Mathematics III

Curriculum Guideline

Effective Date:
Course
Discontinued
No
Course Code
MATU 0411
Descriptive
Mathematics III
Department
Mathematics Upgrading
Faculty
Science & Technology
Credits
4.50
Start Date
End Term
Not Specified
PLAR
No
Semester Length
15 weeks
Max Class Size
20
Course Designation
None
Industry Designation
None
Contact Hours

Lecture: 6 hours/week

Method(s) Of Instruction
Lecture
Learning Activities

Classroom time will be used for lectures, demonstrations, discussions, problem solving practice, and/or individual or group in-class assignments. Work outside of class time may include individual or group assignments and online participation and/or quizzes. 

Course Description
This course covers topics in geometry, trigonometry, and algebra - including relations and functions - and meets the requirement for a B.C. Precalculus 11 equivalent. It is designed for students who plan to take further courses in mathematics for College/University credit.
Course Content
  • Basic Algebraic Skills
  • Solving Linear Equations and Inequalities
  • Graphing Relations and Functions
  • Systems of Linear Equations and Inequalities
  • Polynomial Expressions, Equations and Functions
  • Variation, Rational Expressions, and Equations
  • Radical Expressions and Equations
  • Quadratic Equations and Functions
  • Trigonometry
Learning Outcomes

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.

Means of Assessment

Assessment will be in accordance with the ÁñÁ«ÊÓƵ Evaluation 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:

Unit tests (minimum of two, each worth) 10-20%
Cumulative Midterm test 20-30%
Assignments 0-10%
Attendance 0-5%
Participation 0-5%
Quizzes 0-10%
Cumulative Final exam 20-30%
Total: 100%

Note: If indicated in an individual instructor’s course outline, students may be required to obtain a minimum grade of 30% on the both the midterm and final examination in order to receive a final grade of C- or higher in the course.

Textbook Materials

Consult the ÁñÁ«ÊÓƵ Bookstore for the latest required textbooks and materials. A course Pack may be required and purchased from the ÁñÁ«ÊÓƵ Bookstore. Students are required to supply a scientific calculator with direct algebraic logic (D.A.L. or S.-V.P.A.M.)

Example textbooks may include:

Marvin Bittinger. (11th Edition). Intermediate Algebra. Pearson.

 

 

Prerequisites

MATU 0410 or permission of instructor

Which Prerequisite

MATH 1105 and other ÁñÁ«ÊÓƵ courses that require BC Math 11.