﻿ Introductory and Intermediate Algebra What's New

# Introductory and Intermediate Algebra - What's New

## Enhancements

• This year, the software has been updated to correspond with the release of the 2nd edition of the Introductory & Intermediate Algebra textbook.
• Instruct screens have been improved in over 50 lessons, and five new lessons have been added to the software
• Over 200 new question types have been added. The new question types, including twelve word problems, provide greater correlation with the exercises in the textbook.
• Additionally, some existing question types were split into separate questions in order to allow instructors greater control of the content that their students will see.
• Graphs of linear inequalities have been changed to use parentheses and brackets rather than open and closed circles.
• A few lessons have been merged in order to streamline som of the topics and to correlate with the new text.

## New Lessons

2.5 More Linear Equations: ax+b=cx+d
• This lesson concentrates on solving linear equations with variables on both sides of the equation.
3.5a Solving Absolute Value Equations
• Solving absolute value equations now has its own lesson in order to strengthen students’ understanding and familiarity with absolute value equations.
6.2 Factoring Trinomials: Leading Coefficient I
• This lesson provides an excellent foundation for learning how to factor trinomials by focusing on trinomials with a leading coefficient of 1.
6.5 Additional Factoring Practice
• Based on numerous instructor requests, this lesson simply asks the student to factor given equations using any method of factoring they learned in the previous lessons.
11.6 Common Logarithms and Natural Logarithms
• Logarithms prior to this section are shown with a base and now common and natural logarithms are grouped together.

## New Questions & Improvements by Lesson

1.2 Addition with Real Numbers
• Added two problems involving addition with decimal numbers.
• Added one problem involving vertical addition.
1.3 Subtraction with Real Numbers
• Added eleven problems from the Fall 2010 lesson 1.8c Applications: Change in Value.
1.4 Multiplication and Division with Real Numbers
• Added six problems involving finding the average of a set of numbers.
• Added four problems involving multiplication and division with decimal numbers.
1.5 Exponents, Prime Numbers, and LCM
• Added thirty problems from the Fall 2010 lesson 1.8 Order of Operations which involve evaluating expressions with exponents.
1.6a Reducing Fractions
• Added a total of eighteen problems that require reducing fractions with and without variables.
• Six problems came from the Fall 2010 lesson 1.6a Reduction of Proper Fractions.
• Six problems came from the Fall 2010 lesson 1.6b Reduction of Improper Fractions.
1.8 Order of Operations
• Added one problem involving fractions and the order of operations.
2.3a Solving Linear Equations Using Addition and Subtraction
• Added two problems from the Fall 2010 lesson 1.2 Addition with Integers where the student must determine if a given value is a solution to an equation.
• Added two problems from the Fall 2010 lesson 1.3 Subtraction with Integers where the student must determine if a given value is a solution to an equation.
• Added six problems that involve solving linear equations using only addition and subtraction
2.5 More Linear Equations ax+b=cx+d New Lesson!
• Added a total of twenty-two problems. Of those
• One problem has no solution as an answer.
• One problem has all real numbers as an answer.
• Twelve problems use the distributive property in order to solve.
• Three problems were added where the student must determine if a given equation is a conditional equation, an identity, or a contradiction.
2.6c Applications of Linear Equations: Multiplication and Division
• Improved one problem so that the base of the triangle is indicated by b rather than x in order to match the formula for the area of a triangle.
3.1 Working with Formulas
• Added two problems that provide a formula and ask the student to solve for a particular variable.
3.2 Formulas in Geometry
• Added four word problems that require the use of algebra rather than plugging values into a formula.
3.4 Solving Linear Inequalities
• Added seven problems that require the answer in interval notation instead of algebraic notation.
• Added one problem that requires the student to graph a set of integers on a number line.
3.5a Solving Absolute Value Equations New Lesson!
• Added a total of thirteen problems.
• Ten problems were added where the student must solve absolute value equations.
• Three problems were added where the student must determine the number of solutions, if any, and then solve.
3.5b Solving Absolute Value Inequalities
• Split four problems into nine separate problems for better control over the type of inequality found within the problem. The new problems only have two steps: to answer in interval notation and then to graph the answer on a number line.
4.2 Graphing Linear Equations by Plotting Points
• Split three problems into six for better control over integer and fractional answers.
4.3 Graphing Linear Equations in Slope-Intercept Form
• Added two problems involving vertical and horizontal lines.
• Added four problems to solve for the slope when given two points.
• Added two problems where the student is given the graph of a line and they must determine the slope, y-intercept, and equation of the line.
4.4a Finding the Equation of a Line
• Reorganized the problems in this lesson to more accurately reflect the examples shown in this lesson.
4.4b Graphing Linear Equations in Point-Slope Form
• Added three problems involving parallel and perpendicular lines.
• Split five problems into ten for better control over questions involving parallel and perpendicular lines.
• Added two problems where the student is given the equation of a line and must determine the equation of the line in slope-intercept form that is either parallel to or perpendicular to the given line and another point.
• Added one problem where the student is given an equation of a line in standard form and must determine the slope of a line parallel to and perpendicular to the given line.
4.5 Introduction to Functions and Function Notation
• Added two problems where the student must find the domain of a given function.
5.3 Identifying and Evaluating Polynomials
• Added two problems that require the student to evaluate a function at something other than a real number. For example, “Given g(x) find g(a+3).”
6.1a Greatest Common Factor of Two or More Terms
• Made improvements to the answer format of seven problems.
6.2 Factoring Trinomials: Leading Coefficient 1 New Lesson!
• Added a total of twelve problems involving factoring trinomials with a leading coefficient of 1.
6.5 Additional Factoring Practice New Lesson!
• Added a total of twenty-six problems that ask to factor a given equation without asking for a specific method of factoring.
6.6 Solving Quadratic Equations by Factoring
• Added three problems where the student must solve a factored equation.
7.1a Defining Rational Expressions
• Added two problems that ask to state any restrictions on the given expression where “No Restrictions” is the answer to both problems.
7.3 Complex Fractions
• Added two problems to simplify a given expression involving multiple operations.
7.4a Solving Equations: Ratios and Proportions
• Added five problems where the student must state any restrictions on an equation and then solve.
• Added four word problems where the student must set up a proportion and then solve.
7.4b Solving Equations with Rational Expressions
• Added three problems where the student must state any restrictions on the equation and then solve.
8.2 Solving Systems of Linear Equations by Substitution
• Added two word problems.
8.4 Applications: Distance – Rate – Time, Number Problems, Amounts and Costs
• Added five problems from the Fall 2010 lesson 14.2 Applications: Systems of Equations.
8.5 Applications: Interest and Mixture
• Added two word problems.
• Added one problem involving the square root of a decimal perfect square.
• Added four problems where the student must determine if the given radical is rational, irrational, or nonreal.
• Added one problem that uses a calculator to find the value of a radical expression.
• Added twelve problems that utilize the properties of square roots.
9.3 Rational Exponents
• Split one problem into two in order to separate problems with and without a negative sign.
• Added three problems where the student must simplify algebraic expressions with rational exponents.
• Split two problems into five for better control over the types of problems students receive.
9.4c Rationalizing Denominators
• Added eight problems involving rationalizing binomial denominators.
• Added two simple rationalization problems.
9.6 Functions with Radicals
• Split three problems into six for better control of the types of problems students receive.
10.1a Quadratic Equations: The Square Root Method
• Split one problem into three problems where the answer reduces, reduces partially, or does not reduce at all.