# Pre-Calculus

These pre-calculus lessons are meant to bridge the gap between Math SN5 and Calculus 1. Many students who go directly from Math SN5 to Calculus 1 have difficulty with some of the algebraic procedures that are essential to Calculus but are not covered in the Quebec SN5 curriculum. These lessons provide a solid foundation that students will need in order to be successful in Calculus. (Additional lessons are in development.)

**The primary objectives of these lessons are to provide:**

**• Review and consolidation** **of **essential secondary high school **topics covered in the Math SN4/SN5 courses.**

**• Additional algebra instruction** that picks up where Math SN4/SN5 leave off, and covers topics essential to successfully study Calculus 1 and 2.

**• Enrichment**, which may include introductory Calculus topics, such as *Limits & the Derivative of a Function.*

PLEASE NOTE: No sign-in is required to view these lessons. Simply click the arrow on the lower left-hand side of the slide to play. Use the arrows on the lower right-hand side of the slide to advance the slides.

LEARN Design and Development Team: Author/Lead Teacher: Audrey McLaren, BSc, DipEd; Editor: Steven Rossy, MD; and Instructional Designer: Kristine Thibeault, MEd

# Slope of a Line

This lesson gives a visual definition of slope of a line, as well as a formula to calculate slope. GeoGebra is used to demonstrate the concept, to provide the student with practice, and to encourage the opportunity to explore independently.

**Additional Resources:**

GeoGebra: Demonstrating slope and its properties (as per slide 1)

Practice GeoGebras related to slope (as per slide 2)

# Parallel and Perpendicular Lines

**Additional Resources:**

GeoGebra: Demonstrating slopes of parallel lines (as per slide 1)

GeoGebra: Demonstrating slopes of perpendicular lines (as per slide 2)

GeoGebra: An Interactive investigation of slopes of perpendicular lines (as per slide 3)

# Finding the Rule of a Linear Function

This lesson outlines a procedure for finding the standard algebraic representation of a linear function given various types of information about the line. Included are several worked out examples which progress from simple (given slope and y intercept) to more complex (given 2 points, or the equation of perpendicular line and y intercept). GeoGebra is used to provide the student with practice and immediate feedback.

**Addtional Resources:**

GeoGebra: Unlimited practice finding equation of a line given slope and one point (as per slide 1)

GeoGebra: Unlimited practice finding equation of a line given two points (as per slide 2)

GeoGebra: Unlimited practice finding equation of a line involving parallel and perpendicular lines (as per slide 3)

# Linear functions: Standard Form & General Form

Outlines procedures for transforming an equation to/from the standard form

**y = ax + k and Ax + By + C = 0. **

Graspable Math and GeoGebra are used to demonstrate the concept, and to provide the opportunity to explore independently.

**Additional Resources:**

Graspable Math: An interactive example of how to convert from general form to slope-intercept form (as per slide 1)

Graspable Math: An interactive example of how to convert from slope-intercept form to general form (as per slide 2)

GeoGebra: Unlimited practice converting linear equation forms (as per slide 3)

**The Exponent Rules Boot Camp Series** is made up of five lessons that are meant to be viewed in sequence. Each lesson builds on the properties covered in those prior to it. Each Boot Camp ends with examples that gradually spiral through all the exponent rules, thus enabling students to simplify more and more complex expressions, both numerical and algebraic.

# Exponent Boot Camp 1: Product and Quotient Properties

# Exponent Boot Camp 2: Negative and Zero Exponents

# Exponent Boot Camp 3: Power of a Power

**The Trigonometric Identity Series** is comprised of nine lessons that cover what the main trigonometric identities are and what they are used for. It also gives plenty of algebraic practice within the context of proving more complex identities. Most of these topics are covered in Quebec’s grade 11 curriculum, but topics 7, 8, and 9 are not.

# Trig Identities 3: Using Identities to Find Trigonometric Ratios

# Radicals 3: Multiplying/Dividing Radical Expressions

This lesson includes multiplication of monomial and binomial radicals, as well as special cases of squaring binomial radicals and the product of conjugates.

**Additional Resources:**

GeoGebra: Infinite Practice - Multiplying/Dividing Radicals (Slide 24)

Graspable Math Examples - Multiplying Radical Binomials (Slide 26)

GeoGebra: Infinite Practice - Squaring a Monomial Radical (Slide 39)

GeoGebra: Infinite Practice - Multiplication of Conjugates (Slide 56)

**The Limits Series **introduces students to an important concept for Calculus - Limits. All of this content is covered in any typical Calculus 1 course. It is included here because of the connections to other lessons in our Pre-Calculus course, such as factoring and rationalization.