MCR3U: Functions (University Preparation)
PREREQUISITE: Principles of Mathematics, Grade 10, Academic
GRADE: 11 (University)
AVAILABILITY: Spark Asher Academy Online
THE ONTARIO CURRICULUM: Mathematics
Course Overview
This course is designed to empower students to use mathematical language with confidence, versatility, and proficiency. It utilizes a diverse array of instructional strategies to provide learning experiences that cater to various learning styles, abilities, and interests. Throughout the course, students will develop their skills in problem-solving, selecting appropriate tools and computational strategies, connecting mathematical concepts to real-world applications, and using different representations—including concrete, visual, and symbolic. Additionally, the course emphasizes the importance of self-assessment, enabling students to evaluate their own understanding of the concepts learned.
UNIT ONE
Algebraic Tools
- Essential Question: How can we determine the most effective problem-solving strategies for different situations?
In this unit, students will begin by refreshing their understanding of fundamental algebraic tools through review lessons. They will then advance their skills by building on these foundational concepts, enhancing their ability to solve more complex algebraic problems.
UNIT TWO
Introduction to Functions
- Essential Question: How can recognizing patterns help us predict unknown values?
Students will expand on the algebraic concepts learned in the previous unit by exploring functions. They will delve into concepts such as domain and range, transformations of basic functions, and inverse functions. This unit introduces new notations and foundational skills essential for understanding the function concept in depth.
UNIT THREE
Exponential Functions
- Essential Question: What are the benefits and limitations of using mathematical models for predictions? Can any model be completely accurate?
This unit focuses on exponential functions, identifying their unique characteristics through graphical and algebraic representations. Students will apply transformations to exponential function graphs and solve exponential equations using algebraic techniques and exponent laws. They will also tackle real-world problems using exponential models to analyze situations and predict outcomes.
UNIT FOUR
Trigonometry
- Essential Question: What are the potential limitations of using trigonometric models for predictions?
Students will revisit trigonometric basics such as SOH CAH TOA, Sine law, and Cosine law, and extend these concepts to trigonometric functions. By the end of the unit, students will understand how to use trigonometric functions to model real-world phenomena like pendulum swings.
UNIT FIVE
Sequences and Series
- Essential Question: How can we summarize observed numerical patterns to make reliable predictions?
Students will explore sequences and series, a form of discrete function. This unit will build on their existing knowledge of identifying patterns in sequences and extend it to modeling these using functions, allowing them to predict any term within a sequence.
UNIT SIX
Financial Applications
- Essential Question: How and why should mathematical strategies be applied to real-world financial decisions?
This unit applies algebraic tools, functions, and exponential functions to financial contexts, addressing real-life applications of these mathematical concepts. Students will see the practical use of mathematics in finance, answering the common question, “When will we ever use this?”
Assessment
The final grade will reflect students’ achievement of the course expectations and their ability to apply learned skills effectively. It is divided as follows:
- 70% Coursework: This component is based on evaluations conducted throughout the course, reflecting the most consistent level of achievement by the student. Recent improvements in performance may also be considered.
- 30% Final Evaluation: This includes a culminating project worth 10% and a final proctored exam worth 20%. These evaluations aim to assess the comprehensive understanding and application of the course material.
For more details on final exams and the exam fee, please consult to us directly via contact page. Additional information can be found in our download section in courses page.
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