Precalculus for Non-Science Students

Curriculum Guideline

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Course
MATH 1115
Discontinued
No
Course Code
MATH 1115
Descriptive
Precalculus for Non-Science Students
Department
Mathematics
Faculty
Science & Technology
Credits
3.00
Start Date
End Term
201330
PLAR
No
Semester Length
15 weeks
Max Class Size
35
Contact Hours
4 hours per week
Method(s) Of Instruction
Lecture
Learning Activities

Lecture

Course Description
This is a one semester course for those students who wish to prepare for MATH 1125, the calculus course for business and social sciences students. The course includes the study of linear, quadratic, inverse, exponential and logarithmic functions, sequences, elementary series and an introduction to probability. Applications are drawn from business and financial models.
Course Content
  1. Applications of linear and quadratic equations and inequalities
  2. Functions and function notation
  3. Quadratic functions
  4. Polynomial functions
  5. Translating and stretching graphs
  6. Rational functions
  7. Composite functions
  8. Inverse functions
  9. Exponential and logarithmic functions
  10. Systems of linear equations
  11. Binomial theorem
  12. Sequences, series and summation notation
  13. Arithmetic and geometric sequences
  14. Permutations and combinations
  15. Probability
  16. Mathematics of finance
Learning Outcomes

At the end of the course, the successful student should be able to:

  • solve word problems involving linear and quadratic equations and inequalities
  • solve systems of linear equations in two and three unknowns
  • translate applied problems into systems of equations and solve
  • determine whether or not a relation (given as a graph, equation, or set of ordered pairs,) is a function
  • find the domain and range of a given function
  • sketch the graphs of linear, quadratic, absolute value, greatest integer, radical, factored polynomial, rational, exponential and logarithmic functions
  • sketch the graphs of piecewise-defined functions
  • use translation and reflection techniques to sketch graphs
  • find the vertex of a parabola given the quadratic function
  • solve optimization problems involving quadratic functions
  • evaluate composite functions and determine the domain of a composite function
  • find the inverse of a given function and determine its domain and range
  • translate logarithmic statements into exponential form and vice versa
  • evaluate simple logarithms without using a calculator
  • use the properties of logarithms to rewrite logarithmic expressions
  • solve exponential and logarithmic equations involving any base
  • use the change of base formula to evaluate the logarithm of a number to any base using a calculator
  • apply logarithms and exponentials to solving problems (e.g. growth, decay, and compound interest)
  • use the binomial theorem to expand binomials
  • find any term in a sequence given a formula for the nth term
  • find the general expression for the nth term given a sequence
  • find the sums of sequences using sigma notation and appropriate formulas
  • find the sum of a geometric series (where possible)
  • determine the sample space for a given experiment
  • represent a sample space with a Venn diagram or tree diagram where appropriate
  • distinguish between permutations and combinations and apply the appropriate formulas in order to count the number of outcomes
  • determine the probability of a particular outcome
  • determine conditional probabilities
  • determine binomial probabilities
  • solve problems related to the mathematics of finance, specifically: compound interest, present value, increasing and decreasing annuities and amortization.

 

Also, if time permits:

  • apply the factor theorem, remainder theorem and rational root tests to find roots of polynomials
  • convert from degree measure to radian measure and vice versa
  • determine the six trigonometric ratios for a given acute angle of a right angle triangle
  • state the trigonometric ratios for 30o, 45o and 60o  and use them to solve problems
  • use a calculator to find the trigonometric function values for any acute angle, and given the function value for an acute angle, find the angle
  • given the function value for an acute angle, find the function values for its complement
  • given a function value for an acute angle, find the other five function values
  • solve simple trigonometric equations given only the acute angle solution
  • solve word problems involving right triangles
Means of Assessment

Evaluation will be carried out in accordance with Douglas College policy. The instructor will present a written course outline with specific evaluation criteria at the beginning of the semester. Evaluation will be based on some of the following:

  1. Weekly tests
  2. Mid-term tests
  3. Assignments
  4. Attendance
  5. Participation
  6. Final Examination
 0–40%
20–70%
0–15%
0–5%
0–5%
0–40%

Note: All sections of a course with a common final examination will have the same weight given to that examination.

 

Textbook Materials

Gustafson, R. David and Frisk, Peter D., College Algebra, 6th Edition, Brooks/Cole Publishing Company, 1998.

 

Prerequisites

MATH 1101 or equivalent

Which Prerequisite

MATH 1125 and MATH 1160