MCR 3U: Essential Skills Review
MCR 3U UNIT 1: Introduction to Functions
1.1 Relations and Functions
Pages 10-11 # 1-3, 4-7,9,14
Website Video Clips with Solutions:
Defining which relation are Functions
Mapping a diagram
Recognizing Functions by Vertical Line Test
Curriculum: A 1.1 & A 1.3
1.2 Function Notation
Website Video Clips with Solutions:
Khan Academy Exercises:
Pages 22-24 # 1, 2, 4-9,13 and 18
Introduction to Function Notations
Evaluating Functions
Evaluating Functions Example 1
Evaluating Functions Example 2
Function Notation
Go to topic “Algebra” and click on “Functions” then click on “Function Notation”
Functions Practice 1
Functions Practice 2
Curriculum: A 1.2 & A 1.3
1.4 Domain and Range of a
Function
Website Video Clips with Solutions:
Khan Academy Exercises:
Pages 35-37 # 1-4,6,7,9-14
Domain and Range Example
Domain and Range Example 2
Restricting Domain and Range application problem example
Explaining the domain of a function
Domain and Range
Go to topic “Algebra” and click on “Functions” then click on “Domain and Range”
Domain of a Function
Range of a Function
Curriculum: A 1.3
1.5 The Inverse of a Function
Pages 46-49 #1,2,3,5,6,8-10,12,15
Website Video Clips with Solutions:
Inverse of a Function
Go to topic “Algebra” and click on “Functions” then click on “Inverse of Functions”
Khan Academy Exercises:
Inverse of a Function practice
Curriculum: A 1.4, A 1.5, A 1.6
1.3 & 1.6 Transformations of Parent
Functions (Using technology)
Khan Academy Exercises:
Additional Support tools:
Pages 28 #1-3 and Pages 51 #1-3
Practice Shifting and Reflecting Functions
Transformation of Quadratics in vertex form
This site allows you to explore the effects of stretches and translations on quadratic functions by using a graph
creator. This site also allows you to create your own graphs by using the tools under the activity tools section.
Graphing Calculator Emulator
Download free graphing Calculator software
Curriculum: A 1.8 & A 1.9
1.7 Exploring Transformations of
Functions
Website Video Clips with Solutions:
Pages 58-60 #3-6,8,10,11,14
Vertical Stretch Example
Reflections of a Vertical stretch
Horizontal translation example
Vertical Translation example
Curriculum: A 1.3, A 1.7, A 1.8
1.8 Using Transformations to Graph
Functions
Pages 70-73 #4-11,17-20
Website Video Clips with Solutions:
Connecting transformations to graphs
Using transformations to graph functions example
Curriculum: A 1.3, A 1.7, A 1.8
Unit 1 Review
Pages 76-78
MCR 3U UNIT 2: Equivalent Algebraic Expressions
2.1 Adding and Subtracting
Polynomials
Website Video Clips with Solutions:
Additional Support tools:
Pages 88-90 #1-6 (eol), 8, 11 (See Simplifying Polynomial Video for help), 16
Simplifying Polynomials Example 1
Simplifying Polynomials Example 2
Simplifying Application Polynomial example
Domain and Range
Adding and Subtracting Polynomial example
Go to topic “Algebra” and click on “Polynomials” then click on “Adding/Subtracting Polynomials”
Practice problems
Guided Instruction and Practice problems for adding and subtracting polynomials
2.2 Multiplying Polynomials
Pages 95-97 #1-6, 8-12, 14 + Curious Math # 1-4
Website Video Clips with Solutions:
Multiplying Polynomials Examples
Go to topic “Algebra” and click on “Polynomials” then click on “Multiplication with Polynomials”
Additional Support tools:
Practice problems
Guided Instruction and Practice problems for multiplying polynomials
2.3 Factoring Polynomials
Pages 102-104 # 3-9, 11, 14
Website Video Clips with Solutions:
Review of Factoring by Grouping
Polynomial Factoring Examples
Go to topic “Algebra” and click on “Factoring” then click on “Grouping”
Additional Support tools:
Practice problems
Guided Instruction and Practice problems for factoring polynomials
2.4 Simplifying Rational Functions
Pages 113-114 #4-8, 10,11
Website Video Clips with Solutions:
Simplifying Rational Functions Explanation
Simplifying Rational Function example 1
Simplifying Rational Function Example 2
Additional Support tools:
Practice problems
Guided Instruction and Practice problems for Simplifying Rational functions
2.5 Exploring Graphs of Rational
Functions
Pages 115-116
Website Video Clips with Solutions:
2.6 Multiplying and Dividing
Rational Expressions
Website Video Clips with Solutions:
Additional Support tools:
Rational Function Graph example 1
Rational Function Graph example 2
Rational Function Graph Example 3
Pages 121-123 #1-9 (eol), 12, 13
Multiplying and Dividing Rational Expressions Example
Go to topic “Algebra” and click on “Rational Expressions” then click on “Multiply and Divide”
Multiplying and Dividing Rational expressions example 2
Multiplying and Dividing Rational expressions example 3
http://www.algebralab.org/practice/practice.aspx?file=Algebra1_11-6.xml
Practice problems
Guided Instruction and Practice problems for multiplying and dividing rational expressions
2.7 Adding and Subtracting Rational
Expressions
Website Video Clips with Solutions:
Review
Pages 128-130 #1-10 (eol), 12, 14, 15
Adding and Subtracting Rational Expressions Example
Go to topic “Algebra” and click on “Rational Expressions” then click on “add and subtract”
Adding and Subtracting Rational Expressions Example 2
Adding and Subtracting Rational Expressions Example 3
Pages 10-11 #
Website Video Clips with Solutions:
Khan Academy Exercises:
Additional Practice for fractions and making common denominators
Common denominator Practice
Multiplying Fractions Practice
Dividing Fractions Practice
MCR 3U UNIT 3: Quadratic Functions
3.1 Properties of Quadratic Functions
Pages 145-147 #2,4-11, 13, 15 (See video for max profit)
Website Video Clips with Solutions:
Interpreting Graphs
Maximizing profit example
Quadratic Graphs concept
3.2 Determining Maximum and
Minimum Values of Quadratics
Website Video Clips with Solutions:
Pages 153-154 # 14
Finding Max/Min of Quadratics
Determining max/min of quadratic
Finding max/min example 1
Finding max/min example 2
Maximizing Profit Example
3.3 The Inverse of a Quadratic
Function
Pages 160-162 # 2-7, 9-11, 13-16
Website Video Clips with Solutions:
Inverse of a Function
Go to topic “Algebra” and click on “Functions” then click on “Inverse of Functions”
3.4 Operations with Radicals
Pages 167-168 # 1-11, 15-16
Website Video Clips with Solutions:
Roots and Radicals Review Examples
Go to topic “Algebra” and click on “Roots and Radicals” then watch the videos
Simplifying Radicals example
Multiplying Radicals
Multiplying Radicals 2
Multiplying Radicals 3
Khan Academy Exercises:
Simplifying Radicals Practice
3.5 Quadratic Applications
Pages 177-178 # 1,2,5,8-11, 13,16
Website Video Clips with Solutions:
3.6 Zeros of a Quadratic Functions
Quadratic Functions
Click on “Quadratic Functions” - Solving by Factoring: #26-30 (Number and Type of roots, examples
1 to 4)
Rectangle Application question
Height application problem
Pages 10-11 #
Website Video Clips with Solutions:
Quadratic Functions
Click on “Quadratic Functions” - Solving by Factoring: #26-30 (Number and Type of roots, examples
1 to 4)
Solving using the discriminant
Solving using the discriminant 2
Solving using the discriminant 3
Finding the Vertex, finding axis symmetry example
Finding the intercepts, vertex, axis of symmetry,
3.7 Families of Quadratic Functions
Pages 192-193 #3,4-9, 12,14,16
Website Video Clips with Solutions:
Quadratic Function Graphing example 1
Quadratic Function Graphing example 2
3.8 Liner-Quadratic Application
Pages 198-199 #1-4,6,8,9,10,12
Website Video Clips with Solutions:
Rectangle Application question
Height application problem
Review
Pages 202-203 #
MCR 3U UNIT 4: Exponential Functions
4.2 Working with Integer Exponents
Pages 221-223 #1-9(eol), 11, 13-14, 16,18
Website Video Clips with Solutions:
Exponent Properties
Go to topic “Algebra” and click on “Exponents” then click on the videos
Integer Exponent
Explaining Negative Exponents
Exponent Rules
Khan Academy Exercises:
Exponent Practice 1
Exponent Practice 2
Exponent Rules
4.3 Working with Rational
Exponents
Pages 229-230 # 1-6,10-14, 18a
Website Video Clips with Solutions:
Exponent Rules
Rational Exponent Examples
Click on “Exponential Functions” then Basics: Watch #8-11
Khan Academy Exercises:
Exponent Practice 3
4.4 Simplifying Algebraic
Expressions
Pages 236-237 #1-8, 11,13,14
Website Video Clips with Solutions:
4.5 Exploring Exponential
Functions
Simplifying exponents example
Simplifying Expressions with exponents
Simplifying Expressions with exponents 2
Simplifying Expressions with exponents 3
Pages 243 # 1-2
Website Video Clips with Solutions:
Graphing Exponential Functions
Graphing Exponential functions using technology
Additional Support tools:
Graphing Software: Geogebra
Graphing software that you can use at home: select “Applet start”. From here, you can enter
equations and get the graph. You also have the choice to download the software for free.
Graphing Calculator Emulator
Download the free graphing calculator software
4.6 Transformations of Exponential
Functions
Website Video Clips with Solutions:
4.7 Exponential Function
applications
Pages 252-253 #1,2,4-6, 9,10,12,14
Exponential Graphs
Exponential Graphs Example 2
Exponential Graphs Example 3
Pages 261-263 #1-8, 9-14
Website Video Clips with Solutions:
Exponential Application Example 1
Exponential Application Example 2
Exponential Application Example Growth and Decay
Review
Pages 267-269
MCR 3U UNIT 5: Discrete Functions Part 1: Sequences and Series
7.1 Arithmetic Sequences
Website Video Clips with Solutions:
7.2 Geometric Sequences
Pages 424-425 # 2-5,8i,9,13,15-17
Arithmetic Sequences
Go to topic “Algebra” and click on “Sequences and Series” then click on the video
Arithmetic Sequence Example
Arithmetic Sequence Example 2
Arithmetic Sequence Example 3
Pages 430-431 #1-4,5i,6i,10-11 17-20
Website Video Clips with Solutions:
7.3 Defining Sequences
Website Video Clips with Solutions:
Geometric Sequences
Go to topic “Algebra” and click on “Sequences and Series” then click on the video
Geometric Sequence explanation
Geometric Sequence Example 1
Geometric Sequence Example 2
Pages 439-440 #1,2,4-7,10,11
Sequences
Go to topic “Algebra” and click on “Sequences and Series” then click on “Sequences”
Predicting the next term example
Writing the general term/formula example
7.4 Recursive Sequences
Pages 443 #1-3
Website Video Clips with Solutions:
Recursive Sequences explanation
Recursive Sequence example finding the next 3 terms
Additional Support tools:
Explanation of Recursive Sequences with examples
7.5 Arithmetic Series
Pages 452-453 # 4-8,9,10,14-16
Website Video Clips with Solutions:
7.6 Geometric Series
Arithmetic Series example find sum of 1st 40 terms
Arithmetic Series example find sum of the series
Arithmetic Series example how many terms are there?
Proof of an Arithmetic Series starts at 2:40
Pages 459-461 #2-10,12,14-18
Geometric Series Explanation
Website Video Clips with Solutions:
Geometric Series find the sum of the nth term example
Geometric Series find the sum of the infinite series example
Geometric Series proof
Additional Support tools:
PDF explanation of the Geometric Series Proof
7.7 Pascal’s Triangle and Binomial
Expansions
Pages 466 #1-6,10,11,13
Website Video Clips with Solutions:
Binomial Expansion Review
Go to topic “Algebra” and click on “Sequences and Series” then click on the video
Binomial Expansion and geometric series
Review
Pages 468-469
MCR 3U UNIT 6: Discrete Functions Part 2: Financial Applications
8.1 Simple Interest
Website Video Clips with Solutions:
8.2 Compound Interest 1: Future
Website Video Clips with Solutions:
Pages 481-482 #1-4,6-10,12
Simple Interest Example 1
Simple Interest Example 2
Simple Interest Example 3
Simple Interest Example 4
Simple Interest Example 5
Graphing Simple Interest
Pages 490-492 #1,2,4-6,7-12,14,17
Compound Interest future value example
Graphing compound interest
Compound Interest example 1
Only look at Problem #1
Compound Interest Example 2
Compound interest different types
8.3 Compound Interest 2: Present
Website Video Clips with Solutions:
Pages 498-499 #1-9,11-14
Compound interest present value
8.4 Annuities 1: Future
Pages 511-512 #
Website Video Clips with Solutions:
Simple Annuities
Annuity future value example
8.5 Annuities 2: Present
Pages 520-522 #
Website Video Clips with Solutions:
Website with online annuity calculator
Use this website as a tool to check your answers
8.6 Financial Application Problems
Pages 531-532 #
Website Video Clips with Solutions:
Additional Support tools:
Using a Graphing Calculator to solve Annuity problems
Website with online annuity calculator
Use this website as a tool to check your answers
Using a graphing calculator example
Graphing Calculator Emulator
Download the free graphing calculator software
Review
Pages 534-535 #
MCR 3U UNIT 7: Trigonometric Ratios
5.1 Trigonometric Ratios of Acute
Angles
Website Video Clips with Solutions:
Khan Academy Exercises:
5.2 Trigonometric Ratios for Special
Angles
Website Video Clips with Solutions:
Pages 10-11 #
Trig Ratios video
Click on topic “Trigonometry and Geometry” – D: Finding unknown sides and angles: #18 –24
watch and work through the examples
Evaluating Sin and Cosine at Acute angles
Watch the concept video and the problems #1 to 3
Solving Acute Triangles example
Watch the concept video and the problems #1 to 4
Review your skills
Pythagorean Theorem
Trigonometry Practice 1
Trigonometry Practice 2
Pages 10-11 #
Evaluating Trig ratios at special angles
Watch the concept video and the problems #1 to 3
5.3 Trigonometric Ratios for Angles > 90
Pages 10-11 #
Website Video Clips with Solutions:
Trig Ratios video
Click on topic “Trigonometry and Geometry” – D: Finding unknown sides and angles: #18 –24
watch and work through the examples
5.4 Trigonometric Ratios for Angles
between 0 and 360
Website Video Clips with Solutions:
Pages 10-11 #
Unit Circle and Trigonometric ratios
5.5 Trigonometric Identities
Pages 10-11 #
Khan Academy Exercises:
Identities and Formulas
Go to topic “Trigonometry” and click on “Identities and Formulas” then click on “identities and
Formulas”
Trigonometric Identities
Watch Concept and Problem 1
Review your skills
Trigonometry Identity Practice Questions
5.6 Sine Law Problems
Pages 10-11 #
Website Video Clips with Solutions:
Website Video Clips with Solutions:
5.7 Cosine Law Problems
Website Video Clips with Solutions:
5.8 3-Dimensional Application
Problems
Website Video Clips with Solutions:
Sine Law examples
Click on topic “Trig Functions” – Sine Law B: 4 to 7 – watch and work through the examples
Sine Law example 2
Click on topic “Trigonometry” then click on “Triangles” - Law of Sines examples #1-2
Application Problem
Application Problem 2
Pages 10-11 #
Cosine Law Examples
Click on topic “Trig Functions” – Cosine Law C: 8 to 10 – watch and work through the examples
Cosine Law example 2
Click on topic “Trigonometry” then click on “Triangles” - Law of Cosine example #1
Application Problem
Application Problem 2
Pages 10-11 #
Review
Pages 10-11 #
MCR 3U UNIT 8: Sinusoidal Functions
6.1 Periodic Functions
Pages 352-356 #
Website Video Clips with Solutions:
Properties of Periodic Functions
6.2 Investigating the Properties of
Sinusoidal Functions
Pages 363-364 #
Website Video Clips with Solutions:
6.3 Interpreting Sinusoidal
Functions
Website Video Clips with Solutions:
6.4 Transformations of Sinusoidal
Functions
Website Video Clips with Solutions:
Definition of Trig Functions using a unit circle
Sine Graphs video
Pages 371-373 #
Basic Sine and Cosine Graphs
Go to topic “Trigonometry” and click on “Graphing and Inverse functions” then click on “Basic
Graphs”
Sine and Cosine Graphs
Watch the concept video and the problems #1 to 3
Pages 379 #
Transformations of Sinusoidal Graphs
Click on topic “Trig Functions” – E: Graphing 15 to 10 – watch and work through the
examples of transformations
Transformations of Sine and Cosine Graphs
Watch the concept video and the problems #1 to 3
6.5 Using Transformations to
Sketch Sinusoidal Functions
Website Video Clips with Solutions:
Pages 383-385 #
Transformations of Sinusoidal Graphs
Click on topic “Trig Functions” – E: Graphing 15 to 10 – watch and work through the
examples of transformations
More Transformations of Sine and Cosine Graphical examples
Watch the concept video and the problems #1 to 3
Khan Academy Exercises:
Sine and Cosine Graph Practice Questions
6.6 Investigating Models of
Sinusoidal Functions
Pages 391-393 #
Website Video Clips with Solutions:
“Finding an equation from its graph
Go to topic “Trigonometry” and click on “Graphing and Inverse functions” then click on
“Finding an equation from its graph”
Graphing combinations of functions
Go to topic “Trigonometry” and click on “Graphing and Inverse functions” then click on
“Graphing combination of functions”
6.7 Sinusoidal Application problems
Pages 398-401 #
Website Video Clips with Solutions:
Application question on waves
Watch problem 3
Review
Pages 404-405 #
1.3 & 1.6 Transformations of Parent
Functions
p. 254 #1, 2, 5, 6, 14, 16
Challenge: 18
Website Video Clips with
Solutions:
Quadratic Functions
Click on “Quadratic Functions”- Classifying Relations: #8,9
Click on “Quadratic Functions” - Interpreting Quadratic Graphs: #10, 11
Khan Academy Exercises:
Find the Greatest Common divisor
Finding the greatest common divisor (GCD) is necessary when factoring quadratics. Practice this skill on
Khan Academy.
Additional Support tools:
Instructions