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Algebra 2
5th Edition (new program since March 2010)
Corrections and Clarifications
Textbook.
The Chapters are broken into Sections and the exercises are at the end of each section. The student will usually have 75 to 100 odd problems per section from which to choose, but the good news is that only 25-30 odd problems per section need to be worked. And this will be about every 3rd or 4th odd problem. Section Review Problems start at the end of Section 2.1 on page 68.

Student Solutions Manual. The Chapter 1, Section 1 odd problems start on page 2.

The Mid-Chapter Quiz, End-of-Chapter Test for each chapter, and Cumulative Test every three chapters are fully suppored for both even and odd problems and every problem should be worked.

Section 1.1, Exercise Problems.
The publisher put the answer to each exercise problem in the textbook immediately after each problem. This typo mistake is for Section 1 only.

Section 1.4, problem 105.
The solutions guide includes a part (b) that belongs with problem #106.

Section 3.7, problem 59.
The function listed in the solutions guide is incorrect. The function should be h(x) = x squared + 3.

Chapter 4, Mid-Chapter Quiz.
The publisher by mistake did not include the even numbered problems in the Student Solutions manual. If you work the even numbered problems and have a question please contact Dana Mosely for student technical support.

Section 4.2, #39.

Section 5.4, #111.
The solution is missing in the solutions guide. There are two ways to factor the expression:
8-50x2
-2(25x2 - 4)
-2(5x + 2)(5x - 2)

or

8-50x2
-2(25x2 - 4)
-2(5x + 2)(5x - 2)

Chapter 5 Test, problem 9b.
In the solutions guide, the last term of the answer is missing. The last term should be - b^2.

Section 6.3, problem 21.
In the solutions guide, the (x - 3) factors in the last step can cancel yielding an answer of x - 6.

Section 8.4, problem 61.
In the solutions guide, the denominator in the 5th step should be -2 rather than 2 and the x-intercepts should be x = 3 plus or minus square root of 2.

Section 9.1, problem 41.
In the solutions guide, the value of f(x) corresponding to x = 12 should be -0.5 rather than -5.

Section 9.3, problem 129(c).
The answer in the solutions manual should be (0,22.9). The calculation in the solutions manual does not consider the length of the rope between the boat and the person when finding the position of the person on the y-axis.

Section 9.6, problem 59(b).
In the solutions guide, the solution is calculated incorrectly. The last step should indicate t is approximately equal 9 hours.

Chapter 7, Mid-Chapter Quiz.

Chapter 10, Mid-Chapter Quiz, problem 4.
In the solutions guide, the first binomial of the answer should be squared.

Algebra 2
2nd custom edition, Sept 2000
Corrections and Clarifications
At the end of each section, problems under Integrated Review may be omitted. Problems under Solving Problems may be limited to about 4 to 6 problems. Problems under Explaining Concepts may be omitted.

How to correlate your solutions guide to the textbook.

Solutions to Integrated Review Exercises for Chapters 1-10; Pages 1-65, Index on page 1.

Solutions to Odd-Numbered Exercises for Chapters P, 1-10, Appendix A-D; Pages 71-569, Index on pages 67-69.

NOTE: Light blue divider page in middle of book

Solutions to Even-Numbered Exercises for Chapters P, 1-10, Appendex A-D; Pages 2-456, Index on pages v-vii.

Example of Chapter P Text correlation to Solutions Guide:
Odd exercises on pages 72-86.
Even exercises on pages 2-14. (after light blue divider)
Review exercises on pages 87-90; and pages 15-17 (after light blue divider)
Chapter Test pages 89-90.

Section P.3. Omit problems 67 and 68.

Click here for more information on Solution Guides.

Section 1.2, problem 23.
In the solutions guide, the answer should be 33% rather than 33 1/3%.

Section 1.3, pages 88 and 90, problem 57 and 81.
#57. Set up a table of information involving Part 1 and Part 2 of the overall trip and the Distance, Rate, and Time for each of them. Fill in as much as possible and look for an overall statement of equality. Since you are given a total distance of 317, the general concept can be (Distance traveled in part 1 of the trip) + (Distance traveled in Part 2) = 317. Since Distance = rate x time, each of the distances above is some "rt". >From the chart, the rate in part 1 is 58, and the rate in part 2 it is 52. If you let x stand for the time in part 1, then (5.75 - x) represents the time in part 2. Now you can fill into the equation....
(rt for part 1) + (rt for part 2) = 317
58x + 52(5.75 - x) = 317
Solving the equation you find x = 3 which means the first part of the trip took 3 hours. The second part of the trip is 5.75 - x which is 5.75 - 3, or 2.75 hours.
#81. The general idea for solution in this problem is similar to the one above because you are given TOTAL INTEREST; the concept is (Interest earned at 8%) + (Interest earned at 10%) = Total Interest. Since Interest = prt the equation becomes prt + prt = $3500. If x stands for the amount invested at 10%, then ($40,000 - x) represents the amount invested at 8%; both times are 1 so the equation becomes x(.10) + ($40,000 - x)(.08) = $3500. Solve the equation to find x = $15,000.

Section 1.4, problem 8.
The problem in the textbook should read x < -4.

Section 1.4, problem 108.
In the solutions guide, the right side of the inequality in steps 3 and 4 should contain the number 17,200 rather than 172,000.

Section 2.1, problem 94.
In the solutions guide, omit the x^2 factor on the right side of the first step.

Section 2.6, problem 4.
In the solutions guide, the domain should be - ∞ < x < ∞ rather than - ∞ < x < x.

Section 2.6, problem 16.
In the solutions guide, the domain should be - ∞ < x < ∞ rather than - ∞ < x < x.

Section 2.6, problem 25.
In the solutions guide, there should be a minus sign before the infinity symbol in the inequality describing the range.

Chapter 2 Review Exercises
For even-numbered problems 60 - 128, the equations are written using + signs instead of = signs.

Section 3.1
On the video program there is an on-camera mistake on a mixture problem. The problem involves two investments, one at 8.5% and the other at 11% interest. The total invested is $40,000 and the total amount of interest earned is given. The question asks for the amount of money invested at each interest rate. The incorrect answer given for one investment is $30,000. It should be $34,000.

Section 3.7, problem 59.
In the solutions guide, the answer should be h(x) = x2 + 3.

Chapter 3 Review Exercises, problem 119
The calculation for area in the solutions guide contains periods which should be raised to become times signs.

Section 4.2, problem 34
The problem listed in the solutions guide is not the same as the problem in the textbook. The correct answer is (x-10).

Chapter 4, Mid-Chapter Quiz, problem 1.
In the textbook, page A86, the exponent in the denominator should be positive.

Section 4.4, odd problems #17-97.
In the solutions guide, the last step in each problem should contain an equal sign instead of the plus sign to the right of LCM. All problems appear with plus signs where equal signs should be. Please work only from the even-numbered problems in this section.

Section 4.6, problem 93 (a)
There is not enough information given in the problem to arrive at the domain listed in the solutions guide. Please ignore part (a) of the problem.

Chapter 4 Review, problems 84 and 113b.
Problem 84, in the solutions guide (page 174 in the even section), the last term denominator should have a plus sign between the terms instead of a minus sign. Problem 113b, the answer should be 30 years.

Chapter 4 Test, problem 20.
In the second step, there is an unnecessary factor of x in the second term.

Chapter 4 Test, problem 27.
Change the first sentence to "One painter can do a job in 1-1/2 times the required by another painter.

Chapter 5, Mid-Chapter Quiz, problem 7.
In the answer, the u factor outside the radical does not require an absolute value symbol because u is understood to be positive in the original problem; otherwise the problem would be undefined.

Chapter 5, Review, problem 54.
In the solutions guide, the answer should include absolute value around "s".

Section 6.2, Integrated Review, problem 2.
The answer in the solutions guide is incorrect. The exponent on "a" should be"rs" rather than"8r".

Section 6.3, problem 46.
Notice in the second step the equation is multiplied throughout by 100 to clear the decimals. That technique is fine because, although the graph of the new equation will look different from the original, the two equations will have the same x-intercepts and, therefore, the same solutions.
There are two problems with the method used in the solutions guide. In the last step there is an attempt to undo the operation of multiplying throughout by 100 in the second step, but the process is unnecessary and extremely tricky when fractions and radicals are involved. Also, a minus sign is incorrectly introduced in the first term of the numerator.
Correct solutions are approximately -1.159 and 2.492.

Section 6.4, problem 59.
In the solutions guide, omit the second equal sign in the first step.

Chapter 6 Test, problem 6.
In the solutions guide the solutions in the last step are approximated incorrectly. The solutions should be approximately 3.12 and -1.12.

Chapter 6 Test, problem 18.
The method used in the solutions guide to solve the problem has not been covered at this point in the textbook. (That sometimes happens because the author of the solutions guide is not the same as the authors of the textbook so the methods used up to a particular point in the text are not clear.) There are ways to find the vertex of a parabola other than the one used in the solutions guide but since we have not focused on finding the coordinates of the vertex up to this point please omit this problem from the chapter test.

Section 6.5, page 415, problems 114-122.
The even problems from #144-122 do not appear in the solutions guide. Please skip those problems.

Section 7.1, Integrated Review, problems 11 and 12.
Problem 11. The solution is missing in the Solutions Guide. The function is C = 5.75x + 12,000.
Problem 12. The solution is missing in the Solutions Guide. Since the length is 1.5 times the width, if w represents the width, then the length is represented as 1.5w.
Perimeter = 2(length) + 2(width)
P = 2(1.5w) + 2w
P = 5w

Section 7.3, problem 55.
The expression for the x-intercept should contain 3 rather than -3.

Chapter 7, Review Exercises, problem 79.
The denominator should be x^2 - 4, rather than x^2 - 4x.

Chapter 7, Review Exercises, problem 88.
The problem should state that the force of gravity F is inversely proportional to the square of the distance from the center of the earth.

Chapter 7 Test, problem 12.
Since you have not seen a parabola which opens to the side, you are welcome to skip this problem. However, I will describe the solution anyway.

One comment about the solution in the solutions guide; those solutions are not written by the same author who writes the text so sometimes a technique is used in the solutions guide which is not used in the text. The two techniques are consistent with one another, but it's confusing to see something different from what you have been taught.

You know that when parabolas open up or down that the standard form of the equation is y = a(x -h)^2 + k. Notice that the x is squared and y is to the first degree and that fits with the notion that for each value of y there are two values of x. When the graph opens to the side, there are two values of y (two vertical distances) for each value of x (a horizontal distance). Therefore, it should make sense that the standard form can be...

x = a(y - k)^2 + h

I know you are wondering why the h and k were swapped. It's because they represent an ordered pair of numbers. When written as (h, k) the h is a horizontal distance and k is a vertical distance. In the general form h follows x and k is associated with y. When the form changes for the side-opening parabola, the k has to follow y because it's a horizontal distance. [Hope this makes sense.]

One good thing about swapping the positions of h and k is that the vertex of the parabola is still at (h, k) and that is where we start in the problem.

x = a(y - k)^2 + h
with vertex at (-2, 1) replace h with -2 and k with 1

x = a(y - 1)^2 - 2

Find a using the same technique we used before (it's also used in examples 4 and 5 on page 446). That is, replace x and y with the coordinates of the point on the parabola. The point is (6, 9).

6 = a(9 - 1)^2 - 2 now solve for a...
6 = a(8)^2 - 2
6 = 64a - 2
8 = 64a
8/64 = a
a = 1/8

The equation is x = (1/8)(y - 1)^2 - 2
The same equation can be manipulated into many different forms, one of which is in the solutions guide.

Section 8.1. In the solutions guide, problems 95-105 are omitted. Please do not work any of these on an assignment.

Section 8.3, problem 15. In the solutions guide, fourth group of equations, the third equation is -3x = -9. The equation should be
-3z = -9.

Section 8.3, problem 31. In the solutions guide, the constant in the first equation should be 1 rather than 3. Subsequent steps are correct.

Section 8.3, problem 37, page 428.
In the solutions guide, there are two equations near the bottom, just below 0 = 0, in which the "x" variable should be "z". In the fraction, 5/13x should be 5/13z.

Section 9.1, #76
The equation used in the solutions guide is different from the one in the textbook. The constant in the equation should be +2 rather than +1 and the graph shifted up 2 units rather than 1.

Section 9.4, problem 78.
The problem is written incorrectly in the solutions guide. A minus sign should appear between the terms and the answer should be log6(12/y).

Chapter 9, Mid Chapter Quiz, problem 8.
. In the solutions guide, the formula for compounding is used but the problem is not structured in that context. A more straight-forward approach is to multiply $2.23 by 1.04 (100% + 0.04% or 104%) for each of the 5 years. The expression for the solution is 2.23(1.04)^5.

Chapter 9, Mid Chapter Quiz, problem 19.
. In the solutions guide, the distance the basic graph moved to the right should be 2 units rather than 3 units.

Chapter 9 Test, problem 9.
Since the problem does not include parenthesis, there are two ways to interpret the expression. That is, the problem may be interpreted as

[log(base 5)5^3](6)

or as

log(base5)[5^3(6)]

The latter interpretation is used in the solutions guide.

If the former interpretation is used, the solution is
[log(base 5)5^3](6)
[3log(base 5)5](6)
(3)(6)
18

Section 10.1, problem 35.
The problem in the solutions guide is not the same as the problem in the textbook. The textbook problem should be the one in the solutions guide so either omit the problem or consider the problem to be (n + 1)! / (n - 1)!

Section 10.2, problem 98.
In the solutions guide, the listed keystrokes are not quite correct. The button sequence should be
LIST MATH 5 LIST OPS 5 1000 - 25 XT0 , XT0 , 1 , 40 , 1 ) ENTER
[The difference is the addition of a comma followed by the variable.]

Section 10.2, problem 100.
In the solutions guide, the upper limit of summation should be 20 rather than 40. The remainder of the problem is correct because 20 is used in the solution.

Section 10.4, problem 45.
In the solutions guide, in the third term of the expansion, the factor y should be squared.

Section 10.5, problem 5.
In the solutions guide, since the problem stipulates "without replacement" the number of ways for the sum of the marbles to be 9 is 4 rather than 8.

Section 10.5, problem 23(c).
In the solutions guide, the number 400 itself would not be included in the count, using the method demonstrated. The problem says the number cannot be greater than 400 which implies the number can be 400 itself. Therefore, the total should be 401 rather than 400.

Section 10.6, #44.
In the solutions guide, the numerator should be 30! rather than just 30 and the answer should be 142,506 rather than 142,056.

Algebra II
(previous Intermediate Algebra program)
Corrections and Clarifications
Section 2.2, problem 27. The numerator of the answer should be 2S and not just S.

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