## MATH 040 - Advanced Algebraic Mathematics

Learners extend their study of mathematical skills and concepts in basic arithmetic, geometry, trigonometry and algebra. The course includes algebra, factoring, rational functions, radicals, exponents, graphing, systems of linear equations, problem solving and trigonometry. The Math 040 course is recommended for students requiring Math 11 for further study.

**Hours:** 120 (Lecture: 7.5)

**Total Weeks:** 16

**Prerequisites:**

75% or B in Math 10 or Math 030 Intermediate Math, OR permission of instructor

**Non-Course Prerequisites:**

None

**Co-Requisites:**

None

**Course Content:**

Basic Algebraic Skills Review

- operations with real numbers including absolute value and exponential notation

- rules for order of operations and properties of exponents

- translation of common language into algebraic expressions

- algebraic expressions by substitution

- algebraic expressions with nested parentheses

Solving Linear Equations and Inequalities

- first degree/linear equations in one variable

- simple formulas for a given variable

- solving and graphing linear inequalities in one variable

- setting builder and or interval notation for the solution set or graph of an inequality

- linear equations, formulas and linear inequalities to solve applied problems

- union or intersection of two sets

- solving and graphing compound inequalities(conjunctions and disjunctions)

- absolute value equations

Graphing, Relations, and Functions

- linear equations in slope-intercept form

- linear and non-linear equations using table of values

- linear equations using the y-intercept and slope, and using x- and y-intercepts

- graph for horizontal and vertical lines

- slope of a line given two points on the line

- equation of a line, given graphic data: the slope and y-intercept, the slope and one point, or two points on the line

- pairs of lines parallel, perpendicular or neither

- equation of a line parallel or perpendicular to a given line and through a given point

- definition of a function and the vertical line test to distinguish between functions and non-functions

- function notation interpretation to evaluate functions for given x-values and find x-values for given function values

- determination of the domain and range of a function

- graphing of linear and non-linear functions such as quadratic, cubic, square root, reciprocal, and absolute value functions.

- graphing of linear inequalities in two variables

Optional - Use of the graphing calculator to demonstrate various transformations

Systems of Linear Equations and Inequalities

- systems of linear equations in two variables by graphing, substitution and elimination methods

- determination of systems of equations having one or more solutions

- systems of equations to solve applied problems

Optional - using the graphing calculator or other appropriate technology to solve systems of equations.

Polynomials and Polynomial Functions

- addition, subtraction, multiplication, and division polynomials

- monomials, binomials, trinomials and other polynomials

- factoring polynomials using an appropriate strategy or combination of techniques: common factors, difference of squares, difference and sum of cubes, perfect square trinomials, trial/error, or grouping

- polynomial equations using zero products

- applied problems using polynomial equations/functions

Optional - dividing polynomials and binomials using long division or synthetic division

Rational Expressions and Equations and Variation

- rational expressions using adding, subtracting, multiplying, or dividing

- rational expressions and solutions

- formulas involving rational expressions

- applied problems that can be modeled with rational equations

- complex fractions

- problems involving direct, inverse, joint and combined variation

Radical Expressions and Equations

- addition, subtraction, multiplication and division radical expressions (with or without variables)

- denominators in fractional expressions containing radicals ( including the use of conjugates)

- equations involving radical expressions or powers with rational exponents and extraneous roots

- formulas involving powers and square roots for a given variable

- applied problems which can be modeled by radical equations and reasonable solutions

- imaginary and complex numbers in standard form

- manipulation of complex numbers

Quadratic Equations and Functions

- factoring quadratic equations, principle of square roots, completion of the square and quadratic number

- numbers and types of solutions of quadratic equations

- quadratic equations from its solution

- reasonable reduction of rational and radical to a quadratic pattern

- translations, dilations and reflections of f(x)=a(x-h)2+k

- rational and radical equations reduced to quadratic form

- maximum and minimum problems

- function notation and vertical line test

- domain and range of a function

- non-linear functions such as cubic, square root , reciprocal and absolute value

Trigonometry

- Pythagorean theorem

- sine, cosine and tangent ratios

- scientific calculator use for trigonomicratios

- Law of Sines and Law of Cosines

Optional - quadrant for positive and negative angles, trigonometric definitions

Optional Topics

- Geometry- perpendicular bisector chords, inscribed angles, deductive reasoning

- Data Analysis - use of, misuse of, mean, median, mode, range, standard deviation, percentiles, quartiles, z-scores,

**Learning Outcomes:**

Upon successful completion of this course learners will be able to:

Basic Algebra

- perform operations with real numbers including absolute value and exponential notation

- simplify expressions using the rules of order of operations and properties of exponents

- translate common language into algebraic expressions

- evaluate algebraic expressions by substitution

- simplify algebraic expressions with nested parentheses

Linear Equations and Variation

- solve and use linear equations to solve word problems

- write set builder and interval notation for the solution set or graph of an inequality

-solve absolute value equations

-graph linear equations using tables, slope-intercept method, x and y intercepts

- determine an equation from a graph or a set of data

- find an equation of a line given: slope and one point, two points

Solving Linear Equations and Inequalities

- solve first degree /linear equations and simple formulas given one variable

- solve and graph linear inequalities in one variable

- write set-builder / interval notation for the solution set or graph of an inequality

- find the union or intersection of two sets

- solve and graph compound inequalities (conjunction and disjunctions)

- solve absolute value equations

Graphing, Relations and Functions

- write linear equations in slope -intercept form

- graph linear and non-linear equations using the table of values

- graph linear equations using the y-intercept and slope, and using x- and y-intercepts

- graph horizontal and vertical lines

- find the slope of a line given two points on the line

- find the equation of a line given; the slope and y-intercept, the slope and one point, or two points on the line

- determine whether a pair of lines are parallel, perpendicular or neither

- find the equation of a line parallel or perpendicular to a given line or through a given point

- use the definition of function and the vertical line test to distinguish between functions and non-functions

- use and interpret function notation to evaluate functions for given x-values and find x-values for given function values

- determine the domain and range of a function

- graph linear and non-linear functions such as quadratic, cubic, square root, reciprocal and absolute value functions

- graph linear inequalities in two variables

Systems of Linear Equations and Inequalities

- solve systems of linear equations in two variables by graphing, substitution, and elimination methods

- determine if a system of equations will have one, none or infinite number of solutions

- use systems of equations to solve applied problems

Optional - solve systems of equations in three variables

Optional - use the graphic calculator to solve systems of equations and inequalities

Polynomial and Polynomial Functions

- determine the degree of a polynomial

- distinguish between monomials, binomials, trinomials and other polynomials

- add, subtract, multiply polynomials, divide polynomials by monomials

- factor polynomials using: common factors, difference of squares, difference and sum of cubes, perfect square trinomials, trial/error or grouping

- solve polynomial equations using the principle of zero products

- solve applied problems using polynomial equation/functions

Rational Expressions and Equations and Variation

- simplify rational expressions

- identify situations and find values for which rational expression will be undefined

- add, subtract, multiply and divide rational expressions

- solve rational expressions

- solve formulas, involving rational expressions for a given variable

- solve applied problems with rational equations

- simplify complex fractions

- express variations in the form of equations (direct, inverse, joint, combined)

- solve problems involving the above variations

Radical Expressions and Equations

- write radicals as powers with rational exponents

- use rational exponents to simplify radical expressions

- simplify, add, subtract, multiply and divide radical expressions(numeric or algebraic)

- rationalize denominators in fractional expressions containing radicals

- solve equations involving radical expressions or powers with rational exponents

- solve formulas involving powers and square roots for a given variable

- solve applied problems and determine if solutions are reasonable

Quadratic Equations and Functions

- solve quadradic equations by factoring, principle of square roots, completing the square, and the quadradic formula

- use the discriminate to identify the number and type of solutions of a quadratic equation

- write a quadratic equation given its solutions

- solve rational and radical equations reducible to a quadratic equation

- solve selected polynomial equations that can be factored simplifying to linear and/or quadratic factors

- find the vertex, line of symmetry, minimum or maximum values, x- and y-intercepts domain and range given the function

f(x)= a(x-h)2 +k

- solve problems using quadratic equations

Trigonometry

- label the sides of a right triangle with respect to a given angle

- determine sine, cosine and tangent ratios of an angle in a right triangle

- use a scientific calculator to find the trigonometric for a given angle and the reverse

- solve right triangles and applied problems using the basic trigonometric ratios, Pythagorean theorem and the sum of the angles(180)

- use the Law of Sines and the Law of Cosines to solve non-right angled triangles and applied problems

Option Topics

Geometry - understand the properties of a circle

- demonstrate deductive reasoning in the solution of applied problems

Data Analysis - explain the uses and misuses of statistics

**Knowledge:**

Learners will acquire the mathematical knowledge skills and strategies required to develop meaningful solutions to complex multi-step problems

**Skills:**

**
**Learners will have the prerequisite skills to enter Provincial Mathematics, Vocational or Technical programs

**Grading System:** Letters

**Passing Grade:** D (50%)

**Percentage of Individual Work:** 100

**Textbooks:**Textbooks are subject to change. Please contact the bookstore at your local campus for current book lists.