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# MAT 102 - Intermediate Algebra

Course Department: Mathematics
Last Date of Approval: Spring 2023

4 Credits
Total Lecture Hours: 60
Total Lab Hours: 0
Total Clinical Hours: 0
Total Work-Based Experience Hours: 0

Course Description:
This course covers the following concepts in algebra: polynomial operations, quadratics, rational expressions and equations, radicals and rational exponents, logarithms and exponential equations, and the general study of functions. This course will also help students gain mathematical literacy which will be of vital significance when making important life decisions. In addition, this course will help with any career that involves mathematics, decision making, or problem-solving.

Prerequisites: Proctored ALEKS score of 30+.
Mode(s) of Instruction: traditional/face-to-face

Credit for Prior Learning: There are no Credit for Prior Learning opportunities for this course.

Course Fees: ebook/Access Code: \$90.00

Common Course Assessment(s): None

Student Learning Outcomes and Objectives:
Student Learning Outcomes:

Outcome 1: Apply basic arithmetic operations on polynomials, including factoring.

Outcome 2: Create the graph of a parabola and solve quadratic equations using a variety of methods, including word problems.

Outcome 3: Simplify, perform operations, and solve equations involving rational expressions including word problems.

Outcome 4: Apply the properties of rational exponents as they relate to radicals, perform operations and solve equations involving radicals including word problems.

Outcome 5: Apply the properties of logarithms, perform operations and solve logarithmic and exponential equations, including word problems.

Outcome 6: State the basic nature of a function including domain, range, and how to find its value at a given point.

Unit Objectives:

Outcome 1: Apply basic arithmetic operations on polynomials, including factoring.

Task 1: Simplify polynomial expressions using polynomial addition and subtraction.

Task 2: Simplify polynomial expressions using polynomial multiplication.

Task 3: Perform polynomial division using long division and synthetic division.

Task 4: Be able to completely factor a univariate or multivariate polynomial by finding the greatest common factor.

Task 5: Be able to completely factor a univariate or multivariate polynomial by grouping.

Task 6: Be able to completely factor a quadratic with leading coefficients of 1.

Task 7: Be able to completely factor a quadratic with leading coefficient of greater than 1

Task 8: Be able to completely factor special quadratics.

Outcome 2: Create the graph of a parabola and solve quadratic equations using a variety of methods, including word problems.

Task 1: Solve a quadratic equation by factoring, including word problems.

Task 2: Create the graph of a parabola written in multiple forms.

Task 3: Solve a quadratic equation using square root method.

Task 4: Solve a quadratic equation using the quadratic formula.

Task 5: Solve a quadratic equation by completing the square.

Task 6: State the vertex, intercepts, and axis of symmetry of a graph of a parabola.

Task 7: Discuss the characteristics of a graph of a parabola, including domain and range, shape.

Task 8: Rewrite a quadratic function to vertex form.

Task 9: Find the max or min of a parabola, including in words problem involving minimum or maximum of a quadratic function.

Outcome 3: Simplify, perform operations, and solve equations involving rational expressions including word problems.

Task 1: State the restrictions on a variable in a rational expression.

Task 2: Simplify a ratio of polynomials in factored form.

Task 3: Simplify a ratio of polynomials that need to be factored first.

Task 4: Perform multiplication on rational expressions.

Task 5: Perform division on rational expressions.

Task 6: State the least common denominator of rational expressions.

Task 7: Perform addition and subtractions on rational expressions.

Task 8: Simplify complex fractions without variables.

Task 9: Simplify complex fractions with variables.

Task 10: Solve a proportion, and word problems involving proportions.

Task 11: Solve a rational equation that simplifies to linear.

Task 12: Solve a rational equation that simplifies to quadratic.

Task 13: Use methods of solving rational equations to answer application problems.

Outcome 4: Apply the properties of rational exponents as they relate to radicals, perform operations and solve equations involving radicals including word problems.

Task 1: Evaluate the square root and cube root of a number.

Task 2: Utilize the Pythagorean Theorem to solve problems, including real-world word problems.

Task 3: Evaluate the square root of a perfect square monomial.

Task 4: Find the n^th root of numbers and monomials.

Task 5: Convert an expression between radical and exponent form.

Task 6: Simplify expressions with rational exponents using exponent rules such as product rule, quotient rule, power rule, and negative exponents.

Task 7: Simplify square roots of whole numbers and monomials with variables.

Task 8: Simplify higher roots of whole numbers and monomials with variables.

Task 9: Find the sum or difference of radical expressions with one or more variables.

Task 10: Find the product of radical expressions with one or more variable.

Task 11: Find the quotient of radical expressions with one or more variable.

Task 12: Rationalize a denominator involving roots and higher radicals.

Take 13: Solve radical equations.

Task 14: Solve word problems involving radical equations.

Task 15: Solve an equation with roots other than 2 and other rational exponents.

Task 16: Use i to simplify expressions with square roots of negative numbers.

Task 17: Perform basic operations on complex numbers.

Outcome 5: Apply the properties of logarithms, perform operations and solve logarithmic and exponential equations, including word problems.

Task 1: Create the graph of an exponential function: f (x) = ax

Task 2: Solve word problems involving exponential functions.

Task 3: Convert between logarithmic expressions and exponential expressions.

Task 4: Apply basic properties of logarithms and use them to graph a logarithmic function.

Task 5: Expand and condense logarithmic expressions using properties of logs.

Task 6: Solve logarithmic and natural log equations.

Task 7: Solve exponential equations.

Task 8: Solve real world word problems involving logarithmic and natural log equations.

Outcome 6: State the basic nature of a function including domain, range, and how to find its value at a given point.

Task 1: Identify if a relation is a function.

Task 2: State the domain and range of a function.

Task 3: Write a function in function notation and identify inputs and outputs of the functions.

Task 4: Use function addition and subtraction to write a new function.

Task 5: Write the product or quotient of two functions.

Task 6: Use function composition to write a new function.

Task 7: Write an equation involving direct, inverse, and or combined variation.

Task 8: Solve variation word problems.

Task 9: State the domain of root functions.

Task 10: Evaluate values in a root function.

Task 11: Graph square and cube root functions.

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