MTH149 - Foundations of Mathematics

Outline info
Last revision date 2018-04-10 15:33:05.431
Last review date 2018-04-10 15:33:17.977

Subject Title
Foundations of Mathematics

Subject Description
This course provides a review of fundamental math concepts. These essential math skills are required for success in college programs requiring a solid foundation in mathematics. It is designed to meet the needs of individuals that have completed Grade 12 math but need a quick review in preparation for college level or skills training programs. Successful completion of the course is generally accepted as equivalent to a Grade 12 standing in mathematics. It does not, however, qualify the student for an Ontario Grade 12 math credit.

Credit Status

Learning Outcomes
Upon successful completion of this subject the student will be able to:

1. Demonstrate an understanding of basic mathematical principles.

2. Perform operations involving fractions, decimals, ratios, and percentages.

3. Solve, factor, and graph algebraic equations, quadratic equations, and inequalities.

4. Apply principles of geometry involving points, lines, angles, plane figures, and solid figures.

5. Evaluate basic trigonometric functions and apply the Laws of Sine and Cosine.

6. Understand the concepts of exponential and logarithmic functions.

7. Solve word problems in each of these mathematical topics.

Essential Employability Skills
Respond to written, spoken, or visual messages in a manner that ensures effective communication.

Execute mathematical operations accurately.

Apply a systematic approach to solve problems.

Use a variety of thinking skills to anticipate and solve problems.

Locate, select, organize, and document information using appropriate technology and information systems.

Show respect for diverse opinions, values, belief systems, and contributions of others.

Interact with others in groups or teams in ways that contribute to effective working relationships and the achievement of goals.

Manage the use of time and other resources to complete projects.

Take responsibility for one's own actions, decisions, and consequences.

Cheating and Plagiarism
Each student should be aware of the College's policy regarding Cheating and Plagiarism. Seneca's Academic Policy will be strictly enforced.

To support academic honesty at Seneca College, all work submitted by students may be reviewed for authenticity and originality, utilizing software tools and third party services. Please visit the Academic Honesty site on for further information regarding cheating and plagiarism policies and procedures.

All students and employees have the right to study and work in an environment that is free from discrimination and/or harassment. Language or activities that defeat this objective violate the College Policy on Discrimination/Harassment and shall not be tolerated. Information and assistance are available from the Student Conduct Office at

Accommodation for Students with Disabilities
The College will provide reasonable accommodation to students with disabilities in order to promote academic success. If you require accommodation, contact the Counselling and Disabilities Services Office at ext. 22900 to initiate the process for documenting, assessing and implementing your individual accommodation needs.

Grade 12C Math or Equivalent

Topic Outline
    1.  Introduction to Numbers

    Rounding, Order of Operations, Least Common Muliples
    Real Numbers: Addition, Subtraction, Multiplication and Division

     2.  Fractions

    Fraction Notation and Simplifying
    Converting between fraction and mixed numerals
    Addition, Subtraction, Multiplication and Division

     3.  Decimal Numbers

    Decimal Notation and Rounding
    Converting between fraction and mixed numerals
    Addition, Subtraction, Multiplication and Division

     4.  Ratio and Proportion
     5.  Percentages 

    Converting between Percentages and Decimals or Fractions
    Applications: Percent of Increase or Decrease, Sales Tax, Commission, Discount, Simple Interest and Compound Interest.

     6.  The Metric System and Other Systems of Measurement

    American and Metric Linear Measures, Capacity and Mass
    Conversions within American or Metric System, between American and Metric System
    Time and Temperature

     7.  Algebra and Formulae

    Simplifying Expressions, Order of Operations
    Solving Equations, Evaluating and Solving Formulas
    Exponents and Scientific Notation

     8.  Geometry

    Segments, Rays, Lines, Angles and Polygons
    Perimeter and Area: Rectangles, Squares, Parallelograms, Triangles, Trapezoids and Circles
    Volume and Surface Area: Rectangular Solids, Cube, Cylinders, Spheres and Cones
    Relationships between Angle Measures: Complementary and Supplementary Angles, Congruent Segments and Angles, Vertical Angles, Transversals and Angles
    Congruent and Similar Triangles, Properties of Parallelograms

     9. Linear Equations and Graphing

     Graphing Linear Equations using Tables, Intercepts, Slopes and y-intercept
    Finding Equations of Lines and Applications: Slope and y-intercept, Slope and a point, Two points, Parallel or Perpendicular Lines and a point.
    Solving Systems of Equations in Two Variables by Graphing, Substitution and Elimination

    10.  Sets and Inequalities

    Intersections and Unions
    Solving and Graphing Inequalities
    Absolute-value Equations and Inequalities

    11.  Polynomials: Operations and Factoring

    Polynomials: Addition, Subtraction, Multiplication and Division
    Factoring: Grouping, Trinomials, Trinomial Squares, Differences of Squares, Sums or Differences of Cubes
    Solving Quadratic Equations by Factoring

    12.  Rational Expressions and Equations

    Rational Expressions: Simplifying, Addition, Subtraction, Multiplication, and Division
    Simplifying Complex Rational Expressions
    Solving Rational Equations

    13.  Quadratic Equations and Graphing

    Quadratic Equations, Solving by Principle of Square Roots, Completing the Square and Quadratic Formula; Graphing

    14.  Trigonometry

    Right-angled Triangle and Pythagorean Theorem
    Trigonometric Ratios; Sine, Cosine, Tangent, Cosecant, Secant, Cotangent
    Applicatoins of Right Triangles: Angle of Elevation, Angle of Depression and Concept of Bearing
    Converting between Degree and Radian Measure
    Graphs of Sine, Cosine and Tangent Functions
    Applications: Laws of Sines and Cosines

    15.  Radical Expressions, Functions, Exponential and Logarithmic Functions

    Simplifying Radical Expressions   
    Functions: Definition, Domain, Range, Graphs, Vertical-line Test, Inverse and Composite Functions
    Solving Exponential and Logarithmic Equations

Mode of Instruction
There are two modes of delivery for this course:

1. In-class: Students attend classes on campus each week. All instruction is delivered in a face to face environment.

2. Online: All class work is completed in a fully online environment. Students do not attend any classes on campus; however, the final exam must be written in-person at the Test Centre.

* Students interested in pursuing online courses must have strong time management skills and regular access to a home or office computer with an Internet connection and web access.

Teaching and Learning Methods:
To ensure that students are engaged as much as possible in the learning process, instructors can use such teaching methods as class and small group discussions, essays and research, individual and group presentations, readings, lectures, workshops, in-class exercises, and/or web-based instruction. The mode of delivery will dictate the most appropriate teaching methods available to an instructor.

Prescribed Texts
MyMathLab with e-Text
ISBN 9780321199911

Your instructor will give additional references for e-books from Seneca Library.

MyMathLab with e-Text
ISBN 9780321199911 

Reference Material

Required Supplies

Promotion Policy

Grading Policy
A+ 90%  to  100%
A 80%  to  89%
B+ 75%  to  79%
B 70%  to  74%
C+ 65%  to  69%
C 60%  to  64%
D+ 55%  to  59%
D 50%  to  54%
F 0%    to  49% (Not a Pass)
EXC Excellent
SAT Satisfactory
UNSAT Unsatisfactory

For further information, see a copy of the Academic Policy, available online ( or at Seneca's Registrar's Offices.

Modes of Evaluation
The term work for In-Class sections will constitute 65% of the final grade. The term work for Online sections will constitute 65% of the final grade. In all cases, the instructor’s class schedule will indicate the nature of the weekly activities as well as the assignments, their due dates, and their value. All assignments must be correctly documented and follow the criteria established by the instructor, unless otherwise notified.

All term work assignments must be completed prior to the time of the final exam or last class.  Students must contact faculty in advance of the assignment due date to discuss the possibility of an extension.  Late assignments may be subject to the awarding of a penalty resulting in a lower grade assigned. 

Make-up opportunities for assignments must also be made in advance of the scheduled due date.  If an assignment is missed due to class absence, official documentation must be submitted to the faculty member on or before the next scheduled class. Make-up opportunities may not apply to all graded assignments.

Final Examination:
The final examination for In-Class sections will constitute 35% of the final grade. The final examination for Online sections will constitute 35% of the final grade.
The final exam for Online sections must be written, in-person, at the Test Centre.

In class Section  Online Section
Tests (3) 55% Test 1 (Online) 15%
Assignments (2) 10% Test 2 (Online) 25%
    Project 15%
    Group Discussions 10%
Exam 35% Exam (In person) 35%

Approved by: Fiona Bain-greenwood