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MATH 050 - Provincial Algebra and Trigonometry
Course Details

Course Code:

MATH 050

Calendar Description:
In Provincial Level Mathematics, students study the following types of functions: polynomial, quadratic, logarithmic, exponential, exponential, and trigonometric. This course prepares the adult learners with the necessary skills and knowledge for entry into technical, vocational, and career programs that require Math 12 equivalency as a prerequisite and for future study in higher-level math course at College/University.

Date First Offered:
1998-09-01

Hours:
Total Hours: 120
Lecture Hours: 7.5

Total Weeks:
16

This course is offered online:
No

Pre-Requisites:
75% in Math 040 Advanced Algebraic mathematics, Math 11 or equivalent, or permission of the instructor

Non-Course Pre-Requisites:
None

Co-Requisites:
None

Rearticulation Submission:
No

Course Content:
Algebra Review
- subsets and properties of real numbers
- absolute value, orders of operations, properties of exponents
- addition, subtraction, multiplication, division and factor polynomials
- rational expressions, radical expressions
- imaginary, complex numbers
- linear, quadratic, radical, and reducible equations
- linear, combined, absolute value inequalities
- equations of variation and applied problems
- systems of linear equations in two and three variables

Functions and Graphs
- two points in a plane and midpoint of a segment
- distance and midpoint formulas
- graphs of common functions: linear, constant, quadratic, cubic, square root, absolute value, reciprocal
- vertical line test
- domain, range, intervals of increase, decrease, constant for graphs and graph functions
- real life applications formulas and functions
- symmetry of x- and y-axes, odd or even functions
- translation, reflection, stretching, and shrinking of graph transformation of functions
- sum, difference, product, and quotient of two functions
- two functions, f and g finding formulas for f(g(x)) and g(f(x)), domain of and composite function
- equation defining a relation and equation of the reverse relation
- graph of a relation and graph of the reverse
- horizontal line test to determine if function is one-to-one and therefore has a reverse
- formula for the reverse of a function
- f-1(f(x)) and f(f-1(x))for any number x in the domains of the functions when the reverse of a function is also a function

Polynomial and Rational Functions
- quadratic functions and analysis of function for vertex, line of symmetry, maximum/minimum values, intercepts
- applied problems involving maximum and minimum function values
- graphs of polynomial functions of higher degrees using the leading coefficient test
- real zeros between two real numbers of a function
- graphs of polynomial functions, including real zeros, y-intercept, relative maxima and minima, domain and range
- long division of polynomials
- synthetic division of a polynomial by x - r
- remainder and factor theorems of polynomials
- rational zeros for a polynomial function with integer coefficients
- polynomial functions, finding zeros, specified zeros
- polynomial and rational inequalities

Exponential and Logarithmic Functions
- exponential functions including functions with base e
- inverse relationship between exponential and logarithmic functions
- graphs of exponential and logarithmic functions
- conversions between exponential and logarithmic functions
- common and natural logarithms using calculator
- basic and inverse properties of logarithms
- product rule, quotient rule, and power rule for expansion and condensation of logarithmic expressions
- change of base property
- exponential and logarithmic equations
- real-life applications of exponential growth and decay

Trigonometric Functions
- angles in standard position, positive and negative angles, co-terminal and reference angles
- conversion between between degree and radian measures of angles
- arc length, radian measure of central angle, radius of a circle with formula s= r 0
- special angles on a unit circle
- trigonometric functions of an angle in standard position
- exact values of trigonometric functions of special acute angles
- graphing six trigonometric and their properties
- transformation of the sine and cosine functions- period, amplitude and phase shift
- reciprocal, quotient, and Pythagorean identities
- sum or difference formulas, and double angle formula
- inverse trigonometric function notation and use of calculator
- composite functions with inverse trigonometric functions
- trigonometric equations
- real-life problems and trigonometric functions
-Options - Law of Sines and Cosines and oblique triangles

Sequences and Series
- terms of sequences given the general term or nth term
- formula for the general or nth term given a sequence
- summation notation and series evaluation
- terms of a sequence defined by a recursive formula
- arithmetic and geometric sequences
- nth term formulas to find a specified term
- the sum of first n terms
- sum of an infinite geometric series
- sequences and series to solve real-life problems,

Optional Topics
- conic sections
- permutations and combinations
- binomial expansions
- probability
- calculus

Learning Outcomes:
Upon successful completion of this course, students will be able to:
Functions and Graphs
- find the distance between two points in the plane and the midpoint of a segment
- apply the distance and midpoint formula to solve problems
- recognize graphs of common functions: linear, constant, quadratic, cubic, square root, absolute value, reciprocal
- use the vertical line test to identify functions
- graph and analyze functions, identifying: domain, range, intervals on which the function is decreasing, increasing or constant
- write formulas or functions to model real-life applications
- determine graph or function symmetry with respect to the x-axis, y-axis, and origin
- identify even or odd functions and recognize their symmetry
- graph transformations, translations, reflections, stretchings, and shrinkings of functions
- graph functions defined piecewise
- find the sum of, difference, product, quotient of two functions and determine their domains
- find the composition of two functions f and g finding formulas for f(g(x)) and g(f(x))
- write an equation of the inverse relation given an equation defining the relation
- sketch a graph of its reverse given the graph of the relation or function
- use the horizontal line test to determine if a function is one-to-one and therefore has an inverse
- find a formula for the inverse of a function
- evaluate composite functions

Polynomial and Rational Functions
- graph and analyze quadratic functions identifying the vertex, line of symmetry, minimum/maximum values and intercepts.
- solve applied problems involving minimum and maximum function values
- determine the behaviour of graphs of polynomial functions of higher degree using the leading coefficient test
- determine whether a function has a real zero between two real numbers
- write and manipulate complex numbers
- divide polynomials using long and synthetic division
- demonstrate the use of remainder and factor theorems
- factor polynomial expressions and solve polynomial functions and find the zeros
- find a polynomial equation given its roots

Exponential and Logarithmic Functions
- understand the relationship between exponential and logarithmic functions
- recognize the inverse relationships
- graph and analyze exponential and logarithmic functions
- use the laws of exponents and the laws of logarithms to simplify expressions and solve equations
- use exponential and logarithmic equations to solve real-life applications including exponential growth and decay

Trigonometric Functions
- identify angles in standard position, positive and negative angles, co-terminal and reference angles
- identify special angles and use the unit circle and convert between radians and degrees
- determine the trig function values of an angle in standard position given a point on a terminal arm
- use trig identities and algebra to simply expressions and solve trig equations
- graph and analyze the sine, cosine, and tangent functions
-use a calculator to evaluate inverse trig relations
- use trig functions to model and solve real-life problems

Series and Sequences
- distinguish between and solve problems involving arithmetic and geometric sequences and series
- use the formulas to find terms, positions of terms, arithmetic and geometric means, differences or ratios, sums of series , and sums of series and sums of infinite series.
- use sequences and series to model and solve real-life problems

Knowledge:
Learners will acquire the knowledge, skills and strategies
required to analyze, manipulate, graph and interpret a
variety of mathematical functions

Grading System:
Letters

Passing Grade:
D

Grading Weight:
Final Exam: 30 %
Other: 70 %

Percentage of Individual Work:
100

Course Offered in Other Programs:
No

Supplies:
Please note that textbooks and resources may vary by campus and/or to meet the needs of individual learners. Please contact the instructor at campus of attendance for list of required books.

Text Books:
Required - Blitzer, R., 2007, Algebra and Trigonometry (Pearson, NJ). Chapters Covered: 1-5, 7, 8, 10, 11
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