EMR Directions for Teachers

Directions for Teachers

Purpose
We have prepared a collection of exercises that test many of the skills from pre-university mathematics that are often called upon in university science, commerce, engineering, and mathematics courses. We are making these exercises available on the Internet to anyone who can make use of them.

Format
For each topic there is a very brief explanation of the concepts. These explanations are not meant to be a comprehensive treatment. They should remind the reader of basic mathematical terms and their definitions. In many cases, we have also provided some examples in these summaries or links to worked out examples.

There are three sets of exercises for each topic with the exercises sorted into Introductory, Moderate, or Advanced levels of difficulty. After solving an exercise, the user may want to compare his/her work with a solution via the link provided after each problem. Links to hints are provided for many of the harder questions; these are to be used when frustration is setting in with the particular problem.

Possible uses

As a last minute review for grade 12 students who are planning to go to university, the student could work through these exercises. They should keep a record of numbers of correct solutions for each grouping. In order to be well prepared for university calculus, for example, a student should have a complete facility with all the introductory level exercises, solving them quickly and accurately. They should have a fair success rate with the moderate exercises. The advanced exercises are meant to be a challenge, although some turn out to be easy if looked at the right way.
As enrichment for gifted students in early grades, even down to grade 8, these exercises could help provide challenges. The student who quickly grasps a concept when it is first introduced in the curriculum may enjoy testing her/his skills on the questions dealing with that particular concept.
As a store of extra exercises for teachers, these problems could be useful to copy and use in class or on assignments. But be aware that your students may have found the site as well and will have access to solutions.

Source
We created many of these exercises by working out solutions to all questions on 10 years worth of calculus exams at the University of Saskatchewan. Each time a particular skill from pre-university mathematics was necessary to make a step in solving a problem, we devised a question for this site. The question was formulated, as near as posible, to reflect what the student would have to do in the course of solving the calculus problem. In this way, we hope that our questions truly reflect the most frequently called upon skills from high school.

Variety
We have not posted all our exercises. In fact, we have posted only a small fraction of them. We plan to periodicly add and/or replace exercises. In this process, we will be influenced by your feedback. Please use our teacher response page to send us your comments on which exercises are good, bad or ugly. You may also send us favourite exercises of your own. They would be greatly appreciated.