cemc summer problem solving course

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CEMC at Home

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• Real-World Math
• Resources for Grades 3 to 8
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• Master of Mathematics for Teachers
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CEMC at Home was developed in 2020 to support teachers, students and parents during the COVID-19 pandemic. It included materials at each of four grade levels: Grade 4 to 6, Grade 7/8, Grade 9/10 and Grade 11/12. The goal was to provide a wide variety of fun and educational ways to do mathematics and computer science while at home practicing physical distancing. The resources included games, new problems to solve, applications, videos, pointers to existing materials and more.

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Current Resources (June 19, 2020)

There will be no new resources posted for CEMC at Home from May 13 to May 20. Solutions for past resources will continue to be posted as usual. Check the CEMC at Home webpage on Thursday, May 21 for the next CEMC at Home resources.

Our hope is that these resources make it to as many parents, teachers, and students as possible. Please help us achieve this by forwarding this information to your friends, family and colleagues. Share this information in person or electronically and let's get the conversations going! Many of the activities will encourage exploration and discussion and we hope that you share your thoughts with each other and stay connected.

Solutions and Other Recent Resources

Resources from the last week of CEMC at Home can be found below as well as solutions to some problems.

Each of the following links is to a booklet containing a weekly set of resources and available solutions.

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Advanced Functions and Pre-Calculus

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This courseware extends students' experience with functions. Students will investigate the properties of polynomial, rational, exponential, logarithmic, trigonometric and radical functions; develop techniques for combining functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills. This courseware is considered prerequisite learning for the Calculus and Vectors courseware.

Functions: Transformations and Properties

Polynomial functions, polynomial equations and inequalities, rational functions, exponential and logarithmic functions, trigonometric functions, trigonometric identities and equations, operations on functions, rates of change.

This unit introduces functions along with many terms and notations that will be encountered when working with them. A large portion of the unit deals with sketching functions using transformations. The unit concludes with a look at inverses.

The module begins with the definition of a function and how functions are represented. Domain and range, function notation, and composite functions are introduced and developed in this module.

Often in mathematics, solutions lie on an interval. Three techniques used to describe intervals are presented in this module. The module concludes with an example that is used to present definitions of concepts that will be used throughout the course.

Is there a difference in how an inequality is solved versus the solution of an equation? In this module, this question is examined and a variety of different examples are solved.

In this module we look at the graphs of five base functions: the quadratic function, the square root function, the reciprocal function, the exponential function, and the absolute value function. For each function, we will look at efficient ways to sketch the graph, discuss domain and range, and make observations about some features of each graph.

Our examination of transformations begins with a look at translations. In this module, we develop a general rule for translations, we sketch graphs given a base function and translation, we determine equations of graphs that have been translated, and we find the translation that has been applied to one function to obtain another.

How is the graph or equation of a function affected by a reflection about the \(x\)- or \(y\)-axis? In this module, we develop a general rule for these reflections, we examine even and odd functions, we sketch images which are reflections of base functions, and we determine equations of functions which have been reflected.

When a function is stretched about the \(x\)- or \(y\)-axis, what is the effect on the graph and the equation? In this module, we develop a general rule for these types of transformations, we sketch various functions given a base graph and stretch using words or mapping notation, and we determine the transformation given the equation or graph of the pre-image and image.

In this module, we put all of the transformation pieces together. By looking at an equation, we determine which base function is being transformed and which transformations have been applied. Two methods are presented for sketching functions using transformations.

In this module, inverses are defined algebraically and geometrically. Given the graph of a function, we sketch the inverse, and given the equation of a function, we determine the equation of the inverse.

This unit examines key characteristics and properties of polynomial functions, supportive in determining the shape of their graphs. Focus will be placed on studying the behaviour of 3rd and 4th degree polynomial functions. Through investigation, connections will be made between the algebraic, numeric, and graphical representations of these functions.

This unit develops the factoring skills necessary to solve factorable polynomial equations and inequalities in one variable. Connections are made between the real roots of a polynomial equation and the x -intercepts of the corresponding polynomial function. Skills are applied to solve problems involving polynomial functions and equations.

This unit examines key characteristics and properties of rational functions, supportive in determining the shape of their graphs. Focus will be placed on studying rational functions with linear or quadratic polynomial expressions in their numerators and/or denominators. Through investigation, connections will be made between the algebraic and graphical representations of these functions.

This unit examines key characteristics and properties of exponential and logarithmic functions. Techniques used to solve exponential and logarithmic equations will be taught and applied to solving problems.

In this unit, you will be introduced to functions whose values repeat over regular intervals. The most common such functions are called sinusoidal functions. These functions will be examined graphically and algebraically. The ultimate goal is to be able to solve realistic applications that can be modeled by this type of function.

This unit explores equivalent trigonometric expressions and examines strategies to prove trigonometric identities and solve a variety of trigonometric equations. Knowledge of fundamental trigonometric identities will be extended to include compound angle and double angle formulas.

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Amazing mathematics resource by the University of Waterloo

https://courseware.cemc.uwaterloo.ca/

It has a considerable amount of videos, exercises, and fully written solutions. Here is an example: https://courseware.cemc.uwaterloo.ca/40/assignments/1069/1

They not only have videos at low-level mathematics, they also have videos working through problems that require proof (read: problems that you might find in maths competitions) and have a whole playlist of just problem solving, and developing that.

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Master of Mathematics for Teachers: Courses

Below you will find courses that we anticipate offering in the Master of Mathematics for Teachers (MMT) program. Please note that these courses are subject to change.

For course descriptions, please visit the graduate studies academic calendar .

• MATH 600 - Mathematical Software
• MATH 643 - Theory of Computation
• MATH 647 - Foundations of Calculus I
• MATH 674.004 - Fractals
• MATH 674.005 - Graph Theory
• MATH 685 - Math and Peace
• MATH 692 - Mathematical Proofs
• MATH 630 - Probability
• MATH 641 - Algorithms
• MATH 674.007 - Quantum Information
• MATH 674.009 - Math and Music

Winter 2025 

• MATH 642 - Intro to Computer Science
• MATH 648 - Foundations of Calculus II
• MATH 674.001 - Mathematical Finance I
• MATH 674.002 - Mathematical Finance II
• MATH 681 - Problem Solving
• MATH 682 - History of Math I
• MATH 699 - Capstone Project

Winter 2026 

• MATH 631 - Statistics
• MATH 674.003 - Cryptography
• MATH 674.006 - Math for Global Citizens
• MATH 683 - History of Math II

Spring 2025

• MATH 640 - Number Theory
• MATH 650 - Mathematical Modelling
• MATH 661 Geometry
• MATH 674.008 - Special Relativity
• MATH 690 - MMT Workshop

Spring 2026

• MATH 636 - Linear Algebra
• MATH 661 - Geometry
• MATH 674.010 - Optimization

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