world applications given a numeric or graphical representation
Quiz: Lesson 25
Mini Challenge: Lesson 25
Worksheet: Lesson 25
Lesson 26: Predicting by extrapolating, the future behaviour of a relationship modelled using a numeric or graphical representation of a periodic function
Quiz: Lesson 26
Mini Challenge: Lesson 26
Worksheet: Lesson 26
Lesson 27: Making connections between the sine ratio and the sine function and between the cosine ratio and the cosine function with or without technology
Quiz: Lesson 27
Mini Challenge: Lesson 27
Quiz: Lesson 27/28
Lesson 29: Sketching the graphs of f(x) =sinx and f(x) =cosx for angle measures expressed in degrees
Mini Challenge: Lesson 27/28
Quiz: Lesson 29
Mini Challenge: Lesson 29
Lesson 30A: Trigonometric Functions: Determining and describing their key properties (i.e., cycle, domain, range, and intercepts) (Continuation of previous lesson)
Lesson 30B: Determining and describing their key properties (i.e., amplitude, period, maximum and minimum values, increasing/decreasing intervals and phase shift) (Continuation of previous lesson)
Quiz: Lesson 30
Game Time! Question set
Game Time! Dialog Cards
Mini Challenge: Lesson 30
Lesson 31: Determining the roles of the parameters a, k, d, and c in functions of the form y =af(k(x – d)) + c, where f(x) =sinx or f(x) =cosx with angles expressed in degrees using technology
Quiz: Lesson 31
Mini Challenge: Lesson 31
Lesson 32: Describing the roles in terms of transformations on the graphs of f(x) =sinx and f(x) =cosx (Continuation of previous lesson)
Quiz: Lesson 32
Mini Challenge: Lesson 32
Lesson 33: Determining the amplitude, period, phase shift, domain, and range of sinusoidal functions whose equations are given in the form f(x) = asin(k(x – d)) + c or f(x) = acos(k(x – d)) + c
Quiz: Lesson 33
Mini Challenge: Lesson 33
Lesson 34: Sketching graphs of y = af(k(x – d)) + c by applying one or more transformations to the graphs of f(x) =sinx and f(x) =cosx, and state the domain and range of the transformed functions
Quiz: Lesson 34
Game Time! Drag and drop
Mini Challenge: Lesson 34
Lesson 35: Representing a sinusoidal function with an equation, given its graph or its properties
Quiz: Lesson 35
Game Time! Select the correct equations
Mini Challenge: Lesson 35
Lesson 36: Collecting data that can be modelled as a sinusoidal function with and without technology, from primary sources, using a variety of tools and graph the data
Quiz: Lesson 36
Mini Challenge: Lesson 36
Lesson 37: Identifying periodic and sinusoidal functions, including those that arise from real-world applications involving periodic phenomena, given various representations
Quiz: Lesson 37
Mini Challenge: Lesson 37
Lesson 38: Explaining any restrictions that the real-world context places on the domain and range
Quiz: Lesson 38
Mini Challenge: Lesson 38
Lesson 39: Determining how sinusoidal functions can be used to model periodic phenomena that do not involve angles
Quiz: Lesson 39
Mini Challenge: Lesson 39
Worksheet: Lesson 39
Lesson 40: Predicting the effects on a mathematical model of an application involving periodic phenomena when the conditions in the application are varied
Quiz: Lesson 40
Game Time! Select the appropriate equations
Mini Challenge: Lesson 40
Game Time! Drag and Drop
Worksheet: Lesson 40
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Here are answers to some common questions we are asked
This level is designed for kids ages 11-12 in Grades 6 and 7.
These (virtual) programs are designed to be completely self learnt. Students progress through the curriculum using a variety of real world applications that simulate experience, utilize creative thinking, and allow the students to test their knowledge.
You will receive an e-mail as soon as you connect, providing you with a pin and password to access the learning portal. Please keep this information safe. If you need support, you can email [email protected].
It doesn't matter what curriculum you followed, we have surpassed it! Our program includes all aspects of the following curriculums: Canada (Ontario & BC), British Curriculum, International Baccalaureate (IB), Advanced Placement (AP) and Singapore National Curriculum.