Course

# Algebra & Trigonometry

Faculty
Science & Technology
Department
Mathematics
Course Code
MATH 1105
Credits
3.00
Semester Length
15 weeks
Max Class Size
35
Method(s) Of Instruction
Lecture
Typically Offered
Fall
Summer
Winter

## Overview

Course Description
This course covers the essentials of functions (linear, quadratic, polynomial, logarithmic, exponential, and trigonometric), graphing, solving equations and inequalities, systems of equations, and sequences and series. It is designed to meet the needs of students who plan to go on to take Precalculus (MATH 1110), Calculus for the Social Sciences (MATH 1125) or Introduction to Statistics (MATH 1160), or who require a grade 12-level math course to transfer to technical or vocational programmes.
Course Content
1. Review of Equations and Inequalities
2. Functions
4. Polynomial Functions
5. Exponential and Logarithmic Functions
6. Trigonometric Functions
7. Systems of Equations
8. Sequences and Series
Learning Activities

Lecture

Means of Assessment

Evaluation will be carried out in accordance with the Douglas College 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:

 Quizzes 0 - 40% Term tests 20 - 70% Assignments 0 - 15% Attendance 0 - 5% Class Participation 0 - 5% Final examination 30 - 40%

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

Learning Outcomes

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

• solve word problems involving linear and quadratic equations (applications will include: geometry problems, work problems, motion problems, mixture problems)
• graph relations and functions on the Cartesian coordinate system (including linear, quadratic, polynomial,reciprocal, logarithmic, exponential, trigonometric, absolute value, radical and piecewise functions)
• define a function
• determine domains and ranges of functions and represent them using interval notation
• use the vertical line test to determine whether a relation is a function
• classify functions as periodic, one-to-one, piecewise, or continuous
• identify maxima, minima, and intervals of increase/decrease from the graph of a function
• apply transformations (translations, dilations and reflections) to functions
• find a formula for the inverse of a function and graph the inverse function
• evaluate composite functions
• use linear functions that model real-life situations to solve problems
• find the vertex of a parabola by completing the square
• use quadratic functions that model real-life situations to solve problems including optimization problems
• solve quadratic inequalities both analytically and graphically, and express the solutions in interval notation
• graph polynomial functions
• apply the Remainder Theorem and Factor Theorem when dividing polynomials
• divide polynomials using long division and synthetic division
• solve factorable polynomial equations
• graph exponential and logarithmic functions with any base and be able to identify axis-intercepts, asymptotes, domain and range
• exploit the inverse relationship between exponential and logarithmic functions to solve problems
• convert between logarithmic and exponential forms
• evaluate simple logarithms without using a calculator
• change logarithms from one base to another
• use the properties of logarithms to simplify expressions
• solve logarithmic and exponential equations with any base
• define sine, cosine, tangent, secant, cosecant and cotangent in terms of: right triangles, points-in-the-plane and unit circles
• use a calculator to find the trigonometric values for any acute angle, and given the function value for an acute angle, find the angle
• solve right triangles, and word problems involving right triangles, using trigonometry
• convert from degree measure to radian measure and vice versa
• identify special angles on a unit circle
• use reciprocal and Pythagorean identities to simplify trigonometric expressions
• solve simple trigonometric equations giving only the acute angle solution
• graph the sine and cosine functions
• from the graph of a trigonometric function determine the period, amplitude, domain, range and phase shift
• solve systems of equations in two variables using substitution or elimination methods
• solve systems of equations in three variables using the substitution method
• distinguish between sequences and series (geometric and arithmetic)
• write formulas for arithmetic and geometric sequences both explicitly and recursively
• use formulas to find terms, and the positions of terms, in sequences or series; arithmetic or geometric means; sums of series
• use sigma notation to describe series
• evaluate series described in sigma notation
Textbook Materials

Consult the Douglas College Bookstore for the latest required textbooks and materials. Example textbooks and materials may include:

Algebra and Trigonometry, Jay Abramson, OpenStax, current edition.

## Requisites

### Prerequisites

MATH 1101 or MATU 0411; or

Precalculus 11 with a C or better and a score of 20 of better on the Precalculus Placement Math Assessment; or Precalculus 12 with a C or better and a score of 17 or better on the Precalculus Placement Math Assessment; or Foundations of Math 11 with a C or better and a score of 20 or better on the Precalculus Placement Math Assessment; or Foundations of Math 12 with a C or better and a score of 17 or better on the Precalculus Placement Math Assessment. See the Douglas College website for information on eligibility to write the Precalculus Placement Math Assessment Test.

### Corequisites

No corequisite courses.

### Equivalencies

No equivalent courses.

## Course Guidelines

Course Guidelines for previous years are viewable by selecting the version desired. If you took this course and do not see a listing for the starting semester / year of the course, consider the previous version as the applicable version.

## Course Transfers

These are for current course guidelines only. For a full list of archived courses please see https://www.bctransferguide.ca

Institution Transfer Details for MATH 1105
Alexander College (ALEX) No credit
Camosun College (CAMO) CAMO MATH 107 (3)
Capilano University (CAPU) CAPU MATH 1XX (3)
Columbia College (COLU) COLU MATH 100 (3)
Coquitlam College (COQU) COQU MATH 120 (3)
Kwantlen Polytechnic University (KPU) KPU MATH 1102 (3)
Kwantlen Polytechnic University (KPU) DOUG MATH 1105 (3) & DOUG MATH 1110 (3) = KPU MATH 1112 (3)
Langara College (LANG) LANG MATH 1152 (3)
Simon Fraser University (SFU) No credit
Thompson Rivers University (TRU) TRU MATH 1XXX (3)
Thompson Rivers University (TRU) TRU MATH 1XXX (3)
Trinity Western University (TWU) TWU MATH 1XX (3)
University of British Columbia - Okanagan (UBCO) No credit
University of British Columbia - Vancouver (UBCV) No credit
University of Northern BC (UNBC) UNBC MATH 115 (3)
University of the Fraser Valley (UFV) UFV MATH 110 (3)
University of Victoria (UVIC) UVIC MATH 120 (1.5)
Vancouver Island University (VIU) VIU MATH 151 (3)

## Course Offerings

### Summer 2024

CRN
Days
Dates
Start Date
End Date
Instructor
Status
CRN
22297
Wed Fri
Start Date
-
End Date
Start Date
End Date
Instructor Last Name
TBA
Instructor First Name
(Faculty)
Course Status
Open
Section Notes

Open lab as per posted schedule. The tentative schedule is available at https://www.douglascollege.ca/programs-courses/explore-programs-courses…

Max
Enrolled
Remaining
Waitlist
Max Seats Count
35
Actual Seats Count
32
3
Actual Wait Count
0
Days
Building
Room
Time
Wed Fri
Building
New Westminster - South Bldg.
Room
S1814
Start Time
8:30
-
End Time
10:20