MTH149 - Foundations of Mathematics

Semester | |

School | |

Last revision date | 2018-01-29 19:43:18.575 |

Last review date | 2018-01-29 19:43:18.577 |

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Subject Title
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Foundations of Mathematics

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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.

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Credit Status
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Credit

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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.

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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.

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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 http://library.senecacollege.ca for further information regarding cheating and plagiarism policies and procedures.

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Discrimination/Harassment
**

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 student.conduct@senecacollege.ca.

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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.

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Prerequisite(s)
**

Grade 12C Math or Equivalent

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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

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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.

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Prescribed Texts
**

__In-class:__

MyMathLab with e-Text

ISBN 9780321199911

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

__Online:__

MyMathLab with e-Text

ISBN 9780321199911

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Reference Material
**

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Required Supplies
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None

**
Promotion 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) |

OR | |

EXC | Excellent |

SAT | Satisfactory |

UNSAT | Unsatisfactory |

For further information, see a copy of the Academic Policy, available online (http://www.senecacollege.ca/academic-policy) or at Seneca's Registrar's Offices.

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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% |