Basic Algebra

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