COQUITLAM COLLEGE
COURSE NUMBER: MATHEMATICS 100-3
TITLE: Pre-Calculus
DESCRIPTION:
Emphasis will be placed upon relations, functions and transformations;
linear and quadratic functions and inequalities; exponential and logarithmic
functions; trigonometry; polynomials and rational functions; and conic
sections.
PRE-REQUISITE:
B.C. High School Mathematics 11 (or equivalent) with a grade of at least
C. B.C. High
School Mathematics 12 (or equivalent) is highly
recommended.
TEXT:
Precalculus, E.W. Swokowski, J.A. Cole, 11th Edition, Brooks /Cole
DURATION:
13 weeks, 4 hours/week.
TOPICS:
1.
Functions and Graphs
Real numbers, exponents, algebraic expressions, coordinate
geometry, graphs of functions, and operations on functions.
2.
Polynomials
Polynomial functions, graphs of polynomials, rational
functions, complex numbers and roots.
3.
Trigonometry
Trigonometric functions, applications, graphing,
trigonometric identities, equations.
4.
Exponentials and Logarithms
Exponential and logarithmic functions, natural and
common logarithms, equations and graphs, exponential growth and decay.
5.
Conic Sections
Circles, ellipses, hyperbola, parabola.
LEARNING OUTCOMES:
After successfully completing the course students will
be able to:
- Simplify and perform arithmetic
operations on rational algebraic expressions including those with radicals
and rational exponents.
- Simplify difference quotients
involving a variety of functions.
- Solve a variety of equations in
one variable including absolute value, radical, quadratic, polynomial,
rational, exponential and logarithmic equations.
- Solve a variety of inequalities in
one variable including absolute value, polynomial and rational
inequalities.
- Find the slope of a
line and find its equation using the point-slope formula or slope
intercept formula.
- Find
the center and radius of a circle by converting its equation to standard
form.
- Understand the basic concept of
functions and their graphs, and be fluent with function notation,
including the operations of sum, difference, product, quotient and
composition of functions.
- Graph the basic functions and
piecewise defined functions.
- Analyze the basic properties of
functions and their graphs, including domain, range, symmetry (even/odd),
one-to-oneness, intervals of increase and decrease, extreme values,
intercepts, end behavior and asymptotes.
- Understand how to use
transformations such as translation, reflection, stretching and shrinking
to obtain the graph of y=f(x) +a, y=f(x-a), y=af(x), y=f(ax), y=|f(x)| and
y=f(|x|) from the graph of y=f(x).
- Perform long division and
synthetic division on polynomials and apply root finding theorems and
tests in order to factor polynomials or solve polynomial equations.
- Graph linear, quadratic,
polynomial, rational, exponential, logarithmic, trigonometric and inverse
trigonometric functions.
- Use functions to model and solve
real-world problems.
- Find the inverse of a one-to-one
function and find its domain, range and graph.
- Perform calculations using
exponents and logarithms to any base, and convert between logarithms of
different bases
- Apply exponents and logarithms to
model and solve real-world problems involving compound interest and
uninhibited growth and decay.
- Use angles in both degree and
radian measure.
- Establish the values and
properties of the six trigonometric functions using right triangles and
the unit circle.
- Solve right and oblique triangles
for both special angles and non-special angles, and solve application
problems that involve triangles.
- Manipulate, derive and use
trigonometric identities.
- Solve trigonometric equations and
solve application problems that involve such equations.
- Identify and graph a conic section
(circle, ellipse, hyperbola and parabola) by converting its equation to
standard form.
EVALUATION:
Class
Participation 5%
Weekly
Quizzes 25%
Mid-term
Exam 30%
Final
Examination 40%
Revised Nov/09