Math 50 Modern College Arithmetic and Pre-Algebra
Math 50 Student Learning Outcomes
1. Demonstrate the ability to add, subtract, multiply, and divide whole numbers, integers, fractions,
mixed numbers, and decimals.
2. Solve Linear Equations by:
a) Using the Addition/Subtraction property of equality,
b) Using the Multiplication/Division property of equality.
c) Using both the above properties together.
3. Translate English sentences to algebraic equations.
4. Simplify mathematical statements using the correct order of operations.
5. Calculate the perimeter and area of rectangles and triangles. Calculate the area and
circumference of a circle.
6. Find equivalent forms of number (i.e. change fractions to decimals, change percents to fractions,
change fractions to percents, change decimals to fractions, change decimals to percents, change
percents to decimals, change mixed numbers to improper fractions, change improper fractions to
mixed numbers).
7. Round whole numbers and decimals appropriately as directed.
8. Apply the concept of percent to real-world application such as sales tax, discount, and simple
interest.
Math A Elementary Algebra
Math A Course Outcomes
February 2004
1. Simplify algebraic expressions using the correct order of operations.
2. Solve formulas and linear equations for a specified variable.
3. Solve application problems by defining a variable, setting up and solving an equation and
interpreting the result.
4. Perform algebraic operations on polynomials: factor, add, subtract, multiply, and divide by a
monomial.
5. Given a linear equation, graph the line, identify, and interpret x and y intercepts and slope.
6. Write and graph linear equations given a) two points and b) one point and a slope.
7. Solve a system of two linear equations and interpret the solution graphically and algebraically.
8. Solve quadratic equations by factoring and the quadratic formula, including simplifying whole
number square roots.
9. Simplify rational expressions with quadratic numerators and denominators.
Objectives and Suggested Homework Assignments for Math BA using Introductory Algebra for College Students, 4th
edition, by Robert Blitzer, (Prentice Hall, 2006).
Please provide feedback and suggestions to Tom Greenwood, Donna Starr, or Rick Brantley so this list can be modified as
needed. Thanks in advance for your help!
Chapter 1 The Real Number System
Section 1.1 Fractions
Convert between mixed numbers and improper fractions.
Write the prime factorization of a composite number.
Reduce or simplify fractions.
Multiply fractions.
Divide fractions.
Add and subtract fractions with identical denominators.
Add and subtract fractions with unlike denominators.
Solve problems involving fractions.
1 – 89 odd, 95 – 105 odd, 117, 118
Section 1.2 The Real Numbers
Define the sets that make up the real numbers.
Graph numbers on a number line.
Express rational numbers as decimals.
Classify numbers as belonging to one or more sets of the real numbers.
Understand and use inequality symbols.
Find the absolute value of a real number.
1 – 33 odd, 45 – 89 odd
Section 1.3 Ordered Pairs and Graphs
Plot ordered pairs in the rectangular coordinate system.
Find coordinates of points in the rectangular coordinate system.
Interpret information given by line graphs. 1 – 59 odd, 65, 67
Section 1.4 Basic Rules of Algebra
Evaluate algebraic expressions.
Use commutative properties.
Use associative properties.
Use distributive properties.
Combine like terms.
Simplify algebraic expressions.
1 – 17 odd, 21 – 25 odd, 31 – 73 odd, 83
Section 1.5 Addition of Real Numbers
Add numbers with a number line.
Find sums using identity and inverse properties.
Add numbers without a number line.
Use addition rules to simplify algebraic expressions.
1 – 65 odd, 71 – 79 odd, 89
Section 1.6 Subtraction of Real Numbers
Subtract real numbers.
Simplify a series of additions and subtractions.
Use the definition of subtraction to identify terms.
Use the subtraction definition to simplify algebraic expressions.
1 – 85 odd, 89 – 95 odd, 101 – 105 odd, 113
Section 1.7 Multiplication and Division of Real Numbers
Multiply real numbers.
Multiply more than two real numbers.
Find multiplicative inverses.
Use the definition of division.
Divide real numbers.
Simplify algebraic expressions involving multiplication.
1 – 95 odd, 99, 105 – 109 odd, 119
Section 1.8 Exponents, Order of Operations, and Mathematical Models
Evaluate exponential expressions.
Simplify algebraic expressions with exponents.
Use the order of operations agreement.
Evaluate formulas.
1 – 51 odd, 53 – 87 eoo
Chapter 2 Linear Equations and Inequalities in One Variable
Section 2.1 The Addition Property of Equality
Check whether a number is a solution to an equation.
Use the addition property of equality to solve equations.
1 – 43 odd, 53, 55
Section 2.2 The Multiplication Property of Equality
Use the multiplication property of equality to solve equations.
Solve equations in the form  x  c .
Use the addition and multiplication properties to solve equations.
1 – 53 odd, 63 – 67 odd, 73
Section 2.3 Solving Linear Equations
Solve linear equations.
Solve linear equations containing fractions.
Identify equations with no solution or infinitely many solutions.
1 – 63 odd, 73 – 77 odd, 83, 84
Section 2.4 Formulas and Percents
Solve a formula for a variable.
Express a decimal as a percent.
Express a percent as a decimal.
Use the percent formula.
Solve applied problems involving percent change.
1 – 59 odd, 71 – 75 odd, 81 – 85 odd
Section 2.5 An Introduction to Problem Solving
Translate English phrases into algebraic expressions.
Solve algebraic word problems using linear equations.
1 – 33 odd
Section 2.6 Solving Linear Inequalities
Graph the solutions of an inequality on a number line.
Use set-builder notation.
Solve linear inequalities.
Identify inequalities with no solution or infinitely many solutions.
1 – 57 odd
Chapter 3 Problem Solving
Section 3.2 Ratio and Proportion
Find ratios.
Solve proportions.
Solve problems using proportions.
1 – 41 odd
Chapter 4 Linear Equations and Inequalities in Two Variables
Section 4.1 Graphing Equations in Two Variables
Determine whether an ordered pair is a solution of an equation.
Find solutions of an equation in two variables.
Use point plotting to graph linear equations.
Use point plotting to graph other kinds of equations.
Use graphs of linear equations to solve problems.
1 – 49 odd
Section 4.2 Graphing Linear Equations Using Intercepts
Use a graph to identify intercepts.
Graph a linear equation in tow variables using intercepts.
Graph horizontal or vertical lines.
1 – 61 odd
Section 4.3 Slope
Compute a line’s slope.
Use slope to show that lines are parallel.
Calculate rate of change in applied situations.
1 – 25 odd, 35 – 45 odd
Section 4.4 The Slope-Intercept Form of the Equation of a Line
Find a line’s slope and y-intercept from its equation.
Graph lines in slope-intercept form.
Use slope and y-intercept to graph Ax + By = C.
Use slope and y-intercept to model data.
1 – 59 odd
Section 4.5 The Point-Slope Form of the Equation of a Line
Use the point-slope form to write equations of a line.
Write linear equations that model data and make predictions.
1 – 37 odd
Section 4.6 Linear Inequalities in Two Variables
Determine whether an ordered pair is a solution of an inequality.
Graph a linear inequality in two variables.
Solve applied problems involving linear inequalities in two variables.
1 – 35 odd
Chapter 5 Systems of Linear Equations and Inequalities
Section 5.1 Solving Systems of Linear Equations by Graphing
Decide whether an ordered pair is a solution of a linear system.
Solve systems of linear equations by graphing.
Use graphing to identify systems with no solution or infinitely many solutions.
1 – 49 odd
Section 5.2 Solving Systems of Linear Equations by the Substitution Method
Solve linear systems by the substitution method.
Use the substitutions method to identify systems with no solution or infinitely many solutions.
Solve problems using the substitution method.
1 – 39 odd
Section 5.3 Solving Systems of Linear Equations by the Addition Method
Solve linear systems by the addition method.
Use the addition method to identify systems with no solution or infinitely many solutions.
Determine the most efficient method for solving a linear system.
1 – 63 odd
Section 5.5 Systems of Linear Inequalities
Graph the solutions of systems of linear inequalities. 1 – 43 odd
Chapter 6 Exponents and Polynomials
Section 6.1 Adding and Subtracting Polynomials
Understand the vocabulary used to describe polynomials.
Add polynomials.
Subtract polynomials.
1 – 35 odd, 39, 41, 47, 55 – 71 odd, 75 – 81 odd
Section 6.2 Multiplying Polynomials
Use the product rule for exponents.
Use the power rule for exponents.
Use the products-to-powers rule.
Multiply monomials.
Multiply polynomials when neither is a monomial.
1 – 63 odd, 67 – 73 odd, 79 – 83 odd, 101, 103
Section 6.3 Special Products
Use FOIL in polynomial multiplication.
Multiply the sum and difference of two terms.
Find the square of a binomial sum.
Find the square of a binomial difference.
1 – 33 odd, 45 – 55 odd, 63 – 73 odd, 83 – 87 odd
Section 6.4 Polynomials in Several Variables
Evaluate polynomials in several variables.
Understand the vocabulary of polynomials in several variables.
Add and subtract polynomials in several variables.
Multiply polynomials in several variables.
1 – 45 odd, 77, 89
Section 6.5 Dividing Polynomials
Use the quotient rule for exponents.
Use the zero-exponent rule.
Use the quotients-to-powers. Rule.
Divide monomials.
Check polynomial division
Divide a polynomial by a monomial.
1 – 75 odd
Section 6.7 Negative Exponents and Scientific Notation
Use the negative exponent rule.
Simplify exponential expressions.
Convert from scientific notation to decimal notation.
Convert from decimal notation to scientific notation.
Compute with scientific notation.
1 – 109 eoo, 143 – 147 odd
Chapter 7 Factoring Polynomials
Section 7.1 The Greatest Common Factor and Factoring by Grouping
Factor monomials.
Find the greatest common factor.
Factor out the greatest common factor of a polynomial.
Factor by grouping.
7 – 83 odd, 95
Section 7.2 Factoring Trinomials Whose Leading Coefficient is One
Factor trinomials with a leading coefficient of one.
1 – 65 odd, 77, 83, 85
Section 7.3 Factoring Trinomials Whose Leading Coefficient is Not One
Factor trinomials by trial and error.
Factor trinomials by grouping
1 – 85 odd
Section 7.4 Factoring Special Forms
Factor the difference of two squares.
Factor perfect square trinomials
Factor the sum and difference of two cubes.
1 – 87 odd, 107
Section 7.5 A General Factoring Strategy
Recognize the appropriate method for factoring a polynomial.
Use a general strategy for factoring polynomials.
1 – 91 odd, 109
Section 7.6 Solving Quadratic Equations by Factoring
Use the zero-product principle.
Solve quadratic equations by factoring.
Solve problems using quadratic equations.
1 – 59 odd, 67, 69, 89
Chapter 8 Rational Expressions
Section 8.1 Rational Expressions and Their Simplification
Find numbers for which a rational expression is undefined.
Simplify rational expressions.
Solve applied problems involving rational expressions.
1 – 83 odd
Section 8.2 Multiplying and Dividing Rational Expressions
Multiply rational expressions.
Divide rational expressions.
1 – 63 odd
Section 8.3 Adding and Subtracting Rational Expressions with the Same Denominator
Add rational expressions with the same denominator.
Subtract rational expressions with the same denominator.
Add and subtract rational expressions with opposite denominators.
1 – 63 odd
Section 8.4 Adding and Subtracting Rational Expressions with the Different Denominators
Find the least common denominator.
Add and subtract rational expressions with different denominators.
1 – 81 odd
Section 8.5 Complex Rational Expressions
Simplify complex rational expressions by dividing.
Simplify complex rational expressions by multiplying by the LCD.
1 – 39 odd
Section 8.6 Solving Rational Equations
Solve rational equations.
Solve problems involving formulas with rational expressions.
1 – 43 odd
Section 8.7 Applications Using Rational Equations and Variation
Solve problems involving motion.
Solve problems involving work.
Solve problems involving similar triangles.
1 – 23 odd
Chapter 9 Roots and Radicals
Section 9.1 Finding Roots
Find square roots.
Use a calculator to find decimal approximations for irrational square roots.
1 – 25 odd, 31 – 45 odd
Section 9.2 Multiplying and Dividing Radicals
Multiply square roots.
Simplify square roots.
1 – 91 eoo
Section 9.3 Operations with Radicals
Add and subtract radicals
1 – 49 odd
Section 9.4 Rationalizing the Denominator
Rationalize denominators containing one term.
1 – 23 odd
Chapter 10 Quadratic Equations and Functions
Section 10.1 Solving Quadratic Equations by the Square Root Property
Solve quadratic equations using the square root property.
Solve problems using the Pythagorean Theorem.
Find the distance between two points.
1 – 39 odd
Section 10.3 The Quadratic Formula
Solve quadratic equations using the quadratic formula.
Determine the most efficient method to use when solving a quadratic equation. 1 – 51 odd