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  • Real World Applications

    Build confidence in your new skills with a variety of hands-on activities, quizzes, projects and real life simulations.

Course curriculum

  • 01

    Registration

    • Registration Information

    • Required Student Information

  • 03

    Characteristics of Functions

    • Lesson 1: Rates of change (how to represent rates of change as well as real-world examples)

    • Quiz: Lesson 1

    • Mini Challenge: Lesson 1

    • Worksheet: Lesson 1

    • Lesson 2: Explore situations in which the rate of change is zero, constant, or changing (include real world applications)

    • Quiz: Lesson 2

    • Mini Challenge: Lesson 2

    • Worksheet: Lesson 2

    • Lesson 3: Calculating rates of change for various functions (linear, quadratic, sinusoidal etc)

    • Worked Out Example: Lesson 3

    • Quiz: Lesson 3

    • Mini Challenge: Lesson 3

    • Worksheet: lesson 3

    • Lesson 4: Average rate of change vs. Instantaneous rate of change

    • Quiz: Lesson 4

    • Mini Challenge: Lesson 4

    • Worksheet: Lesson 4

    • Lesson 5: Review: What are tangent lines and what does "normal to the tangent" mean

    • Quiz: Lesson 5

    • Game Time! Select the correct answer

    • Game Time! Guess the Answer

    • Mini Challenge: Lesson 5

    • Worksheet: Lesson 5

    • Lesson 6: Making connections between the slope of a secant on the graph of a function and the average rate of change

    • Quiz: Lesson 6

    • Mini Challenge: Lesson 6

    • Worksheet: Lesson 6

    • Lesson 7: Making connections between the slope of a tangent to a point on a graph of a function and the instantaneous rate of change of a function at that point

    • Quiz: Lesson 7

    • Mini Challenge: Lesson 7

    • Worksheet: Lesson 7

    • Lesson 8: Determine the approximate slope of the tangent to a given point on the graph of a function by using the slopes of secants through the given point and make connections to average and instantaneous rates of change

    • Quiz: Lesson 8

    • Mini Challenge: Lesson 8

    • Worksheet: Lesson 8

    • Lesson 9: Solve problems involving average and instantaneous rates of change, including problems arising from real-world applications (can use tech like desmos)

    • Quiz: Lesson 9

    • Game Time! Drag the words (L6 - 9)

    • Mini Challenge: Lesson 9

    • Worksheet: lesson 9

    • Lesson 10: What is the limit of a function?

    • Quiz: Lesson 10

    • Mini Challenge: Lesson 10

    • Worksheet: lesson 10

    • Lesson 11: Key features (domain, range, max, min, etc) of the graphs of functions created by adding,subtracting,multiplying,or dividing functions( [e.g., f(x) = 2-x sin 4x, g(x) = x2 + 2x , h(x) =sin x/cos x & describe factors that affect these properties

    • Quiz: Lesson 11

    • Mini Challenge: Lesson 11

    • Worksheet: lesson 11

    • Lesson 12: Real-world applications of combinations of functions

    • Quiz: Lesson 12

    • Game Time! Flip and learn (L11 - 12)

    • Mini Challenge: Lesson 12

    • Worksheet: lesson 12

    • Lesson 13: Explain properties (i.e., odd, even, or neither; increasing/decreasing behaviours) of functions formed by adding, subtracting, multiplying, and dividing general functions [e.g., f(x) + g(x), f(x)g(x)]

    • Quiz: Lesson 13

    • Game Time! Even or odd? (L13)

    • Mini Challenge: Lesson 13

    • Worksheet: Lesson 13

    • Lesson 14: Composite functions / Composition of functions, interpret the notation of composite functions

    • Worked Out Example: Lesson 14

    • Quiz: Lesson 14

    • Mini Challenge: Lesson 14

    • Worksheet: Lesson 14

    • Lesson 15: Composition of two functions: real world applications

    • Quiz: Lesson 15

    • Mini Challenge: Lesson 15

    • Worksheet: Lesson 15

    • Lesson 16: Algebraically determine the composition of two functions

    • Quiz: Lesson 16

    • Game Time! Drag and drop (L14 - 16)

    • Mini Challenge: Lesson 16

    • Worksheet: Lesson 16

    • Lesson 17: Understand how to represent complex functions as composites of simpler functions

    • Worked Out Example: Lesson 17

    • Quiz: Lesson 17

    • Mini Challenge: Lesson 17

    • Worksheet: lesson 17

    • Lesson 18: Demonstrate, by giving examples for functions represented in a variety of ways

    • Quiz: Lesson 18

    • Mini Challenge: Lesson 18

    • Worksheet: Lesson 18

    • Lesson 19: Make connections, through investigation using technology, between transformations

    • Quiz: Lesson 19

    • Game Time! Fill in the blanks (L17 - 19)

    • Game Time! Identify the transformations (L19)

    • Mini Challenge: Lesson 19

    • Worksheet: Lesson 19

    • Lesson 20: Compare various functions with one another (polynomial, rational, trigonometric, exponential, logarithmic)

    • Mini Challenge: Lesson 20

    • Worksheet: Lesson 20

    • Lesson 21: solve graphically and numerically equations and inequalities whose solutions are not accessible by standard algebraic techniques (can use desmos or GDC)

    • Quiz: Lesson 21

    • Mini Challenge: Lesson 21

    • Worksheet: Lesson 21

    • Lesson 22: locate approximately a root of an equation, by means of graphical considerations and/or searching for a sign change

    • Quiz: Lesson 22

    • Game Time! Find the correct solutions (L21 - 22)

    • Mini Challenge: Lesson 22

    • Game Time! Crossword

    • Worksheet: Lesson 22

  • 04

    Polynomials and Rational Functions

    • Quiz: Lesson 1

    • Quiz: Lesson 1 Part 2

    • Mini Challenge: Lesson 1

    • Mini Challenge: Lesson 1 Part 2

    • Worksheet: Lesson 1

    • Lesson 2: Finding the degree from the equation in expanded or factored form

    • Worked Out Example: Lesson 2

    • Quiz: Lesson 2

    • Mini Challenge: Lesson 2

    • Worksheet: Lesson 2

    • Lesson 3: Finding the leading coefficient from the equation in expanded or factored form

    • Quiz: Lesson 3

    • Game Time! Is it a polynomial?

    • Mini Challenge: Lesson 3

    • Worksheet: Lesson 3

    • Lesson 4: Comparing (using graphing technology) the numeric, graphical, and algebraic representations of polynomial (i.e., linear, quadratic, cubic, quartic) functions

    • Quiz: Lesson 4

    • Mini Challenge: Lesson 4

    • Worksheet: lesson 4

    • Quiz: Lesson 5

    • Game Time! Flip and learn

    • Mini Challenge: Lesson 5

    • Worksheet: Lesson 5

    • Lesson 7: Making connections (using graphing technology) between a polynomial function given in factored form [e.g., f(x) = 2(x – 3)(x + 2)(x – 1)] and the x-intercepts of its graph

    • Worked Out Example: Lesson 7

    • Quiz: Lesson 6/7

    • Mini Challenge: Lesson 6/7

    • Worksheet: Lesson 6/7

    • Lesson 8: Sketching the graph of a polynomial function given in factored form using its key features.

    • Quiz: Lesson 8

    • Game Time! Select the right graph

    • Mini Challenge: Lesson 8

    • Worksheet: Lesson 8

    • Lesson 9: Determining (using technology, desmos is fine) the roles of the parameters a, k, d, and c in functions of the form y = af(k(x – d)) + c, and describe these roles in terms of transformations on the graphs of f(x) = x and f(x) = x

    • Quiz: Lesson 9

    • Game Time! Put the graphs in the correct order

    • Mini Challenge: Lesson 9

    • Worksheet: Lesson 9

    • Lesson 10: Determining an equation of a polynomial function that satisfies a given set of conditions (In the lesson include that there may be more than one polynomial function that can satisfy a given set of conditions)

    • Worked Out Example: Lesson 10

    • Quiz: Lesson 10

    • Mini Challenge: Lesson 10

    • Worksheet: lesson 10

    • Worked Out Example: Lesson 11

    • Quiz: Lesson 11

    • Mini Challenge: Lesson 11

    • Worksheet: Lesson 11

    • Lesson 12: Determining and comparing the properties of even and odd polynomial functions, and determine whether a given polynomial function is even, odd, or neither

    • Worked Out Example: Lesson 12

    • Quiz: Lesson 12

    • Game Time! Drag and drop

    • Mini Challenge: Lesson 12

    • Worksheet: Lesson 12

    • Lesson 13: Determining (with and without technology) key features (i.e., vertical and horizontal asymptotes, domain and range, intercepts, positive/negative intervals, increasing/decreasing intervals)

    • Worked Out Example: Lesson 13

    • Quiz: Lesson 13

    • Mini Challenge: Lesson 13

    • Worksheet: Lesson 13

    • Lesson 14: Determining (with and without technology) key features (i.e., vertical and horizontal asymptotes, domain and range, intercepts, positive/negative intervals, increasing/decreasing intervals)

    • Quiz: Lesson 14

    • Mini Challenge: Lesson 14

    • Worksheet: Lesson 14

    • Lesson 15: Sketching the graph of a simple rational function using its key features, given the algebraic representation of the function

    • Worked Out Example: Lesson 15

    • Quiz: Lesson 15

    • Mini Challenge: Lesson 15

    • Worksheet: lesson 15

    • Lesson 16: Understanding the connection between vertical asymptotes and limits that equal to ∞

    • Quiz: Lesson 16

    • Mini Challenge: Lesson 16

    • Worksheet: Lesson 16

    • Lesson 17: Given the equation of a rational function, determine the equation of the horizontal asymptote

    • Quiz: Lesson 17

    • Mini Challenge: Lesson 17

    • Worksheet: Lesson 17

    • Lesson 19: Given the equation of a polynomial or rational function, draw an accurate sketch showing all key features

    • Quiz: Lesson 18/19

    • Game Time! Question set

    • Mini Challenge: Lesson 18/19

    • Worksheet: Lesson 19

    • Lesson 20: Performing long division of polynomials, perform synthetic division of polynomials, state the restrictions, and write the division statement

    • Worked Out Example: Lesson 20

    • Quiz: Lesson 20

    • Mini Challenge: Lesson 20

    • Worksheet: lesson 20

    • Lesson 20B: Performing long division of polynomials, perform synthetic division of polynomials, state the restrictions, and write the division statement

    • Worked Out Example: Lesson 20B

    • Quiz: Lesson 20 B

    • Game Time! Drag and drop

    • Mini Challenge: Lesson 20B

    • Worksheet: Lesson 20B

    • Lesson 21: Making connections (using technology) between the polynomial function f(x), the divisor x – a, the remainder from the division f(x)/x-a, and f(a) to verify the remainder theorem and the factor theorem

    • Quiz: Lesson 21

    • Mini Challenge: Lesson 21

    • Worksheet: lesson 21

    • Lesson 22: Using the factor theorem to determine whether a binomial is a factor of a higher-order polynomial

    • Worked Out Example: Lesson 22

    • Quiz: Lesson 22

    • Game Time! Find the factors

    • Mini Challenge: Lesson 22

    • Worksheet: Lesson 22

    • Lesson 23: Factoring polynomial expressions in one variable, of degree no higher than four, by selecting and applying strategies (i.e., common factoring, difference of squares, trinomial factoring, factoring by grouping, remainder theorem, factor theorem)

    • Worked Out Example: Lesson 23

    • Quiz: Lesson 23

    • Mini Challenge: Lesson 23

    • Worksheet: Lesson 23

    • Lesson 24: Determining (using technology) the connection between the real roots of a polynomial equation and the x-intercepts of the graph of the corresponding polynomial function, and describe this connection

    • Worked Out Example: Lesson 24

    • Quiz: Lesson 24

    • Mini Challenge: Lesson 24

    • Worksheet: Lesson 24

    • Lesson 26: Solving polynomial equations in one variable, of degree no higher than four (e.g., 2x3 – 3x2 + 8x – 12 = 0), by selecting and applying strategies

    • Worked Out Example: Lesson 25-26

    • Quiz: Lesson 26

    • Game Time! Drag and drop

    • Mini Challenge: Lesson 26

    • Worksheet: Lesson 26

    • Lesson 27: Determining (using technology) the connection between the real roots of a rational equation and the x-intercepts of the graph of the corresponding rational function, and describe this connection

    • Quiz: Lesson 27

    • Mini Challenge: Lesson 27

    • Worksheet: Lesson 27

    • Lesson 28: Solving simple rational equations in one variable algebraically, and verify solutions using technology

    • Worked Out Example: Lesson 28

    • Quiz: Lesson 28

    • Game Time! Flip and learn

    • Mini Challenge: Lesson 28

    • Worksheet: Lesson 28

    • Lesson 29: Solving problems involving applications of polynomial and simple rational functions and equations (In the lesson include problems involving the factor theorem or remainder theorem, such as determining the values of k for which the function f(x)

    • Worked Out Example: Lesson 29

    • Quiz: Lesson 29

    • Game Time! Guess the Answer

    • Mini Challenge: Lesson 29

    • Worksheet: Lesson 29

    • Lesson 30: Explaining, for polynomial and simple rational functions, the difference between the solution to an equation in one variable and the solution to an inequality in one variable, and demonstrate that given solutions satisfy an inequality

    • Quiz: Lesson 30

    • Mini Challenge: Lesson 30

    • Worksheet: lesson 30

    • Lesson 31: Determining solutions to polynomial inequalities in one variable & to simple rational inequalities in one variable by graphing the corresponding functions,using graphing technology, & identifying intervals for which x satisfies the inequalities

    • Worked Out Example: Lesson 31

    • Quiz: Lesson 31

    • Mini Challenge: Lesson 31

    • Worksheet: Lesson 31

    • Lesson 32: Solving factorable polynomial inequalities algebraically and by graphing

    • Worked Out Example: Lesson 32

    • Quiz: Lesson 32

    • Game Time! Question set

    • Mini Challenge: Lesson 32

    • Worksheet: Lesson 32

    • Lesson 33: Given the equation of a higher-order polynomial: - Predict the behaviour of the graph near the x-intercepts - Predict the end behaviour - Determine the maximum number of turning points

    • Quiz: Lesson 33

    • Mini Challenge: Lesson 33

    • Worksheet: Lesson 33

    • Lesson 34: Drawing a detailed sketch illustrating the main features from previous lesson

    • Worked Out Example: Lesson 34

    • Quiz: Lesson 34

    • Game Time! Fill in the blanks

    • Mini Challenge: Lesson 34

    • Worksheet: Lesson 34

    • Lesson 35: Solving linear inequalities and factorable polynomial inequalities in one variable and represent the solutions on a number line and algebraically

    • Worked Out Example: Lesson 35

    • Quiz: Lesson 35

    • Mini Challenge: Lesson 35

    • Game Time! Drag and Drop

    • Worksheet: Lesson 35

  • 05

    Exponential and Logarithmic Functions

    • Lesson 1: Recognizing the logarithm of a number to a given base as the exponent to which the base must be raised to get the number

    • Worked Out Example: Lesson 1

    • Quiz: Lesson 1

    • Mini Challenge: Lesson 1

    • Worksheet: Lesson 1

    • Lesson 2: Recognizing the operation of finding the logarithm to be the inverse operation

    • Worked Out Example: Lesson 2

    • Quiz: Lesson 2

    • Mini Challenge: Lesson 2

    • Worksheet: Lesson 2

    • Lesson 3: Determining (with technology) the approximate logarithm of a number to any base, including base 10

    • Worked Out Example: Lesson 3

    • Quiz: Lesson 3

    • Mini Challenge: Lesson 3

    • Worksheet: Lesson 3

    • Quiz: Lesson 4

    • Mini Challenge: Lesson 4

    • Worksheet: Lesson 4

    • Lesson 5: Solving simple exponential equations by rewriting them in logarithmic form

    • Worked Out Example: Lesson 5

    • Quiz: Lesson 5

    • Game Time! Question set

    • Mini Challenge: Lesson 5

    • Worksheet: lesson 5

    • Lesson 7: Making connections between laws of exponents and the laws of logarithms and verify the laws of logarithms with or without technology

    • Quiz: Lesson 7

    • Mini Challenge: Lesson 7

    • Worksheet: Lesson 7

    • Lesson 8: Using the laws of logarithms to simplify and evaluate numerical expressions

    • Worked Out Example: Lesson 8

    • Quiz: Lesson 8

    • Mini Challenge: Lesson 8

    • Worksheet: Lesson 8

    • Lesson 9: Laws of logs: PROOFS (log ab = log a + log b), (log a/b = log a- log b), (log a^x = x log a)

    • Quiz: Lesson 9

    • Mini Challenge: Lesson 9

    • Worksheet: Lesson 9

    • Quiz: Lesson 10

    • Game Time! Fill in the blanks

    • Mini Challenge: Lesson 10

    • Worksheet: Lesson 10

    • Lesson 11: Determining (with and without technology) key features (i.e., vertical and horizontal asymptotes, domain and range, intercepts, increasing/decreasing behaviour)

    • Worked Out Example: Lesson 11

    • Quiz: Lesson 11

    • Mini Challenge: Lesson 11

    • Worksheet: Lesson 11

    • Lesson 12: Using logarithms to transform a given relationship to linear form, and determine unknown constants by considering the gradient and/or intercept

    • Quiz: Lesson 12

    • Mini Challenge: Lesson 12

    • Worksheet: Lesson 12

    • Lesson 13: The relationship between an exponential function and the corresponding logarithmic function to be that of a function and its inverse

    • Quiz: Lesson 13

    • Mini Challenge: Lesson 13

    • Worksheet: lesson 13

    • Worksheet: Lesson 14/2 MERGED

    • Quiz: Lesson 14/2 MERGED

    • Game Time! Inverse Functions

    • Mini Challenge: Lesson 14/2 MERGED

    • Lesson 15: Determining the roles of the parameters d and c in functions of the form y=log10(x–d)+c & the roles of the parameters a & k in functions of the form y=alog10(kx), & describe these roles in terms of transformations on the graph of f(x)=log1

    • Quiz: Lesson 15

    • Game Time! Question set

    • Game Time! Find the right graph

    • Game Time! Find the right graph

    • Game Time! Find the right graph

    • Game Time! Find the right graph

    • Mini Challenge: Lesson 15

    • Worksheet: Lesson 15

    • Lesson 16/17: Explore Ln xLesson 18: Finding the equation of the inverse given the equation of an exponential or logarithmic function

    • Quiz: Lesson 16/17

    • Mini Challenge: Lesson 16/17

    • Worksheet: Lesson 16/17

    • Lesson 18: Finding the equation of the inverse given the equation of an exponential or logarithmic function

    • Worked Out Example: Lesson 18

    • Quiz: Lesson 18

    • Game Time! Question set

    • Mini Challenge: Lesson 18

    • Worksheet: Lesson 18

    • Lesson 19: Posing problems based on real-world applications of exponential and logarithmic functions and solve these problems by using a given graph or a graph generated with technology from a table of values or from its equation

    • Worked Out Example: Lesson 19

    • Quiz: Lesson 19

    • Game Time! Drag and drop

    • Mini Challenge: Lesson 19

    • Worksheet: Lesson 19

    • Lesson 20: Recognizing equivalent algebraic expressions involving logarithms and exponents, and simplify expressions of these types

    • Quiz: Lesson 20

    • Mini Challenge: Lesson 20

    • Worksheet: Lesson 20

    • Lesson 22: Solving simple logarithmic equations in one variable algebraically

    • Worked Out Example: Lesson 22

    • Quiz: Lesson 22

    • Mini Challenge: Lesson 22

    • Worksheet; Lesson 22

    • Lesson 23: Solving logarithmic equations, including checking for inadmissible solutions that would give a negative base or argument

    • Quiz: Lesson 23

    • Game Time! Fill in the blanks

    • Mini Challenge: Lesson 23

    • Worksheet: Lesson 23

    • Lesson 25: Understanding how logarithmic scales are used to measure earthquakes, sound, and acidity

    • Quiz: Lesson 25

    • Game Time! Question set

    • Mini Challenge: Lesson 25

    • Game Time! Flip and Learn

    • Worksheet: Lesson 25

  • 06

    Trigonometric Functions

    • Lesson 1: Defining the radian measure of an angle as the length of the arc that subtends this angle at the centre of a unit circle, and develop and apply the relationship between radian and degree measure

    • Quiz: Lesson 1

    • Mini Challenge: Lesson 1

    • Worksheet: Lesson 1

    • Lesson 2: Representing radian measure in terms of π and as a rational number

    • Quiz: Lesson 2

    • Mini Challenge: Lesson 2

    • Worksheet: Lesson 2

    • Lesson 3: Determining, with technology, the primary trigonometric ratios (i.e., sine, cosine, tangent) and the reciprocal trigonometric ratios (i.e., cosecant, secant, cotangent) of angles expressed in radian measure

    • Quiz: Lesson 3

    • Mini Challenge: Lesson 3

    • Worksheet: Lesson 3

    • Lesson 4: Determining, without technology, the exact values of the primary trigonometric ratios and the reciprocal trigonometric ratios for the special angles 0, π/6, π/4, π/3, π/2, and their multiples less than or equal to 2π

    • Worked Out Example: Lesson 4

    • Quiz: Lesson 4

    • Mini Challenge: Lesson 4

    • Worksheet: Lesson 4

    • Lesson 5: Predicting the signs of trig ratios, given the quadrant

    • Quiz: Lesson 5

    • Game Time! Question set

    • Mini Challenge: Lesson 5

    • Worksheet: Lesson 5

    • Lesson 6: Understanding the concept of periodic graphs

    • Quiz: Lesson 6

    • Mini Challenge: Lesson 6

    • Worksheet: Lesson 6

    • Lesson 7: Sketching the graphs of f(x) = sin x and f(x) = cos x for angle measures expressed in radians, and determine and describe some key properties in terms of radians

    • Quiz: Lesson 7

    • Mini Challenge: Lesson 7

    • Worksheet: Lesson 7

    • Lesson 8: Identifying the features (including period, amplitude, principal axis) of the basic trig graphs, including y = tan θ

    • Quiz: Lesson 8

    • Mini Challenge: Lesson 8

    • Worksheet: Lesson 8

    • Lesson 9: Understanding the connection of the vertical asymptotes in y = tan θ to the x, y, r definitions

    • Lesson 10: Using the basic trig graphs to determine the values of some trig ratios

    • Quiz: Lesson 9/10

    • Mini Challenge: Lesson 9/10

    • Worksheet: Lesson 9/10

    • Lesson 11: Making connections between the tangent ratio and the tangent function by using technology to graph the relationship between angles in radians and their tangent ratios (continued in next lesson)

    • Quiz: Lesson 11

    • Game Time! Fill in the blanks

    • Mini Challenge: Lesson 11

    • Worksheet: Lesson 11

    • Lesson 13: Making connections between the equations, graphs, and features of transformed trig functions

    • Quiz: Lesson 12/13

    • Mini Challenge: Lesson 12/13

    • Worksheet: lesson 12/13

    • Lesson 14: Graphing, with technology and using the primary trigonometric functions, the reciprocal trigonometric functions (i.e., cosecant, secant, cotangent) for angle measures expressed in radians

    • Quiz: Lesson 14

    • Mini Challenge: Lesson 14

    • Worksheet: Lesson 14

    • Lesson 15: Determining and describing key properties of the reciprocal functions

    • Quiz: Lesson 15

    • Game Time! Question set

    • Mini Challenge: Lesson 15

    • Worksheet: lesson 15

    • Lesson 16: Determining the amplitude, period, and phase shift of sinusoidal functions whose equations are given in the form f(x) = a sin (k(x – d)) + c or f(x) = a cos(k(x – d)) + c, with angles expressed in radians

    • Quiz: Lesson 16

    • Mini Challenge: Lesson 16

    • Worksheet: Lesson 16

    • Lesson 17: Sketching graphs of y = a sin (k(x–d)) + c a & y = a cos(k(x–d))+c by applying transformations to the graphs of f(x)=sin x & f(x)=cos x with angles expressed in radians, & state the period, amplitude, & phase shift of the transformed function

    • Worked Out Example: Lesson 17

    • Quiz: Lesson 17

    • Game Time! Drag and drop

    • Mini Challenge: Lesson 17

    • Worksheet: lesson 17

    • Lesson 18: Representing a sinusoidal function with an equation, given its graph or its properties, with angles expressed in radians

    • Worked Out Example: Lesson 18

    • Quiz: Lesson 18

    • Game Time! Question set

    • Mini Challenge: Lesson 18

    • Worksheet: Lesson 18

    • Lesson 19: Posing problems based on applications involving a trigonometric function with domain expressed in radians & solve these problems by using a given graph or a graph generated with or without technology from a table of values or from its equation

    • Quiz: Lesson 19

    • Game Time! Find the right trig functions

    • Mini Challenge: Lesson 19

    • Worksheet: Lesson 19

    • Quiz: Lesson 20/21

    • Lesson 20/21: Using special triangles to find the exact values of trig ratios for 30°, 45°, and 60°

    • Mini Challenge: Lesson 20/21

    • Worksheet: Lesson 20/21

    • Lesson 22: Solving simple trig equations with a calculator but without using graphing technology

    • Quiz: Lesson 22

    • Mini Challenge: Lesson 22

    • Worksheet: Lesson 22

    • Lesson 24: Finding all the solutions of simple trigonometric equations lying in a specified interval (general forms of solution are not included)

    • Quiz: Lesson 23/24

    • Game Time! Drag and drop

    • Mini Challenge: Lesson 23/24

    • Worksheet: Lesson 23/24

    • Lesson 25/26: Exploring the algebraic development of the compound angle formulas and use the formulas to determine exact values of trigonometric ratios

    • Quiz: Lesson 25/26

    • Game Time! Drag and drop

    • Game Time! Dialog Cards

    • Mini Challenge: Lesson 25/26

    • Worksheet: lesson 25/26

    • Lesson 27: Recognize that trigonometric identities are equations that are true for every value in the domain

    • Quiz: Lesson 27

    • Mini Challenge: Lesson 27

    • Worksheet: Lesson 27

    • Lesson 28: Using trig identities for the simplification and exact evaluation of expressions

    • Worked Out Example: Lesson 28

    • Quiz: Lesson 28

    • Mini Challenge: Lesson 28

    • Worksheet: lesson 28

    • Lesson 29: Selecting an identity or identies appropriate to the context (Include: Sec2θ = 1 + tan2θ and cosec2θ = 1 + cot2θ, The expansions of sin (A+ B), cos(A+ B) and tan(A+ B), The formulae for sin2A, cos2A and tan2A , The expression of a sinθ + b cosθ

    • Quiz: Lesson 29

    • Game Time! True or false

    • Game Time! Find the correct solution

    • Mini Challenge: Lesson 29

    • Worksheet: Lesson 29

    • Lesson 30: Solving linear and quadratic trigonometric equations, with and without graphing technology, for the domain of real values from 0 to 2π, and solve related problems (could be split into two lessons if too much)

    • Quiz: Lesson 30

    • Game Time! Drag and drop

    • Mini Challenge: Lesson 30

    • Game Time! Memory Game

    • Worksheet: Lesson 30

  • 07

    Tinkering Project

    • Let's Tinker!

    • Find a solution using Math to the UN Sustainable Goal: Clean Water and Sanitation

    • Find a solution using Math to the UN Sustainable Goal: Life on Land

Reviews

“Great program. I love math and I'm always looking for new ways to approach it. This course teaches advanced functions in a creative and comprehensive way.”

Student, Age 17

Aakash

“This virtual course really helped me prepare for the concepts taught in Advanced Functions at school. Nothing caught me off guard so I had plenty of time to do my homework, without struggling to understand the concepts. It made this semester a lot less stressful. ”

Student, Age 16

Grace

“There should simply be more courses like this available to high school students. They shouldn't be expected to succeed in mathematics without support and alternative learning options. I'm glad this course exists.”

Parent

Bill

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Frequently Asked Questions

Here are answers to some common questions we are asked

  • What grade is this level for?

    This level is designed for kids ages 11-12 in Grades 6 and 7.

  • How is this course taught?

    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.

  • How will I get access to the learning platform?

    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].

  • Can you explain your currriculum?

    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.

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  • BBC review of Explorer Hop
  • Global News review of Explorer Hop
  • CP24 review of Explorer Hop
  • CTV review of Explorer Hop
  • Readers Digest review of Explorer Hop
  • Toronto Star review of Explorer Hop

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