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; 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.
Parallel and Perpendicular Lines
GeoGebra: Demonstrating slopes of parallel lines (as per slide 1)
GeoGebra: Demonstrating slopes of perpendicular lines (as per slide 2)
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.
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.
GeoGebra: Unlimited practice converting linear equation forms (as per slide 3)
Exponent Boot Camp 1: Product and Quotient properties
Exponent Boot Camp 2: Negative and Zero Exponents
Exponent Boot Camp 3: Power of a Power
Exponent Boot Camp 4: Power of a Product
Exponent Boot Camp 5: Rational Exponents
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
Trig Identities 7: The Sum and Difference Identities
Trig Identities 9: Related Angle Identities
This lesson demonstrates visually, as opposed to algebraically, the trigonometric relationships between angles such as θ and θ + π.