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Math 265 Challenge Exam

Math Diagnostic Test

Fac. of Science IT Support


Department of Mathematics & Statistics

MS 476, Math Sciences Building
University of Calgary
2500 University Dr NW
Calgary, AB T2N 1N4 Canada
T. 403.220.5203

Mathematics Diagnostic Test

Students who do not have the required 70% in Math 30-1 or Pure Math 30, as prerequisite for first year linear algebra and calculus courses, may be eligible to meet this prerequisite requirement by obtaining a satisfactory grade on the Mathematics Diagnostic Test. This test is designed to assess general problem solving skills from High School mathematics in the areas of algebra, geometry and trigonometry. Questions have been selected which provide a high degree of correlation between success on the Diagnostic and success in first year mathematics.

The Test consists of ten multiple choice questions done on the computer. No calculators or other aids are permitted. Results of the Test are immediate.  

There is a maximum of 2 attempts at the Diagnostic Test allowed.  Students unable to successfully pass the test within 2 attempts are advised to contact Continuing Education regarding upgrade alternatives (see alternatives link listed below).

The Mathematics Diagnostic Test has the same status as a University final examination. Accordingly, any form of cheating is considered grounds for suspension or expulsion from the University. Proof of identity is required during the test. Students more than 30 minutes late will not be admitted to the examination.

Topics of particular importance emphasized on the Test include :

  1. Polynomials: factorization, roots and their relationship to factors, polynomial division. Quadratic equations, sum and product of roots, nature of roots (discriminant).
  2. Simplification: algebraic expressions, rational forms involving exponents, roots, radicals. Sums, products, quotients.
  3. Equations: Solving simple equations and systems of two linear equations in two unknowns. Checking solutions to problems.  isolating one variable in an equation with multiple variables.
  4. Inequalities: solving linear and compound inequalities.
  5. Distance: Pythagorean Theorem, absolute value. Applications.
  6. Cartesian Coordinates: Distance, equations of circles, completing the square.
  7. Straight Lines: Slope, intercepts, slopes of perpendicular lines.
  8. Geometry: Use of similar figures, congruent triangles, formulas for area, surface area and volume.
  9. Functions: Function notation, domain and range of a function, composition of functions, properties of quadratic functions.
  10. Trigonometry: Sine, Cosine, Tangent functions and their graphs, trigonometric functions of special angles, identities. Radian measure. The law of cosines, the law of sines.  Solving simple trigonometric equations.
  11. Word Problems: Formulation of equations for the solution of word problems. Solving and checking solutions for correctness.
  12. Logarithms and exponents: Definitions, basic properties, simplification, use in calculations, solving equations.

Study Guides :

  • Paul's Online Math Notes provides an Algebra/Trig Review.
  • Openstax provides a free online Algebra and Trigonometry Textbook.
  • PatrickJMT provides online videos for most mathematics topics.
  • The Student Success Centre offers free math tutoring appointments.  Appointments can be booked by going to or by stopping by the front desk of the Student Success Centre on the third floor of TFDL and selecting 'Foundational Pre-University Math' as your appointment type.  It is recommended that students study the material prior to the appointment and come prepared with questions.
  • At the University Bookstore, Chapters or Amazon: Practice and review can be found in a number of study guides available in the Bookstore, for example the Schaum's Outline series for Algebra and Trigonometry. Also suggested is the book: "Just in Time, Algebra & Trigonometry for students of Calculus", by Guntram Mueller & Ronald Brent (Addison Wesley Pub.).

Additional Resources:


A Scheduled Test is offered during the week preceding the start of classes in each of the Fall, Winter, Spring/Summer Sessions.

To register for a Scheduled Test, please CLICK HERE

NOTE: Students should register for a Scheduled Test at least two weeks prior to start of classes.

Students who cannot attend one of these scheduled Tests should contact the Department immediately, either by visiting MS 476, or calling 220-5203. There will be a $50.00 fee for writing the Test which must be paid at the Enrollment Services  (Registrar's Office) in advance of the Test date. Students will be required to present proof of payment and picture I.D. for admission to the Test.  

Alternatives to the Test:

For a variety of alternatives to taking the Diagnostic Test to meet prerequisites, see Prerequisite Alternatives.

Test Dates

Day Time Location

Tuesday May 9, 2017 

10:00 am

MS 515


How to Write the Exam:

When you feel confident about the subject material:

  1. Pay your Diagnostic Test Registration Fee at the Enrolment Services (MLB 117)
  2. Register for a Scheduled Test:  CLICK HERE

  3. Bring your fees receipt and valid picture I.D. to your exam.

Diagnostic Test Registration Fee: $50.00 per attempt (max 2 attempts) - payable at Enrollment Services/Service Stop MLB 122

Test Duration: 1 hour

Results: immediate