Course Overview
The course builds on high school mathematics material so that students are able to relate basic algebra, trigonometry, geometry and vectors to their technical field. Through working examples students develop the ability, confidence and versatility to deal with physical situations involving mathematical solutions.
Prerequisite(s)
- No prerequisites are required for this course.
Credits
3.0
- Retired
- This course has been retired and is no longer offered. Find other Flexible Learning courses that may interest you.
Learning Outcomes
Upon successful completion, the student will be able to:
Chapter 1 - Arithmetic and Basic Concepts Review
- Demonstrate competency in basic mathematics.
Chapter 2 - Review of Algebra
- Algebraic Expressions
- To add, subtract, multiply and divide algebraic expressions.
- Simple Equations and Problems
- To solve first-degree equations.
- To express word problems as algebraic equations and to solve these equations.
- To solve literal equations for a specified variable.
- Relations and Functions
- To distinguish between functions and relations.
- To write functional relationships between variables.
- To evaluate functions.
- To graph functional relationships.
- To solve an equation by finding the zeros of the corresponding function.
- Factors and Factoring
- To review the following factoring techniques: common factors, difference of two squares, for trinomials, sum or difference of two cubes, and grouping.
- Fractions and Fractional Equations
- To review the addition, subtraction, multiplication and division of fractions.
- To review the manipulation of complex fractions.
- To solve fractional equations.
- To solve word problems that yield fractional equations.
- To review the concepts of ratio and proportion.
Chapter 3 - Review of Geometry
- Straight Lines and Angles
- To use the geometrical properties of a figure to determine the measure of certain angles of the figure.
- To use the geometrical properties of a figure to determine the lengths of certain line segments.
- Polygons
- To be aware of the relationship between the number of sides and the sum of the interior angles of a polygon.
- To distinguish between different types of triangles and to be aware of the various properties specific to each.
- To find the area of a triangle.
- To investigate the properties of similar triangles.
- To determine the special properties of the general right triangle, the 45° right triangle and the 30-60-90 right triangle.
- Quadrilaterals
- To identify the particular geometrical properties of various quadrilaterals.
- To compute the area of certain quadrilaterals.
- The Circle
- To calculate the circumference and area of circular parts.
- To review the more important geometrical properties of the circle.
- To solve problems requiring a knowledge of the geometrical properties of the circle.
- Volumes and Areas of Solids
- To identify the formulas for the volume and surface area of certain solid shapes.
- Similar Figures
- To identify the relationship between the areas of similar figures.
- To identify the relationship between the volumes of similar figures.
Chapter 4 - Systems of Linear Equations and Determinants
- Systems of Linear Equations
- To solve systems of two simultaneous linear equations graphically.
- To solve systems of two simultaneous equations algebraically.
- Systems of Fractional, Non-Linear and Literal Equations
- To solve systems of linear equations having fractional coefficients.
- To solve systems of equations where the variable appear as the denominators of fractions.
- To solve systems of literal equations.
- Determinants
- To evaluate a second order determinant.
- To use determinants to solve systems of two linear equations.
- Word Problems with Two Unknowns
- To solve problems by formulating two equations in two unknowns and solving these.
- Systems of Three or More Equations
- To solve systems of three or more equations using the addition-subtraction method.
- To solve systems of three or more equations using the substitution technique.
- To evaluate a third order determinant.
- To evaluate a determinant by the method of cofactors.
- To solve systems of three or more equations using determinants.
Chapter 5 - Radical Equations
- Simplification of Radicals
- To review the relationship between radicals and exponents.
- To review the rules of radicals.
- To simplify radicals.
- Operations with Radicals
- To review the techniques for adding and subtracting radicals.
- To review the techniques for multiplying expressions containing radicals.
- To review the techniques for dividing expressions containing radicals.
- Radical Equations
- To solve radical equations.
Chapter 6 - Quadratic Equations
- Terminology and Special Cases
- To write a quadratic equation in general form.
- To test whether a particular value of the variable is a root of the quadratic.
- To identify and solve pure and incomplete quadratics.
- To solve radical equations which yield a quadratic equation.
- Solving Equations
- To solve quadratic equations by factoring.
- Given the roots of a quadratic equation, to construct the equation.
- To solve quadratic equations by completion of the square.
- To develop the formula for solving quadratic equations.
- To solve quadratic equations using the formula.
- To predict the nature of the roots of a quadratic equation without having to solve the equation.
- Applications of Quadratic Equations
- To analyze and solve problems that lead to quadratic equations.
- Graphing the Quadratic Function
- To graph the quadratic function.
- To determine the axis of symmetry and vertex of a quadratic function by completion of the square.
- To solve a quadratic equation graphically.
- Equations of Quadratic Type
- To identify and solve equations of quadratic type.
- Systems of Two Equations Where at Least One Equation is Non-Linear
- To solve systems of two equations where one equation is linear and the other quadratic.
Chapter 7 - Trigonometry
- Trigonometric Functions of Any Angle
- To define standard position for an angle.
- To define the trigonometric functions of an angle in standard position.
- To establish the signs of the trigonometric functions in the four quadrants.
- To determine the trigonometric functions of any angle.
- To solve simple trigonometric equations.
- Right Triangle Trigonometry
- To particularize the definitions of the trigonometric functions of any angle to the right triangle.
- To solve the right triangle given two pieces of information about it.
- To solve problems using right triangle trigonometry.
- Oblique Triangles
- To establish the Sine Rule for a triangle.
- To identify circumstances where the Sine Rule can be applied to solve a triangle.
- To establish the Cosine Rule for a triangle.
- To identify circumstances where the Cosine Rule can be applied to solve a triangle.
- To solve problems using the Sine Rule and/or the Cosine Rule.
- Vectors
- To distinguish between a vector and a scalar.
- To resolve a vector into components.
- To determine the resultant of a system of vectors.
Effective as of Fall 2003
Programs and courses are subject to change without notice. Find out more about BCIT course cancellations.