Lecture
- Sets of numbers: integers, rationals, reals
- Basic algebraic techniques - absolute values, exponents, factoring methods, rational expressions
- Quadratic, polynomial, rational, and absolute value equations
- Inequalities
- Functions and relations; domains and ranges
- Graphing of linear, quadratic, and absolute value functions
- Mathematical modeling (story problems)
- Basic geometric formulas
- Systems of equations in 2- and 3-variables
- Radicals, radical forms, and fractional exponents; radical equations
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 should be able to:
- distinguish between different sets of real numbers
- read and use a variety of notations signifying sets / subsets of real numbers, including set builder, number line, inequality and interval notation
- appropriately use the set operations of intersection and union and the conditions of “and” and “or”
- understand the concept of a solution set
- work with two-dimensional Cartesian co-ordinate system
- work with function notation
- determine if an equation in two variables represents a function or 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
- interconvert 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 (deriving and) 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 solve the original problem
- 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, to calculate distances, and to find midpoints
- 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
- distinguish 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
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 tests | 0-40% |
| Mid-term tests | 20-70% |
| Assignments | 0-15% |
| Attendance | 0-5% |
| Class participation | 0-5% |
| Final exam | 30-40% |
Textbooks and Materials to be Purchased by Students:
Sullivan and Struve, Intermediate Algebra, Current Edition, Prentice Hall.
B.C. Principles of Math 11 with C or better; or
DVST 0411 with C- or better; or B.C. Applications of Math 12 with C or better and a score of 12 or better on the Douglas College Math Assessment Test (DCMAT); or Precalculus 11 with C or better; or
Precalculus 12 with a C or better; or Precalculus 12 with a C- and a score of 15 or better on the DCMAT; or Foundations of Math 11 with a C or better and a score of 15 or better on the DCMAT; or Foundations of Math 12 with a C or better and a score of 15 or better on the DCMAT.