Mathematics III

Upon successful completion of this course, students will be able to:

Basic Algebraic Skills

• perform operations with real numbers including absolute value and exponential notation;
• simplify expressions using rules for order of operations including nested parentheses and properties of exponents;
• translate common language into algebraic expressions;
• evaluate algebraic expressions by substitution;

Solving Linear Equations and Inequalities

• solve first degree/linear equations in one variable;
• manipulate simple formulas to isolate a specified variable;
• solve and graph linear inequalities in one variable;
• write set-builder and/or interval notation for the solution set or graph of an inequality;
• use linear equations, formulas and linear inequalities to solve applied problems;
• find the union (disjunction) and intersection (conjunction) of sets;
• solve and graph compound inequalities;
• solve absolute value equations;

Graphing Relations and Functions

• write linear equations in slope-intercept form;
• graph linear equations using a table of values;
• graph linear equations using the y-intercept and slope and using x- and y-intercepts;
• graph horizontal and vertical lines;
• find the slope of a line given two points on the line;
• find the equation of a line given graphic data: the slope and y-intercept, the slope and one point, or two points on the line;
• determine whether a pair of lines is parallel, perpendicular, or neither;
• find the equation of a line parallel or perpendicular to a given line and through a given point;
• use the definition of function and the vertical line test to distinguish between functions and non-functions;
• use and interpret function notation to evaluate functions for given x-values and find x-values for given function values;
• determine the domain and range of a function;
• use a table of values to graph linear functions and non-linear functions such as quadratic, cubic, square root, reciprocal, and absolute value functions;

Systems of Linear Equations and Inequalities

• solve systems of linear equations in two variables by graphing, substitution, and elimination methods;
• determine if a system of equations will have one, infinite, or no solution(s);
• use systems of linear equations to solve applied problems;

Polynomial Expressions, Equations and Functions

• identify the degree, terms, and coefficients of a polynomial;
• distinguish between monomials, binomials, trinomials, and other polynomials;
• add, subtract, multiply polynomials;
• divide polynomials by monomials;
• factor polynomials using an appropriate strategy or a combination of techniques: common factors, difference of squares, difference and sum of cubes, perfect square trinomials, trial/error, or grouping;
• solve polynomial equations using the principle of zero products;
• solve applied problems using polynomial equations/ functions;

Variation, Rational Expressions, and Equations

• identify situations and find values for which a rational expression will be undefined;
• simplify rational expressions;
• add, subtract, multiply, and divide rational expressions;
• solve rational equations;
• manipulate formulas involving rational expressions to isolate a specified variable;
• solve applied problems that can be modeled with rational equations;
• simplify complex rational expressions;
• express variations in the form of equations (direct, inverse, joint, combined);
• solve problems involving direct, inverse, joint, and combined variation;

Radical Expressions and Equations

• identify situations and find values for which a radical expression will be undefined;
• write radicals as powers with rational exponents and vice versa;
• use rational exponents to simplify radical expressions;
• simplify, add, subtract, multiply, and divide radical expressions (numeric or algebraic);
• rationalize denominators containing radicals (including the use of conjugates);
• solve equations involving radical expressions or powers with rational exponents and check for extraneous roots;
• manipulate formulas involving powers and square roots to isolate a specified variable;
• solve applied problems which can be modeled by radical equations, and determine if solutions are reasonable given the context of the problem;

Quadratic Equations and Functions

• solve quadratic equations by factoring, principle of square roots, completing the square and the quadratic formula;
• use the discriminant to identify the number and type of solutions of a quadratic equation;
• write a quadratic equation given its solutions;
• solve rational and radical equations reducible to a quadratic pattern and check that answers are reasonable;
• solve selected polynomial equations that can be factored simplifying to linear and/or quadratic factors;
• graph quadratic functions of the form f(x) = a(x-h)² + k and demonstrate translations, reflections and stretching/shrinking resulting from changes in the function equation;
• find the vertex, line of symmetry, minimum or maximum values, x– and y-intercepts, domain and range, given the function f(x) = a(x-h)² + k;
• rewrite f(x) = ax² + bx + c as f(x) = a(x-h)² + k by completing the square;
• solve problems that can be modeled using quadratic equations such as maximum and minimum problems;

Trigonometry

• label the sides of a right triangle with respect to a given angle;
• determine sine, cosine, and tangent ratios of an angle in a right triangle using the side lengths;
• use a scientific calculator to find the trigonometric value for a given angle and to find an angle given its trigonometric value;
• solve right triangles and applied problems using the basic trigonometric ratios, the Pythagorean theorem, and sum of the angles (180°);
• use the Law of Sines and the Law of Cosines to solve non-right (oblique) triangles and applied problems.

MATU 0411 meets the required outcomes for ABE Mathematics: Advanced Level - Algebraic in the BC ABE Articulation Handbook 2023/2024 Edition.