MTH149 - Foundations of Mathematics

Outline info
Last revision date 2017-11-21 11:16:17.228
Last review date 2017-11-21 11:16:29.708

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
Your professor will use a variety of appropriate teaching modes and techniques, such as the following:  lecture, question and answer, tutorials, classroom discussion, group work, individual and/or
group presentation, computer-aided instruction, consultation, etc.

Prescribed Texts
Developmental Math ALC with Custom Math & Trigonometry Supp RVP
Publisher: Pearson Education Canada.  Authors: Marvin L. Bittinger & Judith A. Beecher.
ISBN-10: 132303580X

In Class:
Developmental Math ALC
Publisher: Pearson Education Canada. Authors: Marvin L. Bittinger & Judith A. Beecher.
ISBN-13: 9780133919981

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
To be successful in this course, you must complete all course work as specified and achieve an overall grade of 50% or higher. For further information on evaluation and academic standing, see a copy of the Academic Policy available at Seneca registration offices.

Term Work:  All term work assignments must be completed prior to the time of the examination. Unless students have been granted an extension in advance, late take-home assignments will be
penalized one letter grade per day and will not be graded after one week (there is no provision for rewriting late assignments, regardless of the grade).  Students must contact faculty in advance of
due date to discuss extensions.

If a student has to miss any in-class quiz/test, he/she must notify the faculty via email or phone messages prior to start time of the quiz/test date.  Valid documentation
(such as original stamped doctor's note) must be submitted to the faculty on or before the next scheduled class.  Make-up opportunities may be arranged at the Test Centre.

Grading Scheme:  
Tests (3x) 55%
Assignments 10%

Modes of Evaluation
For further information on evaluation and academic standing, see a copy of the Academic Policy available at:

Grading is based on the following marking scheme:

Test 1 15%
Test 2 25%
Project 15%
Group Discussion 10%

Approved by: Fiona Bain-greenwood