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Mathematics IV

Course Code: MATU 0412
Faculty: Science & Technology
Department: Math Upgrading
Credits: 4.5
Semester: 15 weeks
Learning Format: Lecture, Lab, Tutorial
Typically Offered: TBD. Contact Department Chair for more info.
course overview

This course deals with a variety of topics in geometry, trigonometry, quadratic relations, exponential and logarithmic functions, polynomials, sequences and series, and includes an introduction to calculus, and problem solving and follows the curriculum for BC Schools Mathematics 12. It is designed for the student who plans to take further courses in mathematics for transfer credit.

Course Content


  • radian measure
  • reciprocal trigonometric ratios
  • graphs of sine, cosine, and tangent functions
  • period, amplitude, domain, range
  • graphing techniques applied to trigonometric functions
  • trigonometric identities
  • conditional trigonometric equations

Quadratic Relations

  • absolute value equations and inequalities
  • distance, midpoint formula
  • geometric derivation of lines, circles and parabolas
  • the hyperbola and its graph
  • standard forms of all conic sections
  • general form and standard form
  • graphs of systems of equations and inequalities in two variables
  • solving quadratic systems
  • applications of quadratic relations and systems

Exponential and Logarithmic Functions

  • inverse functions
  • the exponential function
  • the logarithmic function
  • rules of operating with logarithms
  • solving exponential and logarithmic equations
  • applications of exponential and logarithmic functions


  • polynomial functions and their graphs
  • remainder and factor theorems
  • solving polynomial equations and inequalities
  • approximating real roots of polynomial equations
  • applications of polynomial functions

Sequences and Series

  • describing sequences algebraically
  • arithmetic sequences and series
  • geometric sequences and series
  • infinite geometric series
  • sigma notation
  • applications of sequences and series

Introduction to Calculus

  • limits and limit notation
  • evaluating the limits of rational functions
  • slope of a tangent line to a curve
  • equation of a tangent line at a point
  • definition of a derivative
  • rules for finding derivatives
  • instantaneous velocity
  • use of the derivative to graph polynomial functions
  • maximum and minimum values of quadratic functions
  • applications of maximum and minimum values

Problem Solving

  • emphasize reasoning skills
  • require concepts from any strand or grade level
  • involve several steps
  • integrate the use of several strands of topics

Methods of Instruction

A combination of different instructional methods will be used in order to balance instructional efficiency with individual student needs.  Group instruction, individual assistance in lab tutorial or scheduled appointments and student-directed learning will be selected where appropriate and possible.

Means of Assessment

Evaluation will be based on examinations and assignments in accordance with college policy.  Details regarding the number and weighting of individual components will be announced in a “Course Information” handout at the beginning of the semester.

Learning Outcomes

The aims of the course are for students to:

  1. extend experience with algebra, geometry and trigonometry;
  2. extend ability to graph to include hyperbolas, conic sections and trigonometric functions;
  3. gain facility in solving exponential and logarithmic equations, solving quadratic systems, polynomial equations and inequalities and arithmetic and geometric sequences and series;
  4. gain experience with calculus through the use of derivatives, tangent lines, and maximum-minimum quadratic functions;
  5. increase reasoning skills by solving application problems of quadratic relations and systems, exponential and logarithmic functions, sequences and series, maximum and minimum values, and to integrate the use of several of the abovementioned topics.

course prerequisites

MATU 0411 or permission of instructor

curriculum guidelines

Course Guidelines for previous years are viewable by selecting the version desired. If you took this course and do not see a listing for the starting semester/year of the course, consider the previous version as the applicable version.

course schedule and availability
course transferability

Below shows how this course and its credits transfer within the BC transfer system. 

A course is considered university-transferable (UT) if it transfers to at least one of the five research universities in British Columbia: University of British Columbia; University of British Columbia-Okanagan; Simon Fraser University; University of Victoria; and the University of Northern British Columbia.

For more information on transfer visit the BC Transfer Guide and BCCAT websites.


If your course prerequisites indicate that you need an assessment, please see our Assessment page for more information.