### Math 0110: Intermediate Algebra

#### Course Description

Math 0110 is a preparatory course for college algebra that carries no credit towards any baccalaureate degree.  However, the grade received in Math 0110 does count towards a student’s overall GPA.  The course covers operations with real numbers, graphs of functions, domain and range of functions, linear equations and inequalities, quadratic equations; operations with polynomials, rational expressions, exponents and radicals; equations of lines.  Emphasis is also put on problem-solving.

#### Textbook and Course Materials:

• MML AUTO ACCESS  -  Required
• INTERMEDIATE ALGEBRA WORKBOOK – Custom Edition -  Required  – A manual containing an outline of class notes.
• TEXTBOOK – Recommended - Intermediate Algebra by Martin-Gay, 7th edition.

#### Sections Covered

Section 1.2  Algebraic expressions and Sets of Numbers

Learning objectives:

• Identify and evaluate algebraic expressions.
• Identify natural numbers, whole numbers, integers, and rational and irrational numbers.
• Find the absolute value of a number.
• Find the opposite of a number.
• Write phrases as algebraic expressions.

Section 1.3  Operations on Real Numbers and Order of Operations

Learning objectives:

• Add and subtract real numbers.
• Multiply and divide real numbers.
• Evaluate expressions containing exponents.
• Find roots of numbers.
• Use the order of operations.
• Evaluate algebraic expressions.

Section 1.4  Properties of Real Numbers and Algebraic Expressions

Learning objectives:

• Use operation and order symbols to write mathematical sentences.
• Identify identity numbers and inverses.
• Identify and use the commutative, associative, and distributive properties.
• Write algebraic expressions.
• Simplify algebraic expressions.

Section 2.1  Linear Equations in One Variable

Learning objectives:

• Solve linear equations using properties of equality.
• Solve linear equations that can be simplifies by combining like terms.
• Solve linear equations containing fractions or decimals.
• Recognize identities and equations with no solutions.

Section 2.2  An Introduction to Problem Solving

Learning objectives:

• Write algebraic expressions that can be simplified.
• Apply the steps for problems solving.

Section 2.3  Formulas and Problem Solving

Learning objectives:

• Solve a formula for a specified variable.
• Use formulas to solve problems.

Section 2.4  Linear Inequalities and Problem Solving

Learning objectives:

• Use interval notation.
• Solve linear inequalities using the addition property of inequality.
• Solve linear inequalities using the multiplication and the addition properties of inequality.
• Solve problems that can be modeled by linear inequalities.

Section 2.5  Compound Inequalities

Learning objectives:

• Find the intersections of two sets.
• Solve compound inequalities containing and.
• Find the union of two sets.
• Solve compound inequalities containing or.

Section 2.6 Compound Inequalities

Learning Objectives

• Solve absolute value equations.

Section 2.7 Absolute Value Inequalities

Learning objectives

• Solve absolute value inequalities of the form |x|<a.
• Solve absolute value inequalities of the form |x|>a.

Section 3.1  Graphing Equations

Learning objectives:

• Plot ordered pairs.
• Determine whether an ordered pair of numbers is a solution of an equation in two variables.
• Graph linear equations.
• Graph nonlinear equations.

Section 3.2  Introduction to Functions

Learning objectives:

• Define relation, domain, and range.
• Identify functions.
• Use the vertical line test for functions.
• Use function notation.

Section 3.3  Graphing Linear Functions

Learning objectives:

• Graph linear functions.
• Graph linear functions by using intercepts.
• Graph vertical and horizontal lines.

Section 3.4  The Slope of a Line

Learning objectives:

• Find the slope of a line given two points on the line.
• Find the slope of a line given the equation of the line.
• Interpret the slope-intercept form in an application.
• Find the slopes of horizontal and vertical lines.
• Compare the slopes of parallel and perpendicular lines.

Section 3.5  Equations of Lines

Learning objectives:

• Graph a line using its slope and  intercept.
• Use the slope-intercept form to write the equation of a line.
• Use the point-slope form to write the equations of a line.
• Write equations of vertical and horizontal lines.
• Find equations of parallel and perpendicular lines.

Section 4.1  Solving Systems of Linear Equations in Two Variables

Learning objectives:

• Determine whether an ordered pair is a solution of a system of two linear equations.
• Solve a system by graphing.
• Solve a system by substitution.
• Solve a system by elimination.

Section 4.3  Systems of Linear Equations and Problem Solving

Learning objectives:

• Solve problems that can be modeled by a system of two linear equations.
• Solve problems with cost and revenue functions.
• Solve problems that can be modeled by a system of three linear equations.

Section 5.1  Exponents

Learning objectives:

• Use the product rule for exponents.
• Evaluate expressions raised to the 0 power.
• Use the quotient rule for exponents.
• Evaluate expressions raised to the negative nth power.
• Convert between scientific notation and standard notation.

Section 5.2  More work with exponents

Learning objectives:

• Use the power rules for exponents.
• Use exponent rules and definitions to simplify exponential expressions.
• Compute using scientific notation.

Section 5.3  Polynomials and Polynomial Functions

Learning objectives:

• Identify term, constant, polynomial, monomial, binomial, trinomial, and the degree of a term and of a polynomial.
• Define polynomial functions.
• Review combining like terms.
• Subtract polynomials.
• Recognize the graph of a polynomial function from the degree of the polynomial.

Section 5.4  Multiplying Polynomials

Learning objectives:

• Multiply two polynomials.
• Multiply binomials.
• Square binomials.
• Multiply the sum and difference of two terms.
• Multiply three or more polynomials.
• Evaluate polynomial functions.

Section 5.5  The Greatest Common Factoring and Factoring by Grouping

Learning objectives:

• Identify the GCF.
• Factor out the GCF of a polynomial’s terms.
• Factor polynomials by grouping.

Section 5.6  Factoring Trinomials

Learning objectives:

• Factor trinomials of the form .
• Factor trinomials of the form .
• Factor by substitution.

Section 5.7  Factoring by Special Products

Learning objectives:

• Factor a perfect square trinomial.
• Factor the difference of two squares.
• Factor the sum or difference of two cubes.

Section 5.8  Solving Equations by Factoring

Learning objectives:

• Solve polynomial equations by factoring.
• Solve problems that can be modeled by polynomial equations.
• Find the x-intercept of a polynomial function.

Section 6.1  Rational Functions and Multiplying and Dividing Rational Expressions

Learning objectives:

• Find the domain of a rational expression.
• Simplify rational expressions.
• Multiply rational expressions.
• Divide rational expressions.
• Use rational functions in applications.

Section 6.2  Adding and subtracting Rational Expressions

Learning objectives:

• Add or subtract rational expressions with a common denominator.
• Identify the least common denominator (LCD) of two or more rational expressions.
• Add or subtract rational expressions with unlike denominators.

Section 6.3 Simplifying Complex Fractions

Learning objectives:

• Simplify complex fractions by simplifying the numerator and denominator and then dividing.
• Simplify complex fractions by multiplying by a common denominator.
• Simplify expressions with negative exponents.

Section 6.5  Solving Equations containing Rational Expressions

Learning objectives:

• Solve equations containing rational expressions.