MOHAWK VALLEY COMMUNITY COLLEGE
UTICA and ROME, NEW YORK
COURSE OUTLINE
MA091
INTRODUCTORY ALGEBRA
Prepared by
Emily Hantsch, December 2013
Reviewed and Revised by Emily Hantsch, May 2014
COURSE OUTLINE
Title:
Introductory Algebra
Catalog Number:
MA091
Contact Hours:
3
Practicum Hours:
0
Credit Hours:
0
Prerequisite:
An appropriate placement test score or MA089 Arithmetic.
Catalog
Description:
This course is for students enrolled in STEM programs or for
students who need to take either MA115 or MA171 who, according to
placement test results, need preparation for subsequent mathematics
courses. It develops basic skills and the understanding of elementary
algebra. Topics include arithmetic computations, measurement and
geometry, percentages, ratio and proportion, linear equations,
polynomials, and an introduction to graphing lines. Prerequisite: An
appropriate placement test score or MA089 Arithmetic.
Major Topics:
For each of the following topics the student will:
Topic 1.
Whole Numbers
1.1 Perform basic operations with whole numbers and identify their properties.
1.2 Approximate quantities using estimation.
1.3 Simplify and/or evaluate arithmetic and variable expressions, including
exponential form, involving whole numbers using order of operations.
1.4 Translate a given verbal expression to symbolic form.
Topic 2.
Integers
2.1 Locate integer values on a real number line and use order relations to
compare given integers.
2.2 Add, subtract, multiply and divide integers.
2.3 Simplify and/or evaluate variable expressions involving verbal and/or
symbolic expressions for the operations on integers.
2.4 Simplify and/or evaluate expressions, including exponential form, additive
inverse and absolute value involving integers using order of operations.
Topic 3.
Rational Numbers
3.1 Simplify fractions.
3.2 Use order relations to compare given fractions.
3.3 Determine the prime factorization of given composite numbers.
3.4 Determine a common denominator for given fractions.
3.5 Add, subtract, multiply and divide given fractions.
3.6 Evaluate variable expressions involving verbal and/or symbolic expressions for
the operations on fractions.
3.7 Simplify and/or evaluate expressions involving fractions using the order of
operation agreements.
Topic 4.
Decimals:
4.1 Perform basic operations on decimals.
4.2 Convert given fractional expressions to decimals including fractions that are
equal to repeating decimals, and convert given decimals to fractional
expressions.
4.3 Use order relations to compare given decimals.
4.4 Approximate the (principal) square root of a given number with the aid of a
calculator.
4.5 Evaluate variable expressions involving verbal and/or symbolic expressions for
the operations on decimals.
4.6 Convert numbers between standard notation and scientific notation.
Topic 5.
Measurements
5.1 Convert, using conversion factors (rates), measurements of length and time in
the U.S. System.
5.2 Convert, using conversion factors (rates), measurements of length, capacity
and mass in the Metric System of measurement.
5.3 Convert between U.S. Units and metric units of length using provided
conversion factors.
Topic 6.
Geometry
6.1 Calculate the perimeter of plane geometric figures.
6.2 Know and use the formulas to calculate the area and circumference of a circle.
6.3 Calculate the area of triangles, rectangles, and squares.
6.4 Recognize the symbol  and use its approximation (from the  key on a
scientific calculator or by using 3.14) to evaluate formulas.
Topic 7.
Ratio, Proportion, and Percents
7.1 Write ratios as fractions and simplify.
7.2 Write rates as fractions and find unit rates.
7.3 Write and solve proportions.
7.4 Solve application problems which use proportions.
7.5 Perform conversions between percents and fractions and between decimals
and percents.
7.6 Use either the basic percent equation (percent X base = amount) or the percent
proportion to solve application problems including percent increase and
decrease.
Topic 8.
Algebraic Expressions and Linear Equations
8.1 Simplify algebraic expressions using the operations of addition and subtraction
and distribution of a constant over an expression.
8.2 Evaluate algebraic expressions.
8.3 Evaluate formulas, including when the desired variable is not isolated.
8.4 Determine solutions to first degree equations by applying the addition and
multiplication properties of equations.
8.5 Translate given verbal sentences into equations and solve the resulting
equations.
Topic 9.
Lines
9.1 Graph ordered pairs on a rectangular coordinate system.
9.2 Determine solutions of given linear equations in two variables.
9.3 Graph solutions of given linear equations in two variables on a rectangular
coordinate system.
9.4 Recognize and graph horizontal and vertical lines from given equations.
9.5 Determine the x and y-intercepts of given linear equations in two variables.
9.6 Determine and interpret the slopes of lines given two points on the line and/or
given the equation of the line.
9.7 Determine an equation of a line given a point and the slope and/or given the
graph of a linear equation.
Topic 10.
Polynomials
10.1 Use the Rules of Exponents to simplify an expression.
10.2 Add and subtract polynomials
10.3 Multiply a monomial by a polynomial, a binomial by a binomial, and divide a
polynomial by a monomial.
10.4 Factor the Greatest Common Factor from a polynomial.
Teaching Guide
Title:
Introductory Algebra
Catalog Number:
MA091
Contact Hours:
3
Practicum Hours:
0
Credit Hours:
0
Prerequisite:
An appropriate placement test score or MA089 Arithmetic.
Catalog
Description:
Text:
This course is for students enrolled in STEM programs or for
students who need to take either MA115 or MA171 who,
according to placement test results, need preparation for
subsequent mathematics courses. It develops basic skills
and the understanding of elementary algebra. Topics
include arithmetic computations, measurement and
geometry, percentages, ratio and proportion, linear
equations, polynomials, and an introduction to graphing
lines. Prerequisite: An appropriate placement test score or
MA089 Arithmetic.
Prealgebra and Introductory Algebra, (Custom), Wright: Hawkes Learning
Systems/Quant Systems Inc. 2012
MVCC Supplement written by Anna Radlowski and bundled with the text
book.
NOTE: Chapter 1, 2, and 3 has mainly review material.
Chapter 1
6 Hours
1.1
Introduction to Whole Numbers – Review
1.2
Addition and Subtraction with Whole Numbers – Review
1.3
Multiplication and Division with Whole Numbers – Review. Long Division is
supplemented by Topic 1 of the supplement.
1.4
Problem Solving with Whole Numbers – New Material
1.5
Solving Equations with Whole Numbers – New Material
1.6
Exponents and Order of Operations – Review
1.7
Introduction to Polynomials – New
1.8
Introduction to Integers – Review
1.9
Addition with Integers – Review
1.10 Subtraction with Integers – Review
1.11 Multiplication, Division, and Order of Operations with Integers – Review
1.12 Applications: Change in Value and Mean -- OMIT
1.13
1.14
Introduction to Like Terms and Polynomials – New Material
Solving Equations with Integers – New Material
Chapter 2
5 Hours
2.1 Tests for Divisibility – OMIT
2.2 Prime Numbers – Review Material
2.3 Prime Factorization – Review Material
2.4 Least Common Multiple – OMIT
2.5 Introduction to Fractions – Review
2.6 Division with Fractions – Review
2.7 Addition and Subtraction with Fractions – Review
2.8 Introduction to Mixed Numbers
2.9 Multiplication and Division with Mixed Numbers – OMIT
2.10 Addition and Subtraction with Mixed Numbers – OMIT
2.11 Complex Fractions and Order of Operations – Complex fractions are new,
Order of Operations is review.
2.12 Solving Equations with Fractions – New
2.13 Ratios and Proportions – New. This section is supplemented by Topic 5 in the
supplement.
Chapter 3
5 Hours
3.1 Reading, Writing, and Rounding Decimal Numbers – Review
3.2 Addition and Subtraction with Decimal Numbers – Review
3.3 Multiplication and Division with Decimal Numbers – Review
3.4 Measures of Center – OMIT
3.5 Decimal Numbers, Fractions, and Scientific Notation – Converting between
decimals and fractions is review but scientific notation is new material.
Scientific Notation is supplemented by Topic 4 in the supplement, converting
fractions to decimals is found in Topic 2 of the supplement.
3.6 Basics of Percent – Review
3.7 Applications of Percent – New Material
3.8 Simple and Compound Interest – OMIT
3.9 Square Roots -- Review
Chapters 4-7 contain only new material.
Chapter 4
6 Hours
4.1 The Metric System - OMIT Objectives D, F, OMIT all questions from Objective
E dealing with equivalent measures of volume. This section is
supplemented by Topic 7.
4.2 U.S. Customary and Metric Equivalents – OMIT Objective A and exercises 1730. This topic is supplemented by Topic 6.
4.3 Introduction to Geometry – OMIT
4.4 Perimeter. Supplement Topic 8
4.5 Area – Supplement Topic 8.
4.6 Volume – OMIT
4.7 Similarity – OMIT
4.8 The Pythagorean Theorem – OMIT
4.9 Reading Graphs – OMIT
Chapter 5
6 Hours
5.1 Simplifying and Evaluating Algebraic Expressions
5.2 Translating English Phrases and Algebraic Expressions
5.3 Solving Linear Equations: x+b=c and ax=c
5.4 Solving Linear Equations: ax+b=c
5.5 Solving Linear Equations: ax+b=cx+d
5.6 Applications: Number Problems and Consecutive Integers
5.7 Applications: Percent Problems
5.8 Working with Formulas
5.9 Applications: Distance – Rate – Time, Interest, Mean, Cost – OMIT
Chapter 6
6.1 The Cartesian Coordinate System
6.2 Graphing Linear Equations in Two Variables
6.3 The Slope – Intercept Form
6.4 The Point – Slope Form
6.5 Linear Inequalities in One or Two Variables – OMIT
6.6 Introduction to Functions and Function Notation - OMIT
6 Hours
Chapter 7: Exponents, Polynomials, and Factoring Techniques
7.1
Exponents
7.2
Introduction to Polynomials
7.3
Addition and Subtraction with Polynomials
7.4
Multiplication with Polynomials
7.5
Special Products of Polynomials – OMIT
7.6
Greatest Common Factor (GCF) and Factoring by Grouping
7.7
Factoring Trinomials: x2+bx+c – OMIT
7.8
Factoring Trinomials: ax2+bx+c – OMIT
7.9
Special Factoring Techniques – OMIT
7.10 Solving Quadratic Equations by Factoring – OMIT
7.11 Applications of Quadratic Equations – OMIT
6 Hours
The teaching guide leaves 3 hours for in class assessment. There will be a two
hour proctored comprehensive final examination. Study guides are prohibited on
the final exam according to math department policy.
Grading Structure – Instructors must explicitly state their grading policy on their
syllabus.
3 hour in class tests, together 50-60%
Final exam 30%
Attendance 0-5%
Other (homework, groupwork, quizzes, etc.) 5–25%