REFERENCE MATERIALS

## Distance Learning

### Credit Recovery/Credit Continuation – Mathematics

#### Mathematics 10F

##### Class # 1846 Mathematics 10F M1: Statistics

You are exposed to a lot of statistical information through advertising, media, and the Internet. This module will help you to analyze that information, and explain how to determine if it is biased or slanted towards one view. It will illustrate how the method of data collecting and the wording of the survey question can seriously affect the results. You will see how making graphs to illustrate the data helps to communicate the results and draw conclusions about it. You will apply these considerations to case studies and, in a project where you will collect and organize data, display it and draw conclusions based on your interpretation of the statistics.

Assignment Number Assignment Title
Assignment 1.1 Cover Assignment
Assignment 1.2 Populations and Samples
Assignment 1.3 Bias in Data Collection
Assignment 1.4 Case Study
Assignment 1.5 Displaying Data
Assignment 1.6 Data Analysis
Assignment 1.7 Developing a Project
##### Class # 1847 Mathematics 10F M2: Number Sense

Number sense is tough to define but once you’ve got it, it makes math so much more fun! Number sense includes an understanding of the value ofnumbers, and their order or magnitude. It helps you to see patterns and relationships, and understand the effect of operations on numbers. The lessons in this module aim to provide you with useful strategies to improve your number sense abilities. You will work with big and small, positive and negative numbers, fractions, decimals, percentages, and square numbers and their roots. You will use these different representations of values to help youput numbers in order, perform operations on numbers, solve problems, and practice mental math and estimating with perfect square numbers and roots.

Assignment Number Assignment Title
Assignment 2.1 Cover Assignment
Assignment 2.2 Decimal Numbers
Assignment 2.3 Operations with Fractions
Assignment 2.4 Conversions
Assignment 2.5 Perfect Square Numbers
Assignment 2.6 Estimating Square Roots
##### Class # 1848 Mathematics 10F M3: Powers

In the last module, you learned about working with decimals. In this module, you will learn about working with powers. Powers are numbers or variables with exponents.

Assignment Number Assignment Title
Assignment 3.1 Cover Assignment
Assignment 3.2 The Meaning and Uses of Powers
Assignment 3.3 Order of Operations
Assignment 3.4 Operations with Powers
Assignment 3.5 Powers with Like Bases
Assignment 3.6 More Power Laws
##### Class # 1849 Mathematics 10F M4: Polynomials

You communicate with others using expressions composed of words. Mathematics uses expressions composed of numbers and letters. In mathematics, a polynomial is an expression that is constructed from one or more terms including parts like variables and constants, using the operations of addition, subtraction, multiplication, and division. In this module, you will learn to communicate using polynomial expressions.

Assignment Number Assignment Title
Assignment 4.1 Cover Assignment
Assignment 4.2 Introduction to Polynomials
Assignment 4.3 Collecting Like Terms
Assignment 4.4 Distribute the Negatives
Assignment 4.5 Multiplication
Assignment 4.6 Division and Equivalents
Assignment 4.7 Geometry and Polynomials
##### Class # 1850 Mathematics 10F M5: Linear Relations

TV shows with crime scene investigation themes capture viewers’ attention because it’s interesting to figure things out, to look at clues or patterns and try to find a solution. This is the basic concept behind linear relations. In this module, you will find patterns and describe them to help you solve problems using equations, tables, and graphs. You will be able to verify or prove your solutions by substituting values back into the expression or equation to make sure it is correct. You will also look at situations where there is more than one possible answer.

Assignment Number Assignment Title
Assignment 5.1 Cover Assignment
Assignment 5.2 Patterns and Translations
Assignment 5.3 Writing Equations
Assignment 5.4 Working with Graphs
Assignment 5.5 Operations with Equations
Assignment 5.6 Inequalities and Graphing
Assignment 5.7 Inequalities and Problems
##### Class # 1851 Mathematics 10F M6: Circle Geometry

The next three modules of this mathematics course focus on geometry. In Module 6, the spotlight is on circles, and then in Modules 7 and 8, the focus shifts to 2-D and 3-D shapes. Module 6 investigates four unique properties of circles. You will learn new terminology and review your angle measurement skills. Next, you will determine how angles, lines, arcs, tangents, and chords are related in circles. You will also apply the properties of circles to problemsolving situations, and learn how to find the exact centre of a circle. To begin, however, the cover assignment for this module looks back at some of the ideas introduced in Module 1: Statistics. You will investigate examples from the media that use probability in decision making and report on them.

Assignment Number Assignment Title
Assignment 6.1 Cover Assignment
Assignment 6.2 Measurement and Terminology
Assignment 6.3 Central and Inscribed Angles
Assignment 6.4 More Inscribed Angles
Assignment 6.5 Tangents
Assignment 6.6 Perpendicular Bisectors
Assignment 6.7 Solving Problems
##### Class # 1852 Mathematics 10F M7: 2-D and 3-D Objects

The specific outcomes of Modules 6, 7, and 8 focus on geometry. You have explored circle geometry and now in Module 7, you will concentrate on two and three-dimensional objects of various shapes. You will determine the surface area of composite objects, work with similar polygons, and draw scale diagrams. Problem solving will help you apply your skills in these three major areas.

Assignment Number Assignment Title
Assignment 7.1 Cover Assignment
Assignment 7.2 Composite Objects
Assignment 7.3 Similarity
Assignment 7.4 Drawing Polygons
Assignment 7.5 Scale Drawings
##### Class # 1853 Mathematics 10F M8: Symmetry

This module introduces you to line symmetry and rotational symmetry. You will look at shapes, designs, art, and tessellations to see what kind of symmetry they have. Who said math couldn’t be beautiful?

Assignment Number Assignment Title
Assignment 8.1 Cover Assignment
Assignment 8.2 Line Symmetry
Assignment 8.3 Rotation Symmetry
Assignment 8.4 Art and Tessllations

### Essential Mathematics 20S

##### Class # 1838 Essential Mathematics 20S M1: Gross Pay, Time Cards and Percents

In this module, you will learn to calculate your gross earnings for when you start a job. In Lesson 1 and 2 you will review and use your skills with percentages and fractions in solving problems. There are many methods of being paid for your work, many of which will be examined in Lessons 3 and Lesson 4.

Assignment Number Assignment Title
Cover Assignment Yearning for Earnings
Assignment 1.1 Percents
Assignment 1.2 Fractions and Percent Rate of Change
Assignment 1.3 Gross Income
Assignment 1.4 Overtime Pay
Assignment 1.5 Time Cards and Late Penalties
Assignment 1.6 Comparisons
Assignment 1.7 Job Exploration Project
##### Class # 1839 Essential Mathematics 20S M2: Net Pay

In this module, you will learn to calculate net pay. Gross income is what you earn, but that is not usually the amount you take home. Various deductions are subtracted from your gross pay. This module examines the three mandatory deductions, and teaches you how to calculate them. You will use the CPP, EI, and income tax tables from the Government of Canada as well as formulas to find specific deductions. Your net pay is your gross pay minus the deductions.

Assignment Number Assignment Title
Cover Assignment Pay Yourself First / The Sales Representative
Assignment 2.1 Common Deductions
Assignment 2.2 CPP
Assignment 2.3 EI
Assignment 2.4 Income Tax
Assignment 2.5 Net Pay
Assignment 2.7 Formulas and Errors
##### Class # 1840 Essential Mathematics 20S M3: Measurement

In this module, you will learn about measurement. Most countries around the world, including Canada, use the metric system, sometimes referred to as SI (système international). This system of measurement includes such units as centimetres, grams, and litres. The United States uses the Imperial system of measurement, which includes such units as miles, feet, ounces, and quarts. This module examines both the metric and imperial systems of measurement, and conversions between the two.

Assignment Number Assignment Title
Cover Assignment Following and Writing Instructions
Assignment 3.1 Powers of Ten
Assignment 3.2 Metric System
Assignment 3.3 Imperial System
Assignment 3.5 Conversions
Assignment 3.6 Calipers
Assignment 3.7 Micrometers
Assignment 3.8 Formulas
Assignment 3.9 Problems
##### Class # 1841 Essential Mathematics 20S M4: Geometry

In this module, you will learn to calculate the area of various shapes using metric and imperial measurements.

Assignment Number Assignment Title
Cover Assignment Tower of Hanoi
Assignment 4.1 Multiplication Skills
Assignment 4.2 Area of Shapes
Assignment 4.3 Scale Drawings
Assignment 4.4 Area of Odd Shapes
Assignment 4.5 Conversions
Assignment 4.3 Problems
##### Class # 1842 Essential Mathematics 20S M5: Working with Angles

This module deals with angles—identifying, measuring, drawing, bisecting and copying them. Also, you will work with supplementary and complementary angles, along with finding properties of angles using parallel lines and a transversal.

Assignment Number Assignment Title
Cover Assignment Problem Analysis; Analysis of Games and Numbers
Assignment 5.1 Identify Angles
Assignment 5.2 Estimate Angles
Assignment 5.3 Copy and Bisect Angles
Assignment 5.4 Lines and Angles
Assignment 5.5 Parallel Lines and Angles
Assignment 5.6 Perpendicular or Parallel
##### Class # 1843 Essential Mathematics 20S M6: Consumer Decisions

In this module, you will learn to calculate the unit price of items. You will also examine various sales promotion techniques, and determine the real cost of these promotions. The third lesson revisits the determination of percent discounts. Also, in this module, you will use various methods to determine foreign currency exchanges.

Assignment Number Assignment Title
Cover Assignment Pizza Party
Assignment 6.1 Unit Pricing
Assignment 6.2 Unit Prices Project
Assignment 6.3 Percents
Assignment 6.4 Percent Increase or Decrease
Assignment 6.5 Sales Promotion
Assignment 6.6 Currency Exchange
##### Class # 1844 Essential Mathematics 20S M7: Trigonometry

This module deals with ratio and proportion, similarity, right triangles, Pythagorean Theorem, and the three basic trigonometric ratios. You will be solving problems using the Pythagorean relation and the three basic trigonometric ratios.

Assignment Number Assignment Title
Cover Assignment Drawing Similar Figures
Assignment 7.1 Ratio and Proportion
Assignment 7.2 Similarity
Assignment 7.3 Pythagoras and Right Triangles
Assignment 7.4 Tangent Ratio
Assignment 7.5 Sine Ratio
Assignment 7.6 Cosine Ratio, Sine Ratio, and Tangent Ratio
Assignment 7.7 Problems
##### Class # 1845 Essential Mathematics 20S M8: Transformations

A transformation involves movement of a shape from one position to another, usually on a page of paper. You will study 2-dimensional shapes as you slide, rotate, and reflect them while maintaining the exact size of the shape. This module also deals with dilating shapes, where the shape becomes larger or smaller while the measurements remain proportional and the shapes similar. You will apply your knowledge of transformations to various designs and tessellations.

Assignment Number Assignment Title
Cover Assignment Nested Shopping Carts
Assignment 8.1 Translations
Assignment 8.2 Rotations
Assignment 8.3 Reflections
Assignment 8.4 Combinations
Assignment 8.5 Dilations
Assignment 8.6 Applications

#### Essential Mathematics 30S

##### Class # 1754 Essential Mathematics 30S M1: Interest and Credit

In Grade 10 Essential Mathematics, you studied payment for work, including gross pay and net pay. This module will focus on two topics that relate to what you do with the money you earn. The first two lessons deal with interest, both on investments and loans. The following lessons talk about credit—where you can get it and how to use it. You may wonder what this has to do with you, but interest and credit will probably be an important part of your financial world. Money deposited in a savings account earns interest. On the other hand, if you borrow money or use a credit card, you will likely pay interest—sometimes a lot. Sometimes you may need credit to purchase an expensive item, such as a car, laptop, or even a house!

Assignment Number Assignment Title
Cover Assignment Loyalty Programs
Assignment 1.1 Interest
Assignment 1.2 What is Credit?
Assignment 1.3 Credit Payment Calculations
Assignment 1.4 Credit Card Calculations
##### Class # 1755 Essential Mathematics 30S M2: 3-D Geometry

In Grade 10 Essential Math, you studied imperial and metric systems of measurement. You explored linear measurement and two-dimensional (2-D) geometry. In this module, you move on to three-dimensional (3-D) geometry, where you will study prisms, pyramids, spheres, cylinders, and cones. You will learn about surface area, volume, and capacity, and make comparisons among the three ways of measuring 3-D objects. Part of these comparisons will be finding patterns to help you improve your understanding of 3-D geometry.

For this module, you will need a ruler with both metric and imperial units (centimetres and inches). You will find a paper template for a ruler on page 5 of this module. You may want to cut this out to use it in the course. Having access to a tape measure, a caliper, and a micrometer would be beneficial to your understanding of 3-D geometry, but these items are not necessary to complete this module.

Assignment Number Assignment Title
Cover Assignment Geometric Patterns
Assignment 2.1 Surface Area
Assignment 2.2 Volume
Assignment 2.3 Applications of Volume and Capacity
##### Class # 1756 Essential Mathematics 30S M3: Statistics

In Grade 9, you learned how to collect data, and how to display data on a graph so that it is easy to understand. In this module, you will learn more about displaying data using graphs, as well as how to interpret data. You may choose to draw the graphs by hand or with a computer.

The following is an often-quoted statement said (reportedly) by Benjamin Disraeli, a distinguished British public official. The statement reads: “There are three kinds of lies: lies, damned lies, and statistics.” The statement refers to the misuse of statistics.

In this module, you will learn how to select the most suitable kinds of graphs to present different types of data. You will also learn how graphs are used to emphasize a certain point of view. It is important to recognize how graphs can be used to present data in misleading ways.

Assignment Number Assignment Title
Cover Assignment Statistics in Your Life
Assignment 3.1 Circle Graphs, Bar Graphs, and Histograms
Assignment 3.2 Line Graphs
Assignment 3.3 Interpreting Graphs
##### Class # 1757 Essential Mathematics 30S M4: Managing Money

You began this course by studying credit and interest in Module 1. In this module, you will expand your understanding of personal finance by focusing on personal budgets and managing your finances. You will learn how to create and analyze a personal budget, and how to use a budget to set financial goals and prepare for unexpected expenses. You will also study a variety of services provided by banks and other financial institutions.

Assignment Number Assignment Title
Cover Assignment How Time Affects the Value of Money
Assignment 4.1 Budgets
Assignment 4.2 Bank Accounts
Assignment 4.3 Cheques, Deposit Slips, and Registers
##### Class # 1758 Essential Mathematics 30S M5: Relations and Patterns

In this module, you will study mathematical relationships that are linear. An everyday example of a linear relationship is the relationship between the number of hours you work and the number of dollars you earn. You will express mathematical relationships in four ways:

• word statements
• table of values
• equations
• graphs

You will also show how a change in one quantity (e.g., hours worked) affects the change in another quantity (the number of dollars earned).

Assignment Number Assignment Title
Cover Assignment Applying Patterns
Assignment 5.1 Scatterplots
Assignment 5.2 Patterns and Linear Relations
Assignment 5.3 Slope
Assignment 5.4 Scale
##### Class # 1759 Essential Mathematics 30S M6: Trigonometry

Trigonometry is a branch of mathematics involving the measurement of triangles. The word trigonometry is made up of two Greek words:

• trigonon—triangle
• metria—to measure

In Grade 9 Mathematics, you used trigonometric ratios and other formulas to calculate the side lengths and angle measures of right triangles. You will review these calculations before going on to more complex problems that involve multiple right triangles.

Assignment Number Assignment Title
Cover Assignment Math Operations
Assignment 6.1 Applying Trigonometry
##### Class # 1760 Essential Mathematics 30S M7: Design Modelling

This is the last module! This module will focus on representing 3-D objects in different ways. The ability to translate between 2-D drawings and 3-D objects is necessary in many professions, from construction to interior design to art to clock repairs to putting together your own furniture at home.

Assignment Number Assignment Title
Cover Assignment Four-Colour Problem
Assignment 7.1 Three 2-D Views of 3-D Objects
Assignment 7.2 One-Point Perspective Drawings
Assignment 7.3 Exploded Views and Component Parts

#### Essential Mathematics 40S

##### Class # 1705 Essential Mathematics 40S M1: Home Finance

In previous mathematics courses, you explored personal finances as they apply to you now. This module focuses on financial concerns that you may have in the future. You probably don’t own your own home at this point in your life, so you may not be aware of the costs of home ownership. This module will focus on costs that are associated with buying and owning a home. You will calculate the amount of money you can afford to spend on a house, how much your mortgage would cost, and the costs of home insurance, property taxes, and buying compared to renting a house. You will also become aware of the various expenses that are incurred when you buy a house.

Assignment Number Assignment Title
Assignment 1.1 Affordability, Initial Costs, and Morgages
Assignment 1.2 Insurance and Property Tax
Assignment 1.3 Making Decisions
##### Class # 1706 Essential Mathematics 40S M2: Geometry and Trigonometry

In this module, you will review some geometry from previous courses, including five basic “angle rules” and circle formulas. Then you will be introduced to two new trigonometric formulas used to solve non-right triangles. You will also study the properties of various quadrilaterals and other polygons. Trigonometry is a branch of mathematics that is used for land surveying. The properties of polygons are useful for architecture and other design fields.

Assignment Number Assignment Title
Cover Assignment Circle Geometry
Assignment 2.1 Polygons
Assignment 2.2 The Sine Law
Assignment 2.3 Trigonometry
##### Class # 1707 Essential Mathematics 40S M3: Business Finance

Assignment Number Assignment Title
Cover Assignment Marginal Income Tax Rates
Assignment 3.1 Profitability of a Small Business
Assignment 3.2 Income Tax
##### Class # 1708 Essential Mathematics 40S M4: Probability

In this module, you will study probability. You may already know that the chances of winning or losing money when gambling (which includes buying lottery tickets) are based on probabilities. You should also know that probabilities are used to determine

• insurance costs (Autopac, fire insurance, life insurance …)
• medical procedures
• decisions in education (which courses are the best ones to take)
• weather forecasting

And the list goes on and on. You may also hear probabilities presented in the media. For example, if you eat certain foods, you may have an increased or decreased chance of suffering certain physical ailments. During elections, data is collected in surveys and used to predict the probability of a politician being elected. As you gain a better understanding of probability, you should be able to make better decisions in situations involving chance. You should also be better prepared to determine the validity of information presented in the media, including advertising.

Assignment Number Assignment Title
Cover Assignment Applying Probability to Games
Assignment 4.1 Expressing Probability and Odds
Assignment 4.2 Applications of Probability
##### Class # 1709 Essential Mathematics 40S M5: Vehicle Finance

Assignment Number Assignment Title
Cover Assignment Vehicle Analysis
Assignment 5.1 Financing a New Vehicle
Assignment 5.2 Used Vehicles and Using Vehicles
Assignment 5.3 Insurance Costs
##### Class # 1710 Essential Mathematics 40S M6: Career Life

If you, like many students, are not certain about your future career, this module will help you to research and consider career options. If you have already chosen a career, this module will allow you to examine that choice more closely. Some students find that researching their chosen career confirms their choice. Other students find they are less certain about their choice and need to consider other career options. This module is an opportunity for you to think about suitable career possibilities.

Through their research, some students have discovered suitable careers they did not know existed. Other students have decided against pursuing careers they realized would not work for them. Even if you are not sure of your career choice when you complete this module, you should be better informed about choices available to you.

The format of this module is different than other modules in this course. Although the module is presented in lessons, the lessons do not include learning activities. Instead, each lesson has an assignment. Even though there is an assignment after each lesson, these assignments are generally shorter than assignments you have had in previous modules. Also, these assignments include a significant amount of research, and you will be asked to write some reports. You will, however, still need to do some calculations in this lesson! You will be asked to write about your Career Life project on the final examination. Be sure to finish this project and send it in to be marked, so you can have some feedback on it before you write your final examination. Instead of learning new mathematical content, you will be using mathematical skills from Module 1 and Module 5, which deal with Home Finance and Vehicle Finance. You will be applying these mathematical skills to calculate costs, such as housing and transportation, once you are established in your career.

Assignment Number Assignment Title
Cover Assignment Personal Costs and Taxes
Assignment 6.1 Self-Assessment Report
Assignment 6.2 Career Descriptions
Assignment 6.3 Education/Training Requirements
Assignment 6.4 Expected Lifestyle Report
Assignment 6.5 Ŕesume and Reflection
##### Class # 1711 Essential Mathematics 40S M7: Statistics

Statistics is the branch of mathematics that deals with the collection, organization, and analysis of data. Statistics are frequently mentioned in the news, in radio and television commercials, and on the Internet, including the Statistics Canada website. Throughout this module, statistics from the Statistics Canada website are used to provide information. References to the website itself are also mentioned, so that you may visit the website if you are interested.

Statistics are very frequently used by the media to influence your point of view. Statements such as ”92% of the people surveyed…“ or ”nine out of ten doctors recommend…“ are designed to persuade consumers to agree with the people surveyed or the doctors’ recommendations. As a consumer, you need to understand this information and how to interpret it. This will allow you to recognize biases, and thus make informed decisions.

In previous mathematics courses, you considered a number of ways of organizing and analyzing data. You were introduced to three measures of central tendency: the mean, the median, and the mode. In this module, you will study two additional measures of central tendency. You will also study percentiles and how to interpret statistical information.

Assignment Number Assignment Title
Cover Assignment Problem Analysis
Assignment 7.1 Mean, Median, Mode, and Outliers
Assignment 7.2 Five Measures of Central Tendency
Assignment 7.3 Analyzing Percentiles
##### Class # 1712 Essential Mathematics 40S M8: Precision Measurement

It is important for you to be able to measure distances. In previous courses, you have measured distances using many different types of measuring devices, including rulers and tape measures. You probably have rulers and tape measures in your home or tool box. Some people also use laser or electronic means to calculate length. In this module, you will be introduced to two instruments that are used for measuring small distances with great precision and accuracy: the Vernier caliper and the micrometer. It would be helpful if you have both a Vernier caliper and a micrometer, but you do not require them in order to complete this module.

Once you take a measurement, it is important for you to know how exact this measurement is. Take a look around you. You probably see a pencil, pen, table, calculator, ruler, electrical outlet, a light, and maybe even a computer. These were all manufactured with varying degrees of precision and accuracy. Have you ever wondered how mechanical parts can be made in any country in the world, and yet still fit the object you are trying to fix right at home? Precision and accuracy are two concepts that make this possible.

In this module, you will be learning about precision, accuracy, uncertainty, and tolerance. These four concepts are all related to the limitations of any measuring instrument. If you are planning on having a career in engineering, machining, carpentry, or even if you plan on just fixing up your own home one day, what you learn in this module will be very useful for you.

Assignment Number Assignment Title
Cover Assignment Puzzles in Design
Assignment 8.1 Accuracy, Precision, and Uncertainty
Assignment 8.2 Measurements and Tolerances

#### Introduction to Applied and Pre-Calculus Mathematics 20S

##### Class # 1825 IAPM: Introduction to Applied and Pre-Calculus Mathematics 20S M1: Graphs and Relations

This first module forms a foundation for the mathematical concepts you will use in both pre-calculus and applied mathematics in the future, including upcoming modules in this course. It, in turn, is based on ideas and skills developed in previous math courses you have taken. This module will focus on the relationships among data, graphs, and contexts, and use a variety of ways to describe them. Specific attention will be given to linear relations, and their slope, intercepts, domain, and range. You will use words, ordered pairs, tables of values, graphs, and equations as means to describe the characteristics of linear relations.

Assignment Number Assignment Title
Assignment 1.1 Graphing Independent and Dependent Variables
Assignment 1.2 Domain and Range
Assignment 1.3 Slopes, Intercepts, Domain, and Range
Assignment 1.4 What We Can Tell From Slope
Assignment 1.5 Slope-y Intercept Equations
##### Class # 1826 IAPM: Introduction to Applied and Pre-Calculus Mathematics 20S M2: Number Sense

This module will explore factors, multiples, and square and cube numbers along with their roots. You will see how the real number system is organized, and determine connections between radical numbers and powers. You will take what you have learned about exponent laws in Grade 9 and apply it to powers with variable bases and rational and negative exponents.

Assignment Number Assignment Title
Assignment 2.1 Factors and Multiples
Assignment 2.2 Perfect Cubes and Squares
Assignment 2.3 Rational, Irrational, and Radical Numbers
Assignment 2.4 Exponent Laws Review
Assignment 2.5 Exponent Laws with Rational and Negative Exponents
##### Class # 1827 IAPM: Introduction to Applied and Pre-Calculus Mathematics 20S M3: Measurement

Measurements of length, mass, volume, and other quantities can be made using a variety of units and systems. This module will showcase the two different systems in use in Canada today: metric and imperial. The metric system, also called SI (based on the French name for the International System of Units), is used in most countries around the world.

Assignment Number Assignment Title
Assignment 3.1 Units, Area, and Volume
Assignment 3.2 Measuring wiht Vernier Calipers and Micrometers
Assignment 3.3 Unit Conversions
Assignment 3.4 Volume of Prisms and Pyramids
Assignment 3.5 Surface Area of Prisms and Pyramids
Assignment 3.6 Surface Area and Volume of Spheres, Cylinders, and Cones
##### Class # 1828 IAPM: Introduction to Applied and Pre-Calculus Mathematics 20S M4: Trigonometry

This module will introduce you to the three primary trigonometric ratios, named the sine, cosine, and tangent ratios. You will use them to solve for side lengths and angles in triangles. For this module, you will need a protractor and measuring devices such as a metre stick, yard stick, or measuring tape.

Assignment Number Assignment Title
Assignment 4.1 Tangent Ratio
Assignment 4.2 Using Sine and Cosine
Assignment 4.3 Inverse Trig Ratios
Assignment 4.4 Applying Trig Ratios
##### Class # 1829 IAPM: Introduction to Applied and Pre-Calculus Mathematics 20S M5: Relations and Functions

You began this course back in Module 1 by exploring graphs and relations. You looked at the relationships between sets of data and described their characteristics (including slope, intercepts, domain, and range) using graphs, words, equations, and ordered pairs. This module will build on that knowledge, focusing on a special relation called a “function.” You will learn how to express domain and range using different types of notation, and use functional notation to express linear equations. As well, you will review graphing linear functions.

Assignment Number Assignment Title
Assignment 5.1 Relations and Functions
Assignment 5.2 Domain and Range Notation
Assignment 5.3 Functional Notation
##### Class # 1830 IAPM: Introduction to Applied and Pre-Calculus Mathematics 20S M6: Polynomials

This module is a continuation of some of the math topics that you have been learning about since the early years of your education: combining values, recognizing patterns, following rules, and using ”hands-on” tools to help you understand and express theoretical concepts. All these ideas and more come together when you work with polynomials.

Assignment Number Assignment Title
Assignment 6.1 Describing Polynomials and Multiplying Binomials
Assignment 6.2 Multiplying Polynomials
Assignment 6.3 Factoring Binomials and Trinomials
Assignment 6.4 Factoring Tinomials when a ∈ I
Assignment 6.5 Difference of Squares and Module Review
##### Class # 1831 IAPM: Introduction to Applied and Pre-Calculus Mathematics 20S M7: Coordinate Geometry

The game of Battleship® involves strategizing to sink your opponent’s fleet of ships by calling out coordinates. The game is based on a modified Cartesian grid, using letters and positive integers along the x- and y-axis. This module will make extensive use of the Cartesian grid—you will plot points, graph equations, and calculate distances and midpoints using ordered pairs. You will make use of some of the skills and concepts you learned in previous modules, and write linear equations in different forms, and use technology to help you find a way to mathematically describe the relationship between the x- and y-variables.

Assignment Number Assignment Title
Assignment 7.1 Distance and Midpoint
Assignment 7.2 Linear Relations Formulas
Assignment 7.3 Writing Linear Equations Based on Different Information
Assignment 7.4 Line of Best Fit and Correlation
##### Class # 1832 IAPM: Introduction to Applied and Pre-Calculus Mathematics 20S M8: Systems of Equations

Based on previous math lessons, you may be tempted to view a linear equation simply as a problem that needs to be solved. In this module, you will switch that around and use equations to find the solutions to practical problems. You will use pairs of equations that have the same two variables to represent a situation or context, and find solutions to problems by graphing or algebraically solving the system of equations. You will identify the three types of systems of linear equations, describe strategies to solve the systems, and verify solutions.

Assignment Number Assignment Title
Assignment 8.1 Solving Systems of Linear Equations Graphically
Assignment 8.2 Solving Systems of Equations by Elimination

### Applied Mathematics

#### Applied Mathematics 30S

##### Class # 1761 Applied Mathematics 30S M1: Quadratic Functions

In previous math courses, you learned about linear functions, which are functions that form a line when graphed. Module 1 will look at quadratic functions, which form a curved shape that can resemble an arch. A quadratic function can be used to describe the path of a rock as it is thrown in the air or the shape of an arch supporting a bridge. Quadratic functions can be used to model behaviour in our world. For example, they can model relationships that have a maximum value, such as the height of a football as it is thrown to a receiver compared to the time the football is in the air, or the expected revenue for an event compared to the price charged per ticket. You will start the module by exploring the characteristics of the shape of a quadratic function and finish the module by applying what you have learned to contexts in our world.

Assignment Number Assignment Title
Cover Assignment Geometric Patterns
Assignment 1.1 Quadratic Properties and Characteristics
Assignment 1.2 Intercepts, Verticies, and Sketching
##### Class # 1762 Applied Mathematics 30S M2: Mathematics Research Project

Mathematics has been a field of study since at least 1900 BCE. Over the past four thousand years, many new mathematical concepts have been developed and discovered and many mathematical symbols have been invented to help represent these concepts. Mathematics has become a useful tool in many disciplines, such as science, psychology, medicine, linguistics, sports, cooking, flying, exploring, and communicating.

In this module, you will select an historical event or area of interest where quantitative data are used, and use mathematics to help you research and collect data in order to answer a question, analyze and interpret your findings, and create a presentation to showcase your work.

Assignment Number Assignment Title
Cover Assignment Historical Mathematical Problems
Assignment 2.1 Project Proposal: Creating Your Inquiry Question and Identifying Sources
Assignment 2.2 Collecting and Assessing Data
Assignment 2.3 Analyzing and Interpreting Data
Assignment 2.4 Presentation of Your Research Project
##### Class # 1763 Applied Mathematics 30S M3: Reasoning to Solve Problems

Patterns are a common occurrence in the world around you, and you have seen and used numerical and geometric patterns in many contexts. For example, you used a numerical pattern when you learned to recognize whether a number is a multiple of three. You now know that a number is always a multiple of three if the sum of the digits of that number is a multiple of three. This numerical pattern is always true. You will discover and use similar patterns in this module.

You have already observed some geometric patterns in polygons. For example, you know that the sum of the interior angles in a triangle is always 180˚. Similarly, the sum of the interior angles in a quadrilateral is always 360˚. You know that this pattern continues indefinitely, even for polygons with larger numbers of sides.

Some patterns are only valid in certain circumstances, while other patterns are valid in general. Throughout this module, you will be using two types of reasoning in relation to patterns: inductive reasoning and deductive reasoning. You will use inductive reasoning to examine the changes that occur in each step of a pattern to identify a general rule that the pattern follows. For example, if you see the numbers 1, 2, 4, . . ., you might think that the pattern rule is to double each number and use inductive reasoning to conclude that the pattern will continue as 1, 2, 4, 8, 16 . . . . However, with inductive reasoning, the rule many not always be true. Alternatively, you will use deductive reasoning to complete a pattern when you have been given the general rule. Since the rule on which the pattern is based is known, patterns based on deductive reasoning will always be true.

Assignment Number Assignment Title
Cover Assignment Logic Puzzles
Assignment 3.1 Inductive and Deductive Reasoning
Assignment 3.2 Invalid Proofs and Spatial Reasoning
##### Class # 1764 Applied Mathematics 30S M4: Geometry of Angles & Triangles

In this module, you will expand your knowledge of geometry from previous mathematics courses, including your knowledge of the properties of triangles and squares. You will investigate and learn to use the properties of polygons and parallel lines, and their angles. If you look around right now, you should be able to see multiple examples of polygons and of parallel lines (e.g., furniture, paper, walls). These properties are especially useful in construction and building applications. Contractors and architects are examples of professionals who use the properties of parallel lines to ensure their designs and creations are properly constructed. You will be learning more about these properties in this module.

Assignment Number Assignment Title
Cover Assignment Geometry in Tangrams
Assignment 4.1 Polygons and Angles
Assignment 4.2 Angle of Properties of Parallel Lines and Transversals
##### Class # 1765 Applied Mathematics 30S M5: Trigonometry

Trigonometry is defined as the branch of mathematics that studies the relationships among the sides and angles of a triangle. Many professionals use trigonometry in fields such as engineering, surveying, and crime scene analysis. Have you ever noticed how bridges are made up of triangular shapes? Triangles are used in construction because of their inflexible shape. The more triangles included in the construction of a bridge, the stronger the bridge will be.

In previous courses, you learned how to solve for missing angles and side lengths in triangles that contained a right angle. In this module, you will learn how to solve for missing angles and side lengths in triangles that do not contain a right angle. These triangles are called oblique triangles. To do this, you will learn about two different methods, the Sine Law and the Cosine Law.

Assignment Number Assignment Title
Cover Assignment Shape and Space
Assignment 5.1 Solving Acute Triangles
Assignment 5.2 Solving Obtuse Triangles
Assignment 5.3 The Ambiguous Case
##### Class # 1766 Applied Mathematics 30S M6: Statistics

The world around us is full of data. Media (television, radio, newspaper, websites, billboards) provide data for a variety of different reasons. Data can be used for reaching out to the public (such as a “quit smoking” campaign), advertising, and numerous other purposes. Once data is collected, it can be analyzed and interpreted. Many types of statistical analysis can be performed to reach conclusions about the material being analyzed.

In this module, you will investigate how conclusions are drawn in statistical studies when data is collected from a number of sources. Since people are bombarded with statistics, whether it is through advertising, governmental concerns, or other sources, it is important to learn how the data is analyzed and what the statistics are actually saying. This gives you a better understanding of the validity and reliability of the conclusions that are drawn from the data. In Module 6, you will review how to calculate measures of central tendency such as the mean, median, and mode. You will also learn about measures of dispersion, including the range and standard deviation.

Assignment Number Assignment Title
Cover Assignment The Indigenous Identity Population in Canada
Assignment 6.1 Measures of Central Tendency and Dispersion
Assignment 6.2 z-Scores and the Normal Curve
Assignment 6.3 Confidence Intervals
##### Class # 1767 Applied Mathematics 30S M7: Mathematical Models

This module is about solving problems. You will first examine ways in which rates are used to measure such things as speed and money. As well, you will learn how to convert between rates, which is useful knowledge when travelling, as many countries measure distance, velocity, or currency using different units. You will also be introduced to how these rates can be represented in graphical form.

Assignment Number Assignment Title
Cover Assignment Skyscraper Puzzles
Assignment 7.1 Interpreting Rates Algebraically and Graphically
Assignment 7.2 Linear Inequalities and Systems of Linear Inequalities
Assignment 7.3 Optimizing Solutions to Linear Inequalities
##### Class # 1768 Applied Mathematics 30S M8: Scale Factors 2-D & 3-D Shapes

Geometry is a branch of mathematics that deals with the measurement and properties of figures and objects in space. Throughout this course, you have studied various aspects of geometry including angles, triangles, and trigonometry. In this module, you will be studying scale factors and how they relate to both 2-dimensional (2-D) and 3-dimensional (3-D) shapes and objects.

Assignment Number Assignment Title
Cover Assignment Pattern Analysis
Assignment 8.1 Finding and Using Scale Factors of 2-D Shapes and 3-D Objects
Assignment 8.2 Scale Factors and Areas of 2-D Shapes
Assignment 8.3 Scale Factors, Surface Area, and Volue of 3-D Shapes

#### Applied Mathematics 40S

##### Class # 1713 Applied Mathematics 40S M1: Functions

Welcome to your first module of Grade 12 Applied Mathematics! You will begin with a look back at linear and quadratic functions, and then extend these concepts to include cubic, exponential, and logarithmic functions. You will analyze and describe the characteristics of these functions, and match their graphs to the correct equations. You will determine which function best approximates contextual data and use it to solve problems.

Assignment Number Assignment Title
Cover Assignment Number Puzzle
Assignment 1.1 Polynomial Functions
Assignment 1.2 Logarithmic Function Models
##### Class # 1714 Applied Mathematics 40S M2: Mathematics Research Project

Mathematics is many things: a way to count, measure, and quantify; a pattern used to order and organize; a language to describe; and a method to predict or find a value. It is a tool used to manipulate, create, design, and help explain and gather information. Mathematics is useful for science, psychology, medicine, linguistics, sports, cooking, flying, exploring, and communicating. And so much more! In this module, you will select a current event or area of interest and use mathematics to help you research and collect quantitative data in order to answer a question, analyze and interpret your findings, and create a presentation to showcase your work.

Assignment Number Assignment Title
Cover Assignment The Tower of Hanoi
Assignment 2.1 Project Proposal
Assignment 2.2 Collecting and Assessing Data
Assignment 2.3 Interpreting Data
Assignment 2.4 Presentation
##### Class # 1715 Applied Mathematics 40S M3: Logical Reasoning

Welcome to Module 3. In this module, you will be introduced to set theory, look at some of its applications, and solve problems involving conditional statements. This module is part of the logical reasoning topic found in applied mathematics. It is designed to help you develop your ability to think critically and creatively as you solve problems. The skills you use in this module will be applied in many other lessons in this course, and you will find applications for these skills in your daily life as well.

Assignment Number Assignment Title
Assignment 3.1 Sets and Conditional Statements
##### Class # 1716 Applied Mathematics 40S M4: Probability

Welcome to Module 4 of Grade 12 Applied Mathematics! Probability is a natural extension of the logic module you just completed. You will use the language and notation of logic as you consider the mathematics of predictions. The prediction of an event is not the same thing as simply guessing when something could occur. While a prediction and a guess may both be either correct or incorrect, the difference is that a prediction is based on definitive data, while a guess is based on uncertain information. This module will show you that probability is not the same thing as a promise (so don’t blame the weather forecaster when your baseball game gets rained out), and will demonstrate that mathematical predictions are made up of theoretical calculations, include different types of events, can be used in decision making, and can involve subjective judgment. Some examples in this module will be based on games of chance involving dice or cards. This is not intended as an endorsement for gambling, but rather to provide illustrations of possible outcomes and fair games.

Assignment Number Assignment Title
Cover Assignment Strategies
Assignment 4.1 Probability and Odds
##### Class # 1717 Applied Mathematics 40S M5: Financial Mathematics

Welcome to Module 5. In this module, you will apply your number sense to financial situations and consider interest, loans, credit options, renting versus buying versus leasing, and investment strategies. You will use spreadsheets, graphing technology, and a number of online resources in your investigation, analysis, and evaluation of financial mathematics. Financial success is important to most people. However, real success is achieved when you are able to manage your money and have it work for you, rather than against you. This module is designed to help you build the skills and understanding needed to make informed financial decisions—a critical life skill.

Assignment Number Assignment Title
Cover Assignment Crossing the Canal with Cats
Assignment 5.1 Compound Interest
Assignment 5.2 Loans and Investments
Assignment 5.3 Investment Decisions
##### Class # 1718 Applied Mathematics 40S M6: Techniques of Counting

Welcome to Module 6. You likely learned to count before you started Kindergarten, so why is a module on counting techniques included in a Grade 12 Applied Mathematics course? Counting techniques, such as the Fundamental Counting Principle, permutations, and combinations, are ways to enumerate or determine the number of elements in a set, or the number of possible outcomes in an experiment, without having to actually count each one. This is a module about counting shortcuts. Who would have thought that everything you need to know about counting, you did not learn in Kindergarten? This module will continue to develop some of the concepts and skills you used in the probability module.

Assignment Number Assignment Title
Cover Assignment Patterns in Numbers
Assignment 6.1 Fundamental Counting Principle
Assignment 6.2 Applications of Permutations and Combinations
##### Class # 1719 Applied Mathematics 40S M7: Sinusoidal Functions

Welcome to Module 7. By now, you have used many different mathematical models to represent real-world situations. When events happen in a repetitive or periodic manner, such as the height of tides, the time of sunrise, or the average monthly temperatures in Manitoba, a sinusoidal function may be used to model it. In this module, you will represent data using sinusoidal functions and use the functions to solve problems. You will describe the characteristics of the graphs and equations of sinusoidal functions and interpret the graphs that model situations.

Assignment Number Assignment Title
Cover Assignment Playing Fair
Assignment 7.1 Sinusodial Function Models
##### Class # 1720 Applied Mathematics 40S M8: Design and Measurement

Welcome to Module 8. In the senior years Applied Mathematics program you have been given opportunities to solve problems involving surface area and volume of 3-dimensional objects, using both metric and imperial units. You have considered scale diagrams and used proportional reasoning to understand the relationships between scale factors, areas, and volumes in 2-D and 3-D objects. In addition, you have used trigonometry to solve triangle problems. In this module, you will put all of these skills, and others, to use to analyze objects, shapes, and processes to solve cost and design problems. This will also involve using the dimensions of objects and the costs of items and processes to solve design problems within a given budget.

Assignment Number Assignment Title
Cover Assignment Container Conundrum
Assignment 8.1 Design and Cost Decisions
Assignment 8.2 Working within a Project Budget

### Pre-Calculus & Introduction to Calculus

#### Pre-Calculus Mathematics 30S

##### Class # 1769 Pre-Calculus Mathematics 30S M1: Sequences and Series

In previous math courses, you have dealt with patterns in the context of graphs. In this module, you will be dealing with patterns a little differently. Patterns show up all around you in the natural world. The petals in flowers very often appear in a pattern. Pine cones form according to a pattern called a Fibonacci sequence.

Patterns also appear in lists of numbers. Whenever a pattern appears in a list of numbers, it is called a sequence. Sequences have many applications. An automobile will depreciate in value according to a sequence. Real estate and other investments will earn interest or gain in value according to a specific sequence. Loans will be paid according to a predetermined sequence. In this module, you will study two different types of sequences: arithmetic and geometric. You will also study two different types of series: arithmetic and geometric. Series are used when you are trying to find the sum of a large, even infinite, list of numbers. In this module you will learn when it is possible to find the sum of different types of series.

Assignment Number Assignment Title
Assignment 1.1 Arithmetic Sequences and Series
Assignment 1.2 Geometric Sequences and Series
Assignment 1.3 Finding the Sums of Infinite Geometric Series
##### Class # 1770 Pre-Calculus Mathematics 30S M2: Factoring and Rational Expressions

In Module 1, you discovered patterns in the form of arithmetic and geometric sequences and series. In this module, you will build on your knowledge of patterns by looking at patterns found when factoring polynomials. You have learned the basics of factoring in previous courses. However, in this module, you will extend your knowledge of factoring one step further to see how factoring relates to rational expressions. Rational expressions are fractions containing polynomials in the numerator and denominator.

Assignment Number Assignment Title
Assignment 2.1 Factoring
Assignment 2.2 Multiplying, Dividing, and Simplifying Rational Expressions
Assignment 2.3 Adding and Subtracting Rational Expressions
##### Class # 1771 Pre-Calculus Mathematics 30S M3: Quadratic Functions

Tutor/Marker: Iris Oleksuk

Quadratic functions have many applications in everyday life. Quadratic functions appear in many sports including football, basketball, soccer, and even golf. Quadratic functions can also model situations including satellite dishes, suspension bridges, and maximizing the profit of a business.

In this module, you will look at quadratic functions, their important properties, and how to graph them. This will allow you to learn how to create quadratic functions that model a certain situation. By the end of this module, you will be able to solve application problems such as those modelling the situations listed above.

Assignment Number Assignment Title
Assignment 3.1 Quadratic Functions and Transformations
Assignment 3.2 Graphing Quadratic Functions Using Transformations
Assignment 3.3 Completing the Square and Finding the Vertex
Assignment 3.4 Applications of Quadratic Functions
##### Class # 1772 Pre-Calculus Mathematics 30S M4: Solving Quadratic and Rational Equations

In Module 3, you learned about quadratic functions. In this module, you will learn how to solve quadratic equations. There are many different methods used to solve quadratic equations including factoring, taking square roots, using the quadratic formula, and even completing the square. In this module, you will learn when it is best to use each method. You will learn how to derive the quadratic formula and important properties of the discriminant (a part of the quadratic formula). The last part of this module introduces rational equations and presents some problems where, in order to solve them, you will be required to use rational equations.

Assignment Number Assignment Title
Assignment 4.1 Solving Quadratic Equations by Graphing and Taking Square Roots
Assignment 4.3 The Discriminant and Solving Rational Equations
##### Class # 1773 Pre-Calculus Mathematics 30S M5: Radicals

In Module 4, you learned how to solve quadratic equations by taking square roots. You also reviewed your knowledge of simplifying square roots from Grade 10 Introduction to Applied and Pre-Calculus Mathematics. Another name for the math notation for square roots is radicals. In this module, you will build on your knowledge of simplifying radical expressions. You will also learn how to add, subtract, multiply, and divide radical expressions.

Radical expressions have applications in trigonometry, electricity, and driving. They also appear in formulas designed to find the volume or surface area of 3-D objects. It is possible to solve these types of applications problems by solving radical equations. Once you learn how to perform operations on radical expressions, you will learn how to solve radical equations.

Assignment Number Assignment Title
Assignment 5.2 Multiplying and Dividing Radical Expressions
##### Class # 1774 Pre-Calculus Mathematics 30S M6: Systems of Equations and Inequalities

Welcome to Module 6! In this module, you will learn how to solve systems of equations as well as inequalities. When you solve systems of equations, you need to be familiar with how to solve linear as well as quadratic equations. Therefore, some questions in this module allow you to practice skills you learned in earlier modules, such as solving quadratic equations by factoring and by using the quadratic formula. As you will see, these systems of equations appear in situations involving linear and quadratic motion. Some examples include throwing a baseball or a football, jumping off a diving board, or just travelling in a straight line.

Assignment Number Assignment Title
Assignment 6.1 Solving Systems of Equations
Assignment 6.2 Solving Linear Inequalities in Two Variables and Quadratic Inequalities in One Variable
Assignment 6.3 Solving Quadratic Inequalities in Two Variables
##### Class # 1775 Pre-Calculus Mathematics 30S M7: Trigonometry

This module incorporates some of your previous knowledge about trigonometry, including the three primary trigonometric ratios: sine, cosine, and tangent. Trigonometry, including the Sine Law and the Cosine Law, allows you to calculate the length of the sides and the measure of the angles of triangles. Trigonometry has many applications in the real world. Have you ever noticed how bridges are made up of triangular shapes? Triangles are used in construction because of their strong shape. The more triangles included in the construction of a bridge, the stronger the bridge will be. For this reason, trigonometry is helpful in the design of bridges and other buildings.

Assignment Number Assignment Title
Assignment 7.1 Trigonometric Ratios, Reference Angles, and Trigonometric Equations
Assignment 7.2 Patterns in Trigonometric Ratios and the Sine Law
Assignment 7.3 The Cosine Law and the Ambiguous Case
##### Class # 1776 Pre-Calculus Mathematics 30S M8: Absolute Value and Reciprocal Functions

Welcome to the last module of Grade 11 Pre-Calculus Mathematics! In this module, you will be learning about two different types of functions and their graphs.

You will first learn about absolute value functions, which occur when only positive y-values are desired. Absolute value is especially important in distance, as you would never say you are a negative distance away from your destination. You could be 10 kilometres east or 10 kilometres west, but either way you are still 10 kilometres away.

Once you learn about absolute value functions, you will learn about reciprocal functions. Reciprocal functions are used to define many relationships, including gravitational forces between planets, currency exchange, and the amount of time a diver can take to rise to the surface of the water depending on the depth. As you have already studied linear and quadratic functions, you will now learn how to graph the reciprocals of these types of functions in this module.

Assignment Number Assignment Title
Assignment 8.1 Absolute Value
Assignment 8.2 Absolute Value Equations and Graphing Reciprocal Functions: Part 1
Assignment 8.3 Absolute Value Equations and Graphing Reciprocal Functions: Part 2

#### Pre-Calculus Mathematics 40S

##### Class # 1721 Pre-Calculus Mathematics M1: Permutations, Combinations, and the Binomial Theorem

Welcome to your first module of Grade 12 Pre-Calculus Mathematics! In previous mathematics courses, you may have been asked problem-solving questions such as, “How many ways can you assign first, second, and third place in a race if three people are racing?” In this module, you will learn how to answer questions like these quickly and efficiently.

You will learn a method of “fast counting,” called permutations and combinations, that allows you to count large amounts of objects or arrangements accurately and quickly. Anyone can count the number of objects in a set one at a time, but what happens if there are over a million objects to count? You need a method that will produce the answer without it being necessary to count the objects one at a time. Learning these “fast” counting processes is the objective of this module.

This counting method also allows you to expand binomials quickly and efficiently. You will learn how to do this according to a theorem called the Binomial Theorem.

Assignment Number Assignment Title
Assignment 1.1 The Fundamental Counting Principle and Permutations
Assignment 1.2 Permutations and Combinations
Assignment 1.3 The Binomial Theorem
##### Class # 1722 Pre-Calculus Mathematics 40S M2: Function Transformations

A major portion of this course is the study of functions. You studied some functions in detail in Grade 11 Pre-Calculus Mathematics—specifically, the linear, quadratic, absolute value, and reciprocal functions. You also studied the transformations of quadratic functions. In this module, you will expand on this knowledge and study the transformations of the graphs of functions in general. The most common transformations are translations, reflections, and stretches. This module concentrates on the translations and stretches of functions. The study of reflections is addressed in Module 3.

You will also learn about operations on functions and compositions of functions. Operations on functions include adding, subtracting, multiplying, or dividing two or more functions. Compositions of functions occur when the value of one function depends on the value of a second function. This is similar to the food chain, and will be explained more in the last lesson of this module.

Note: Definitions and explanations are often given in the learning activities, as well as in the text of the lessons. For this reason, consider the learning activities as part of the lesson, not as review exercises. The answer keys for the learning activities should also be considered as part of the lesson.

Assignment Number Assignment Title
Assignment 2.1 Transformation of Functions
Assignment 2.2 Combinations of Transformations
Assignment 2.3 Operations on and Compositions of Functions
##### Class # 1723 Pre-Calculus Mathematics M3: Reflections

You first started to look at reflections in Grade 5. Throughout the years that followed, you went from reflecting images using a glass mirror to reflecting points in all four quadrants. In this module, you will expand this knowledge even further to learn about the reflections of functions on a coordinate plane.

In this module, you will learn more about different types of functions, all of which involve reflections. There are three main types of reflections including reflections through the x-axis, reflections through the y-axis, and reflections though the line, y = x. In addition to what you learned about in Module 2, reflections are a type of transformation. After you learn about all the different types of reflections, you will be able to graph any variation of a quadratic function, a cubic function, a square root function, and an absolute value function.

As you will learn, reflections through the line, y = x, are related to inverse functions. The concept of “inverse” has been part of your learning with regard to “actions” in the past. When two actions seem to undo each other, they are inverse actions. For example, the action of opening a door undoes the action of closing the door, or the action of sitting down is “undone” by the action of standing up. In arithmetic, the operation of subtraction is undone by the operation of addition, and the operation of multiplication is undone by the operation of division.

Assignment Number Assignment Title
Assignment 3.1 Reflections in the x-axis and in the y-axis
Assignment 3.2 Inverse Functions and Relations
##### Class # 1724 Pre-Calculus Mathematics M4: Polynomials

Functions are a fundamental topic of mathematics. They describe many relationships in mathematics and science. In this module, you will learn all about polynomial functions up to a degree of five. The concepts of factoring that you have studied in previous modules and in previous pre-calculus courses will be extended to include the remainder theorem and factor theorem. This gives the basis for the study of polynomials, their zeros, and their graphs.

Solving algebraic equations by determining the roots of a polynomial is a very old problem in mathematics. However, these equations used to be written out in words. When the current variable notation was introduced many years ago, it made the solution of the roots of polynomial equations much easier. With the onset of computer technology, the solutions are easier still. When you learn how to find the zeros of a polynomial in this module, you will have learned how to solve one of the problems that stumped ancient mathematicians for years!

Assignment Number Assignment Title
Assignment 4.1 Polynomial Functions
Assignment 4.2 Factoring and Graphing Polynomials
##### Class # 1725 Pre-Calculus Mathematics M5: Trigonometric Functions and Unit Circle

There were 15:58 hours of daylight in Winnipeg on July 13th, 2012. Would you expect that this amount would have been any different on July 13th, 2000, or will be any different from the amount on July 13th, 2040? The answer is no. The reason is that this number of hours of daylight on any given day in any specific place will be approximately the same or repeat itself over the years. This information or data will be different for each place in the world, but it will remain repetitive for that place over the years. This is an example of a function (number of daylight hours over time) that is called periodic. It can be modelled by the sine function or the cosine function and is called a sinusoidal. There are many similar such occurrences in the world (for example, the amount of air in your lungs over time, the average daily temperatures during the year, and many other examples of this repetitive phenomenon).

In this module, you will examine trigonometric functions, which are a type of periodic function, and more of the properties and applications associated with them. First, you will study trigonometric ratios in more detail. You have been studying trigonometric ratios since Grade 10 mathematics. In this module, you will study the graphs of the trigonometric functions. You will look at tables of values of these functions, generate their graphs, and list their properties. Using techniques you have been developing since Module 2, you will also study transformations of these periodic functions.

Assignment Number Assignment Title
Assignment 5.1 Degrees, Radians, and the Unit Circle
Assignment 5.2 The Six Trigonometric Ratios
Assignment 5.3 Trigonometric Functions and Their Graphs
##### Class # 1726 Pre-Calculus Mathematics 40S M6: Trigonometric Equations and Identities

In the last module, you were introduced to the concept of radians and the six trigonometric functions. As well, you were shown how to graph trigonometric functions using transformations. In this module, you will combine all of these concepts in order to solve trigonometric equations and prove various trigonometric identities. In order to find the zeros of various trigonometric functions or to solve the corresponding trigonometric equations, you will develop skills in circular function equation solving. You will also develop relationships amongst these functions called identities.

Identities can be useful as they have the power to reduce what may seem like a very complex expression down to a simpler expression that may involve only one trigonometric ratio. These identities are all constructed from the unit circle. Therefore, you must make sure that you are comfortable dealing with the unit circle and all the concepts discussed in Module 5 before you begin this module!

Assignment Number Assignment Title
Assignment 6.1 Solving Trigonometric Equations
Assignment 6.2 Using Elementary Identities
Assignment 6.3 Sum and Difference and Double Angle Identities
##### Class # 1727 Pre-Calculus Mathematics M7: Exponents and Logarithms

This module introduces you to two very important functions: exponential and logarithmic functions. As the name suggests, these functions are based on the properties of exponents.

These types of functions occur when modelling financial situations and natural processes such as population growth, the decay of a radioactive substance, sound, light, the intensity of an earthquake, the cooling of a dead organism, and even the spread of epidemics. In the last lesson of this module, you will be presented with many application problems that will allow you to see the types of situations in which exponential and logarithmic functions are used as models.

Assignment Number Assignment Title
Assignment 7.1 Exponential Functions and Logarithms
Assignment 7.2 Dealing with Logarithms
Assignment 7.3 Solving Exponential and Logarithmic Equations
##### Class # 1728 Pre-Calculus Mathematics M8: Radical and Rational Functions

This module builds on concepts you learned throughout Grade 11 Pre-Calculus Mathematics and throughout the first seven modules of this course. In Grade 11 Pre-Calculus Mathematics you learned how to solve radical and rational equations algebraically. You will be combining this skill with the function transformation skills you have learned throughout this course in order to be able to solve radical and rational equations graphically. Before you do this, you first need to learn how to graph radical and rational functions using transformations and other properties of functions.

Are you planning on a career in either the medical field or in law enforcement? If you are, you may encounter these types of functions. Radical functions can be used in the reconstruction of traffic accidents, as they can be used to model the stopping distance of a vehicle. Rational functions can be used to model the amount of a drug found in a person’s bloodstream over time. There are many more applications of these functions in different fields, including astronomy and business analysis.

Assignment Number Assignment Title
Assignment 8.3 Rational Functions

#### Introduction to Calculus 45S

##### Class # 1729 Introduction to Calculus 45S M1: Limits

Upon successful completion of this module, you will develop an understanding of the limit concept and how it applies to graphical and analytical functions. You will also be exposed to contextual applications to provide meaning behind this abstract mathematical concept.

Assignment Number Assignment Title
Assignment 1.1 Limits
Assignment 1.2 Limit Theorems
Assignment 1.3 Solving the Indeterminate Form of Limits
Assignment 1.4 Exploring One-Sided Limits
Assignment 1.5 Determining the Asymptotes of a Graph
Assignment 1.6 Continuity
##### Class # 1730 Introduction to Calculus 45S M2: Derivatives

The slope of a line is the same everywhere on the line. The slope of a non-linear function curve is different on different parts of the curve. In this module, you will explore the changing slope of a curve. By using your knowledge of the slope of a line and the tangent line to a curve, you will be able to comment on the slope of a curve. Your understanding of limits will be extended to introduce one of the two main calculus concepts of this course: derivatives.

Assignment Number Assignment Title
Assignment 2.1 Slope of the Tangent Line to a Curve
Assignment 2.2 Definition of the Derivative
Assignment 2.3 Basic Differentiation Rules
Assignment 2.4 Differentiation with Product and Quotient Rules
Assignment 2.5 Differentiation with the Chain Rule and Higher Order Derivatives
Assignment 2.6 Implicit Differentiation
##### Class # 1731 Introduction to Calculus 45S M3: Applications of Derivatives

In Module 2, you learned to calculate the derivative of a function using limits, and you learned to use several derivative rules to differentiate some complex functions. Ultimately, calculus concepts are used to solve problems in a wide variety of applications.

In this module, you will apply your understanding of the derivative to four specific categories: particle motion problems, optimization problems, related rate problems, and curve sketching. In each of these applications, you will need to recall and use all of the differentiation rules and, most importantly, apply your understanding that the derivative is the rate of change of one variable with respect to another.

Assignment Number Assignment Title
Assignment 3.1 Solving Inequalities
Assignment 3.2 Particle Motion Problems
Assignment 3.3 First Derivative Applications
Assignment 3.4 Optimization Problems
Assignment 3.5 Concavity and Sketching Polynomial Functions
Assignment 3.6 Related Rates
##### Class # 1732 Introduction to Calculus 45S M4: Integration

In Module 4, you will learn the inverse operation of differentiation called antidifferentiation, which, as you will see, is related to a process called integration. In some applications of calculus, it will be necessary to use antidifferentiation to find the original function when the derivative is known. In other applications, integration will be used to determine the area under the curve of a function.

Assignment Number Assignment Title
Assignment 4.1 Antidifferentiation and Intergration
Assignment 4.2 Differential Equations
Assignment 4.3 Define Integral
Assignment 4.4 Area under a Curve
Assignment 4.5 Area between Two Functions