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Mathematics II

Course Code: MATU 0410
Faculty: Science & Technology
Department: Math Upgrading
Credits: 4.5
Semester: 15 weeks
Learning Format: Lecture, Lab, Tutorial
Typically Offered: Fall, Summer, Winter
course overview

The course deals with a variety of topics in algebra and analytic geometry including number and number operations, roots and powers; integer and rational exponents; monomial and polynomial operations, factoring ; operations with rational expressions; equation-solving and problems leading to linear, quadratic and rational equations; graphs of linear equations, systems of linear equations solved by substitution or elimination; the graphing and analysis of linear and quadratic equations, and trigonometry.

Course Content

1. Operations with Real Numbers
2. First Degree Equations and Inequalities
3. Polynomials
4. Rational Expressions
5. Linear Equations and Inequalities
6. Systems of Linear Equations
7. Radical Expressions
8. Trigonometry
9. Quadratic Equations

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

Attendance is a course requirement.  The final grade may be UN if more than 30% of classes are missed or if less than 70% of items for evaluation are undertaken.

Evaluation will be carried out in accordance with Douglas College policy.  The instructor will present a written course outline with specific evaluation criteria at the beginning of the semester.  Evaluation will be based on the following:

Tests                     0-60%

Mid-term tests        20-30%

Attendance             0-5%

Class participation   0-5%

Final examination    20-30%

Learning Outcomes

Upon completion of this course students will be able to:

1. Use, simplify, evaluate and perform operations with real numbers and expressions

1.1. write fractions as decimals and repeating decimals as fractions
1.2. add, subtract, multiply and divide rational numbers
1.3. evaluate powers with rational bases and integer exponents
1.4. demonstrate the order of operations with rational numbers
1.5. evaluate radicals with rational radicands and distinguish between exact answers and approximate answers
1.6. simplify, add, subtract, multiply and divide square roots

2. Solve first degree equations and inequalities

2.1. solve first degree equations, in one variable, including those involving parentheses
2.2. solve formulas for a given variable when other variables are known
2.3. solve formulas for a given variable
2.4. solve first degree inequalities in one variable
2.5. solve practical problems using a first degree equation

3. Classify, evaluate, factor and perform operations on polynomials and solve polynomial equations and applied problems

3.1. distinguish between monomials, binomials, trinomials and other polynomials (in one variable only)
3.2. apply the laws of exponents to variable expressions with integral exponents
3.3. evaluate polynomials by substitution
3.4. add, subtract, and multiply polynomials
3.5. factor polynomials by removing the largest common factor
3.6. factor binomials of the form a²x² – b²y²
3.7. factor trinomials of the form ax² + bx + c
3.8. fully factor polynomials using a combination of factoring techniques
3.9. solve quadratic equations using the law of zero products

4. Interpret, simplify and perform operations on rational expressions and solve rational equations

4.1. simplify, by factoring, rational expressions consisting of polynomial numerators and either monomial, binomial, or trinomial denominators
4.2. determine values for which a rational expression is undefined
4.3. multiply and divide rational expressions
4.4. add and subtract rational expressions consisting of monomial and/or binomial denominators
4.5. solve simple rational equations and check solutions
4.6. simplify expressions using exponent laws

5. Graph and solve linear equations and inequalities

5.1. graph a linear equation including the forms x = a and y = b
5.2. given a linear equation or its graph, determine its
   5.2.1. slope
   5.2.2. x- and y-intercepts
5.3. determine the equation of a line, y = mx + b, given
   5.3.1. its graph
   5.3.2. its slope and a point on the line
   5.3.3. two points on the line
5.4. graph a linear inequality

6. Solve systems of linear equations and applied problems

6.1. solve a system of first degree equations in two unknowns by graphing, substitution, and elimination methods
6.2. solve practical problems using a system of equations

7. Simplify and perform operations on radical expressions and solve radical equations

7.1. simplify square roots with variable radicands
7.2. add, subtract, multiply and divide square roots with variable radicands
7.3. solve equations with one square root containing a polynomial radicand and check for extraneous solutions

8. Solve right angle triangles

8.1. solve right triangles using one or more of
   8.1.1. the sine ratio
   8.1.2. the cosine ratio
   8.1.3. the tangent ratio
   8.1.4. the Pythagorean theorem
   8.1.5. the angle sum property of triangles

9. Solve and graph quadratic equations and applied problems

9.1. solve quadratic equations by factoring
9.2. solve equations of the form x² + bx + c = 0 by completing the square
9.3. solve quadratic equations by using the quadratic formula
9.4. graph y = ax² + bx + c and determine its
   9.4.1. x- and y-intercepts
   9.4.2. vertex
9.5. solve practical problems using a quadratic equation

course prerequisites

MATU 0310 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.