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# Basic Algebra

Course Code: MATH 1101
Faculty: Science & Technology
Department: Mathematics
Credits: 3.0
Semester: 15 weeks
Learning Format: Lecture
Typically Offered: Fall, Summer, Winter
course overview

This is a one semester course for students who need to improve their knowledge of algebra. Topics covered include: functions and relations, domain and range; algebraic techniques, factoring, exponents and radicals, polynomial and rational expressions; solving and graphing equations and inequalities in one variable; solving and graphing systems of equations; quadratic equations; graphing lines and parabolas; mathematical modeling; basic geometric formulas.

### Course Content

1. Sets of numbers: integers, rationals, reals
2. Basic algebraic techniques - absolute values, exponents, factoring methods, rational expressions
3. Quadratic, polynomial, rational, and absolute value equations
4. Inequalities
5. Functions and relations; domains and ranges
6. Graphing of linear, quadratic, and absolute value functions
7. Mathematical modeling (story problems)
8. Basic geometric formulas
9. Systems of equations in 2- and 3-variables
10. Radicals, radical forms, and fractional exponents; radical equations

Lecture

### Means of Assessment

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 some of the following:

 Weekly quizzes 0-40% Term tests 20-70% Assignments 0-15% Attendance 0-5% Class participation 0-5% Final exam 30-40%

### Learning Outcomes

At the end of this course, the successful student will have reviewed and strengthened their algebraic skills and have a level of algebraic proficiency which will allow them to continue their mathematical studies to an in-depth study of functions and their associated graphs (specifically, precalculus courses).

At the end of this course, the successful student will be able to:

• distinguish between different sets of real numbers
• appropriately use the set operations of intersection and union and the conditions of  “and” and “or”
• apply the concept of a solution set using set builder and interval notations
• work with two-dimensional Cartesian co-ordinate system
• work with function notation
• determine if an equation in two variables represents a function or simply a relation
• determine the domain and range of a function
• correctly apply properties of commutativity, associativity, distribution, inequality, equality and absolute value, and use the laws of exponents in the course of simplifying expressions and solving inequalities and equations
• simplify linear, polynomial, absolute value, rational, and radical expressions
• inter-convert radical and fractional exponent expressions
• solve linear, quadratic, factorable polynomial, absolute value, rational, and radical equations, check solution(s) and express solution sets using a variety of notations
• solve linear and simple absolute value inequalities and express solutions sets using a variety of notations
• solve quadratic and quadratic form equations by factoring, completing the square or using the quadratic formula
• factor polynomials using grouping, common factors,  difference of squares, sum and difference of cubes
• add, subtract, multiply and divide polynomials, including synthetic division
• translate a problem given in English (story form) into an associated algebraic form, communicate clearly the relationship between the model and the original problem, articulate any restrictions on solutions, solve the algebraic problem and use the solution to answer the original question
• find volumes, areas and perimeters of selected geometric figures and employ the results in the context of story/applied problems
• use the Pythagorean theorem to solve story problems and to calculate distances
• find midpoints of line segments
• solve linear systems of equations (both two-by-two and three-by-three systems) algebraically and graphically
• graph linear equations in general, slope-intercept and slope-point forms, and find linear equations for given graphs
• identify parallel and perpendicular lines
• graph simple absolute value and radical functions
• graph quadratic functions (parabolas) by completing the square

Optional additional subjects, as time allows:

• basic concepts of conic sections: circles, parabolas, ellipses, and hyperbolas
• algebraic and graphical solutions of systems of inequalities in two dimensions
• elements of linear programming
• polynomial and rational function inequalities and their solutions
• supplementary topics in geometry

course prerequisites

BC Precalculus 11 with a C or better; or,

BC Precalculus 12 with a C or better; or,

MATU 0411 with a C- or better; or,

A score of 15 or higher on the Douglas College Precalculus Placement Test.

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.

assessments

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