**Chapter 1 Test.**

**Pages 79 and 80 are missing from the Algebra 1 Complete Solutions Guide,** and
these pages would have covered the end-of-chapter test for Chapter 1,
Algebra 1 textbook. Answers to the Chapter 1 Test are in the back of the
Algebra 1 textbook on page A39, and step by step solutions are below.
Algebra 1

Chapter Test for Chapter1

- (a) 8 and 12/4

The fraction 12/4 is natural because is reduces to 3.

(b) -10, 8, and 12/4

(c) all of the numbers are rational because they can all be written in the form a/b.
- -3/5 _____ -| -2 |

-3/5 ______ -2

Since -3/5 lies to the right of -2 on the number line, -3/5 is greater than -2, so -3/5 > -2
- 16 + (-20)

16 - 20

-4
- -50 - (-60)

-50 + 60

10
- 7 + | -3 |

7 + 3

10
- 64 - (25 - 8)

64 - (17)

64 -17

47
- -5(32)

-160
- -72 / -9

8
- (12 + 9) /7

21 / 7

3
- - (-2) (5) / 10

- (-10) / 10

10 / 10

1
- 5/6 - 1/8

20/24 - 3/24

17/24
- -27 (5/6)

-9 (5/2)

-45/2
- 7/16 ö 21/28

7/16 x 28/21

1/4 x 7/3

7/12
- -8.1/0.3

-27
- -(2/3)2 Notice the base of the exponent is 2/3, so there are two factors of 2/3

-(2/3) (2/3)

- 4/9
- 35 - (50 ö 52)

35 - (50 ö 25)

35 - 2

33
- The Distributive Property
- The Multiplicative Inverse Property
- The Associative Property of Addition (because the grouping of numbers changed)
- The Commutative Property or Multiplication (because the order of the factors changed)
- 30/72 working in easy steps, divide 3 into both numerator and denominator to get 10 /24, now divide 2 into both numerator and denominator, 5/12
- In the first expression the base of the exponent is 3 but in the second expression the base of the exponent is -3.
- Exponentiation (raise 2 to the 3rd power), multiply (3 times 8), subtract (24 from 32)
- Answers vary. Among them are 2/3, 4/6, 6/9, 8/12.

**Chapter 1 Review, problem 11.** In the solutions guide the answer should be -8.5 rather than 8.5.

**Chapter 1 Review, problem 67.** Please also accept as correct the expression n + 10/8 which is technically more correct than a fraction with n + 10 as the numerator and 8 as the denominator. If it were intended for the numerator to be n + 10, then the punctuation in the sentence would be:
**The sum of a number and 10, divided by 8**.

**Section 1.2, problem 124.** In the solutions guide, the prime factorization should contain 3 factors of 3.

**Section 1.3, page 43, problem 153.** The answers for parts "h" and "i" are switched; "h" should be 15 degrees and "i" should be 14 degrees.

**Chapter 2 Review, #94.** In the solutions guide, the minus sign should be a times sign.

**Chapter 2 Review, #99.** In the verbal model, the first item should be "Area of rectangle" rather than "Area of triangle."

**Section 3.1, #69.**
In the solutions guide, the division signs should be equal signs. Also, in the 4th step, 4 should be subtracted from both sides rather than added to both sides.

**Section 3.1, #71.**
In the solutions guide, the division signs should be equal signs.

**Section 3.2, Integrated Review, problem 7.** The answer in the textbook (page A44) is incorrect. The correct answer is x - 4.

**Section 3.5, problem 9.** The solution requires the use of a technique called factoring which is covered in a later chapter. Please omit the problem.

**Section 3.5, problem 65.** In the solutions guide, second step, the first term should contain a factor of x.

**Section 4.2, problems 79 and 81.** In the Solutions Guide, the Xmin values should be negative rather than positive.

**Section 4.3, Integrated Review, problem 6.** The middle term of the answer in the Solutions Guide is incorrect. The answer should be 3x^2y - xy^2 - 5xy.

**Section 4.4, problem 26.** The answer in the solutions guide is correct but, in the second to last step, the denominator fraction should be 17/8 rather than 17/18.

**Section 6.5, problem 11.** The second answer in the solutions guide should be -100/7 rather than 100/7.

**Section 6.5, problem 95 (c).** In the solutions guide when the monomial factor of -4 is taken out of the trinomial, the middle term should be -20x rather than 20x.

**Section 6.5, problem 99 (b).** The answer is incorrect in the solutions guide -- t should be 13 rather than 15 and the year should be 2003 rather than 2005. The window settings must be extended up and to the right in order to view and trace to the positive where y=100 (for 100 million passengers). The corresponding x-value (which stands for time) is approximately 13 rather than 15 listed in the solutions guide so the year is 13 years beyond the basis year of 1990, or the year 2003, rather than 2005 listed in the solutions guide.

**Section 7.4, problem 51.**In the solutions guide, page 306, the product R=8950(96) should be 859,200 rather than 859,000.

**Section 7.4, Integrated Review, problem 2.** The answer in the solutions guide is not related to the problem in the textbook. The correct answer should be: The domain of the function is 2<x<a because those are the values of x for which the equations makes sense.

**Chapter 7 Review, problem 55.** The slope of the line is 4 rather than 3. Therefore the coefficients of x in the equations will change accordingly.

**Section 8.2, problem 26.** The answer in the solutions guide is incorrect. The answer should contain only two factors of the "v" in the numerator.

**Chapter 8, Mid Chapter Quiz, problem 10.** The denominator of the fraction in the textbook should be x+2.

**Chapter 8 Review, problem 32.** In the solutions guide, the missing factor should be (x + 2).

**Section 10.1, Problem 35.** Omit the 2 in the numerator so that the problem matches the solution in the solution guide.

**Chapter 10, Mid Chapter Quiz, problems 16 & 19.**

Problem 16. In the solutions guide, c=-1 rather than 1 so the discriminant is 53 rather than 45. The conclusion in the solutions guide is the same.

Problem 19. The method of solution in the solutions guide uses a formula which has not been discussed in this course. The method below may be used to solve the problem but it is a bit involved so the problem may abe omitted from the quiz or treated as an extra credit problem. The method of solution below involves a system of equations using the simple interest formula and the quadratic formula.

I1 stands for the interest earned in the first year and I2 stands for the interest earned in the second year.

In the first year,

I1 = prt

I1 = 1500(r)(1)

I1 = 1500 r

In the second year the amount of principal is the original principal, $1500 plus the interest earned in the first year.

The total principal, then, is 1500 + 1500 r, so...

I2 = prt

I2 = (1500 + 1500r)(r)(1)

I2 = 1500r + 1500r^2

The total interest earned over the two years can be calculated by taking the amount in the account after two years, $1669.54, and subtracting the original principle, $1500, you get $169.54.

Therefore,

I1 + I2 = $169.54 and substituting

1500r + 1500r^2 + 1500r = $169.54 The equation is quadratic so

1500r^2 + 3000r - 169.54 = 0

From here use the quadratic formula(and your calculator) to find r = .055, so the interest rate is 5.5%

**Chapter 10, Review Exercises, problems 39 and 81.**

Problem 39: In the Solutions Guide, the number under the radical sign should be -11 rather than -9.

Problem 81: In the Solutions Guide, the height should be 6 rather than x. That change leads to a solution of x = 295 meters.