Math 10 - High School Algebra

Course Coordinator

Chris Schultz (cschultz@iastate.edu)


Catalog Description

MATH 010. High School Algebra.
(4-0) Cr. arr. F.S.
For students who do not have adequate facility with topics from high school algebra or do not meet the algebra admission requirement. The course is divided into tracks of one- and two-semester lengths. For most students a diagnostic exam will determine which track must be taken. Students will receive a grade in MATH 25 or MATH 30 respectively depending on the level of material covered. Satisfactory completion of MATH 30 is recommended for students planning to take MATH 140, MATH 142, or MATH 151, while MATH 25 is sufficient for MATH 104, MATH 105, MATH 150, MATH 195, STAT 101 or STAT 105. Students must complete MATH 30 to remove a deficiency in the algebra admission requirement. Topics include signed numbers, polynomials, rational and radical expressions, exponential and logarithmic expressions, and equations. Offered on a satisfactory-fail basis only..


Textbook

book coverSchultz
Introduction to Intermediate Algebra with MyMathLab
ISU Custom Edition
ISBN: 9781269315548



Syllabus

Math 10 places students in one of two tracks, which will address the appropriate prerequisite material needed for specific entry level mathematics courses. Both levels are four- hour non-credit courses with a grading system of satisfactory or fail.

All students initially enrolled in Math 10 are in the algebra course. Based on the result of a placement/scanner (NOT the same as the Mathematics placement exam (ALEKS) taken before orientation), Math 10 students will be placed in a track appropriate for their ability and the future math courses they need to take.

Track A is designed to

  • Teach the material found in approximately the first year of high school algebra – needed by some students to meet ISU admission requirements.
  • Prepare students for Math 104, 105, 195, and Stat 101, and
  • Prepare students for Track B.

Track B is designed to

  • Teach the material from approximately the second year of high school algebra – needed by some students to meet ISU admission requirements, and
  • Prepare students for Math 140, 143X, 145X, 150, and 151.

There are several different syllabi, depending on individual student needs. Students will receive their syllabus during the first week of the semester.


Objectives

Math 10’s primary outcome is to develop students and their Algebra skills so that they can demonstrate what they know and are able to do in a testing situation as well as in their required Iowa State Math class. Many Math 10 students have been away from formal math classes for more than a year and need to now refresh their learning. One of the primary outcomes developed is that of being confident in approaching any math problem and taking an educated risk in its solving. Another outcome to be developed involves attitude: changing the student’s attitude from “I can’t” and “I hate Math” to one of “I can” and “I sort of like Math.” Math 10 involves the teaching of not only Algebra but also the strategies for growing as a learner in Mathematics. The primary objectives from Algebra used to develop these learners are included below for both levels of Math 10.


Objectives for Math 10/25 (Track A)

Variables, Real Numbers & Mathematical Models

  • Perform arithmetic operations with decimals and fractions
  • Classify numbers as belonging to one or more sets of the real numbers
  • Understand and use the vocabulary of algebraic expressions
  • Simplify algebraic expressions involving all operations as well as exponents
  • Use the order of operations
  • Interpret and use Sigma Notation

Linear Equations & Inequalities in One Variable

  • Use the addition and multiplication properties to solve equations
  • Identify equations with no solution & infinitely many solutions
  • Solve a formula for a specified variable
  • Use the percent formula and solve applied problems involving percent change
  • Translate English phrases into algebraic expressions
  • Solve algebraic word problems using linear equations
  • Represent and solve linear inequalities graphically
  • Solve compound inequalities involving either and or or

Linear Equations in 2 Variables

  • Determine whether an ordered pair is a solution of an equation
  • Graph linear equations including horizontal & vertical lines
  • Compute a line’s slope
  • Use slope to show that lines are parallel, perpendicular, or neither
  • Use the point-slope form and the y-intercept form to write equations of a line

Systems of Linear Equations and Inequalities

  • Solve systems of equations by graphing, the substitution method, the addition method, and by utilizing Gauss-Jordan Elimination
  • Solve systems of linear equations in 3 variables
  • Identify inconsistent and dependent systems
  • Graph systems of linear inequalities
  • Add, subtract, and multiply matrices

Exponents & Polynomials

  • Understand the vocabulary used to describe polynomials
  • Add, subtract, and multiply polynomials including those with several variables
  • Use and understand the product rule, the power rule, and the products-to-powers rule for exponents
  • Develop and use The Binomial Theorem
  • Use and understand the quotient rule, the zero-exponent rule, the quotients-to-powers rule, and the negative exponent rule
  • Divide polynomials by a monomial
  • Use long division to divide by a polynomial containing more than one term
  • Use synthetic division
  • Simplify exponential expressions

Factoring Polynomials

  • Factor out the greatest common factor of a polynomial
  • Factor by grouping
  • Factor trinomials
  • Factor the difference of 2 squares
  • Factor the sum or difference of 2 cubes

Objectives for Math 10/30 (Track B)

Linear Equations in 2 Variables

  • Compute a line’s slope
  • Use slope to show that lines are parallel, perpendicular, or neither
  • Use the point-slope form and the y-intercept form to write equations of a line

Systems of Linear Equations and Inequalities

  • Solve systems of equations by graphing, the substitution method, the addition method, and by utilizing Gauss-Jordan Elimination
  • Solve systems of linear equations in 3 variables
  • Identify inconsistent and dependent systems

Exponents & Polynomials

  • Divide polynomials by a monomial
  • Use long division to divide by a polynomial containing more than one term
  • Use synthetic division
  • Simplify exponential expressions

Factoring Polynomials

  • Factor out the greatest common factor of a polynomial
  • Factor by grouping
  • Factor trinomials
  • Factor the difference of 2 squares
  • Factor the sum or difference of 2 cubes
  • Solve quadratic equations by factoring

Rational Expressions

  • Simplify rational expressions
  • Find numbers for which a rational expression is undefined
  • Multiply and divide rational expressions
  • Add & subtract rational expressions with the same denominator, opposite denominator, and different denominators
  • Simplify complex rational expressions
  • Solve rational equaitons
  • Solve a formula for a variable

Basics of Functions and Absolute Value

  • Find the domain and range of a relation
  • Determine whether a relation is a function
  • Evaluate a function
  • Use the vertical line test to identify functions
  • Obtain information about a function from its graph
  • Use the algebra of functions to combine functions and determine domains
  • Form composite functions
  • Find and verify the inverse of a function
  • Solve absolute value equations
  • Solve and graph absolute value inequalities

Radicals, Radical Functions & Rational Exponents

  • Evaluate and simplify square and cube roots
  • Simplify expressions with rational exponents and radical expressions
  • Use factoring and the product rules to simplify radicals
  • Multiply radicals and then simplify
  • Add and subtract radical expressions
  • Use the quotient rule to simplify radical expressions & divide them
  • Multiply radical expressions with more than one term
  • Rationalize denominators and numerators
  • Solve radical equations
  • Add, subtract, multiply, and divide complex numbers

Quadratic Equations and Functions

  • Solve quadratic equations using the square root property and by completing the square
  • Develop and use the quadratic formula
  • Use the discriminant to determine the number and type of solution
  • Write quadratic equations from solutions
  • Recognize characteristics of parabolas
  • Graph quadratic equations
  • Solve equations that are quadratic in form
  • Solve polynomial and rational inequalities

Exponential & Logarithmic Functions

  • Evaluate and graph exponential functions
  • Change between exponential and logarithmic forms
  • Evaluate logarithms and use basic properties
  • Use the product, quotient, and power rules to expand and condense logarithmic expressions
  • Solve exponential and logarithmic equations

Old Exams

(none provided)


Official Math Department Policies

The Math Department Class Policies page describes the official policies that all instructors have to follow. It covers rules on make-up exams, cheating, student behavior, etc.


Students With Disabilities

If you have a documented disability and require accommodations, you should obtain a Student Academic Accommodation Request (SAAR) from the Disability Resources office (Student Services Building, Room 1076, 294-6624 or TDD 294-6335, disabilityresources@iastate.edu or accommodations@iastate.edu). Please contact your instructor early in the semester so that your learning needs may be appropriately met.

More information about disability resources in the Mathematics Department can be found at http://www.math.iastate.edu/Undergrad/AccommodationPol.html.