Introductory and Intermediate Algebra - What's New
- 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.
2.5 More Linear Equations: ax+b=cx+d
3.5a Solving Absolute Value Equations
- This lesson concentrates on solving linear equations with variables on both sides of the equation.
6.2 Factoring Trinomials: Leading Coefficient I
- Solving absolute value equations now has its own lesson in order to strengthen students’ understanding and familiarity with absolute value equations.
6.5 Additional Factoring Practice
- This lesson provides an excellent foundation for learning how to factor trinomials by focusing on trinomials with a leading coefficient of 1.
11.6 Common Logarithms and Natural Logarithms
- 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.
- 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
1.3 Subtraction with Real Numbers
- Added two problems involving addition with decimal numbers.
- Added one problem involving vertical addition.
1.4 Multiplication and Division with Real Numbers
- Added eleven problems from the Fall 2010 lesson 1.8c Applications: Change in Value.
1.5 Exponents, Prime Numbers, and LCM
- Added six problems involving finding the average of a set of numbers.
- Added four problems involving multiplication and division with decimal numbers.
1.6a Reducing Fractions
- Added thirty problems from the Fall 2010 lesson 1.8 Order of Operations which involve evaluating expressions with exponents.
1.8 Order of Operations
- 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.
2.3a Solving Linear Equations Using Addition and Subtraction
- Added one problem involving fractions and the order of operations.
2.5 More Linear Equations ax+b=cx+d New Lesson!
- 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
2.6c Applications of Linear Equations: Multiplication and Division
- 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.
3.1 Working with Formulas
- 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.
3.2 Formulas in Geometry
- Added two problems that provide a formula and ask the student to solve for a particular variable.
3.4 Solving Linear Inequalities
- Added four word problems that require the use of algebra rather than plugging values into a formula.
3.5a Solving Absolute Value Equations New Lesson!
- 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.
3.5b Solving Absolute Value Inequalities
- 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.
4.2 Graphing Linear Equations by Plotting Points
- 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.
4.3 Graphing Linear Equations in Slope-Intercept Form
- Split three problems into six for better control over integer and fractional answers.
4.4a Finding the Equation of a Line
- 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.
4.4b Graphing Linear Equations in Point-Slope Form
- Reorganized the problems in this lesson to more accurately reflect the examples shown in this lesson.
4.5 Introduction to Functions and Function Notation
- 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.
5.3 Identifying and Evaluating Polynomials
- Added two problems where the student must find the domain of a given function.
6.1a Greatest Common Factor of Two or More Terms
- 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).”
6.2 Factoring Trinomials: Leading Coefficient 1 New Lesson!
- Made improvements to the answer format of seven problems.
6.5 Additional Factoring Practice New Lesson!
- Added a total of twelve problems involving factoring trinomials with a leading coefficient of 1.
6.6 Solving Quadratic Equations by Factoring
- Added a total of twenty-six problems that ask to factor a given equation without asking for a specific method of factoring.
7.1a Defining Rational Expressions
- Added three problems where the student must solve a factored equation.
7.3 Complex Fractions
- Added two problems that ask to state any restrictions on the given expression where “No Restrictions” is the answer to both problems.
7.4a Solving Equations: Ratios and Proportions
- Added two problems to simplify a given expression involving multiple operations.
7.4b Solving Equations with Rational Expressions
- 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.
8.2 Solving Systems of Linear Equations by Substitution
8.4 Applications: Distance – Rate – Time, Number Problems, Amounts and Costs
- Added three problems where the student must state any restrictions on the equation and then solve.
8.5 Applications: Interest and Mixture
9.1 Evaluating Radicals
- Added five problems from the Fall 2010 lesson 14.2 Applications: Systems of Equations.
9.2 Simplifying Radicals
- 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.
9.3 Rational Exponents
- Added twelve problems that utilize the properties of square roots.
9.4a Addition and Subtraction with Radicals
- 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.
9.4c Rationalizing Denominators
- Split two problems into five for better control over the types of problems students receive.
9.6 Functions with Radicals
- Added eight problems involving rationalizing binomial denominators.
- Added two simple rationalization problems.
10.1a Quadratic Equations: The Square Root Method
- Split three problems into six for better control of the types of problems students receive.
10.2 Quadratic Equations: The Quadratic Formula
- Split one problem into three problems where the answer reduces, reduces partially, or does not reduce at all.
11.5 Properties of Logarithms
- Adjusted the answer entry format of sixteen problems based on instructor feedback.
11.6 Common Logarithms and Natural Logarithms New Lesson!
- Changed thirteen problems to include a base.
- Added three problems from lesson 11.4 Logarithmic Functions.
12.3 The Distance Formula and Circles
- Added a total of nine problems dealing with common and natural logarithms.
A.1a Decimals and Percents
- Removed the midpoint formula from this lesson.
- Added thirteen problems involving decimals and percents.