Math 0110: Intermediate Algebra
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.
Section 1.2 Algebraic expressions and Sets of Numbers
- 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
- 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
- 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
- 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
- Write algebraic expressions that can be simplified.
- Apply the steps for problems solving.
Section 2.3 Formulas and Problem Solving
- Solve a formula for a specified variable.
- Use formulas to solve problems.
Section 2.4 Linear Inequalities and Problem Solving
- 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
- 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
- Solve absolute value equations.
Section 2.7 Absolute Value Inequalities
- Solve absolute value inequalities of the form |x|<a.
- Solve absolute value inequalities of the form |x|>a.
Section 3.1 Graphing Equations
- 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
- Define relation, domain, and range.
- Identify functions.
- Use the vertical line test for functions.
- Use function notation.
Section 3.3 Graphing Linear Functions
- Graph linear functions.
- Graph linear functions by using intercepts.
- Graph vertical and horizontal lines.
Section 3.4 The Slope of a Line
- 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
- 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
- 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
- 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
- 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
- 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
- Identify term, constant, polynomial, monomial, binomial, trinomial, and the degree of a term and of a polynomial.
- Define polynomial functions.
- Review combining like terms.
- Add polynomials.
- Subtract polynomials.
- Recognize the graph of a polynomial function from the degree of the polynomial.
Section 5.4 Multiplying Polynomials
- 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
- Identify the GCF.
- Factor out the GCF of a polynomial’s terms.
- Factor polynomials by grouping.
Section 5.6 Factoring Trinomials
- Factor trinomials of the form .
- Factor trinomials of the form .
- Factor by substitution.
Section 5.7 Factoring by Special Products
- 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
- 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
- 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
- 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
- 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
- Solve equations containing rational expressions.