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Calculus challenge exam

This examination is held at UNB (Fredericton and Saint John campuses) it is open to students registered in a calculus course at a high school that has made arrangements with the Department of Mathematics and Statistics. A fee will be charged.

If you qualify for credit, you will receive a certificate entitling you to credit for and an exemption from Math 1003 when you register at UNB Saint John. Upon your acceptance of the credit, the letter grade of the exam will be recorded on your transcript.

More information on the 2023 exam will be available soon.

Exam details

  • To be eligible for the exam, a student must be registered in a calculus course at a high school or have completed such a course.
  • In New Brunswick, students should be taking Calculus 120 or have completed it last Fall.
  • Permission to participate in this exam is not granted to students who have already started college or university.
  • Students may only attempt this exam once.

A letter grade of B- or higher must be achieved on the exam to qualify for credit.

Students who pass this examination will receive a certificate from UNB entitling them to credit for an exemption from Math 1003, only if they register at UNB as a full-time student. Accepting credit for Math 1003 is optional.

Upon the student's acceptance of credit, the letter grade of the exam will be recorded on their transcript.

Students who accept credit for Math 1003 should consult their program advisor or the Department of Mathematics and Statistics for individual advising on course choices.


1. Functions and graphs

  • Combinations of functions, including composites, transformations
  • Trigonometric functions
  • Inverse trig functions
  • Hyperbolic functions
  • Exponential and logarithmic functions

2. Limits

  • Limit laws
  • Continuity
  • Limits at infinity and horizontal asymptotes
  • Infinite limits and vertical asymptotes
  • Indeterminate forms and L'Hospital's rule

3. Derivatives

  • Definition of the derivative, calculation from the definition
  • Tangent lines
  • Derivative rules: product, quotient, chain rules
  • Derivatives of trig and inverse trig functions
  • Derivatives of exponential and logarithmic functions
  • Derivatives of hyperbolic functions
  • Implicit differentiation
  • Logarithmic differentiation

4. Antiderivatives

  • Basic integration formulas (from known derivatives)

5. Applications

  • Rates of change, examples in natural and social sciences, position-velocity-acceleration
  • Related rates
  • Local/absolute extrema
  • Curve sketching
  • Optimization

6. Theorems

  • Intermediate Value Theorem
  • Extreme Value Theorem
  • Rolle's Theorem and Mean Value Theorem

Contact us

If you have questions regarding the calculus challenge exam, contact Dr. C. Hope Alderson, hope.alderson@unb.ca, or Mahin Salmani, msalmani@unb.ca.