# MTH 065 : Beginning Algebra II

## Transcript title

Beginning Algebra II

## Credits

4

## Grade mode

Standard letter grades

## Contact hours total

40

## Lecture hours

40

## Recommended preparation

MTH 060 or higher or minimum placement into MTH 065.

## Description

Continues development of manipulative algebra skills from MTH 060. Includes algebraic expressions and polynomials, factoring algebraic expressions, rational expressions, roots and radicals, and quadratic equations.

## Learning outcomes

1. Solve systems of two equations algebraically and graphically.

2. Convert between different polynomial forms using operations and factoring.

3. Simplify expressions containing exponents.

4. Simplify radical expressions and recognize equivalent forms.

5. Solve problems involving quadratic equations using a variety of methods including factoring, the quadratic formula, and graphing.

6. Make predictions and interpret the results for models using linear equations, quadratic equations, and systems of equations.

## Content outline

Algebraic Manipulation and Equivalence

• Students will solve systems of two equations algebraically and graphically

o Use substitution and elimination to solve systems of linear equations, with focus on identifying which strategy might be more efficient

o Solve systems for equations not initially presented in standard form or in terms of x or y

o Know the three types of linear systems of two equations and how these present when systems are solved algebraically

• Students will convert between different polynomial forms using operations and factoring

o Know the meaning of factor, term, monomial, binomial, trinomial, polynomial, degree, coefficient, like terms, polynomial function, quadratic function, parabola, and cubic function.

o Add, subtract, multiply and divide (by monomial and binomial) polynomials and simplify as appropriate

o Recognize the product of binomial conjugates as a special case of binomial multiplication and recognize the resulting product as a difference of squares

o Evaluate polynomial functions using function notation

o Factor polynomials

Factoring out a GCF and its opposite

Factor trinomials of the form

Factor trinomials of the form ( )

Factoring a difference of two squares

Factoring by grouping

Factoring polynomials that requires the use of two of more factoring patterns

o Know the meaning of a prime polynomial

o Know that a sum of squares does not factor, but that a difference of squares and the sum and difference of cubes does factor

o Given the factoring pattern templates, factor a sum or difference of cubes

• Students will simplify expressions containing exponents

o Use the rules and properties of exponents and simplify resulting expressions

Raising a Product to a Power

Quotient Property

Raising a Quotient to a Power

Raising a Power to a Power

Zero exponent (for non-zero x)

o Recognize squaring binomials as an special case of binomial multiplication

• Students will simplify radical expressions and recognize equivalent forms

o Know the meaning of square root and principal square root

o Approximate a principal square root

o Use the rules and properties of square roots to simplify radical expressions and solve quadratic equations

Product Property for Square Roots

Quotient Property for Square Roots

Square Root Property is equivalent to

o Rationalize denominators and recognize this as an equivalent fraction

o Write solutions to square roots of negative numbers using the imaginary unit i, and know the terms imaginary number and complex number

• Students will solve problems involving quadratic equations using a variety of methods including factoring, the quadratic formula, and graphing

o Know the zero factor property

o Use factoring to solve quadratic equations in one variable

o Use the square root property to solve quadratic equations in one variable

o Use completing the square to solve quadratic equations in one variable

o Use the quadratic formula to solve quadratic equations in one variable

o Understand that the quadratic formula can be generated from the completing the square method of solving a quadratic equation

o Evaluate quadratic equations to determine the which method may be most efficient for solving

Graphical Representations

• Students will solve systems of two equations algebraically and graphically

o Understand the relationship between a solution found graphically and that found algebraically

o Use graphs of systems to make predictions about situations that can be modeled by two linear equations

o Know the three types of linear systems of two equations and how these present when systems are solved graphically

Skills associated with learning outcome 6. Students will solve problems involving quadratic equations using a variety of methods including factoring, the quadratic formula, and graphing

o Find the x-intercept(s) of the graph of a polynomial function and recognize when x-intercepts do not exist

o Know the connection between the x-intercepts of the graph of a function and the solutions of a related equation in one variable

o Use graphing to solve a polynomial equation in one variable

o Recognize and graph a quadratic function in vertex form

o Graph a quadratic function given in standard form by using two symmetric points to find the vertex

or by using the vertex formula to find the vertex

Modeling, Applications and Functions

• Students will make predictions and interpret the results for models using linear equations, quadratic equations, and systems of equations

o Model projectile motion and the area of rectangular objects

o Find the domain and range of a quadratic function

o Find an equation of a quadratic model using vertex form

o Find the minimum value or maximum value of a quantity

o Recognize and differentiate between linear and quadratic patterns in ordered paired data, graphs, and equations

## Required materials

Students are required to have a license for web-based software which will include an e-text. Paper copy of the textbook is optional.

## Grading methods

At least three proctored, closed-book examinations (one of which is the comprehensive final) must be given; all exams will consist of primarily free response questions, although limited use of multiple choice, fill in the blank, or matching may be used as appropriate; assessment of written work will include evaluation of the students’ ability to arrive at correct conclusions using proper mathematical procedures and notation.