MATH 050 - Provincial Algebra and Trigonometry

**Course Details**

Course Code:

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