examview - q4 week 2 exponents and...
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Name: ________________________ Class: ___________________ Date: __________ ID: A
1
Q4 Week 2 HW Exponents and Equations
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Write (b)(b)(b)(b)(b) in exponential form.
a. 5bc. b
−5
b. b5
d. b6
____ 2. Write 2 × 2 × 2 × 2 in exponential form.
a. 42c. 25
b. 23d. 24
____ 3. Write 3 in exponential form.
a. 30 c. 31
b. 13 d. 32
____ 4. Evaluate (−2)2.
a. 0 c. –4
b. 22 d. 4
____ 5. Evaluate ax
− (b • c) ÷ d for a = 7, b = 3, c = 2, d = 6, and x = 2.
a. 35 c. 7.5
b. 48 d. 7.2
____ 6. Evaluate (6)−2.
a. –36 c. –1
36
b.1
36d. 36
____ 7. Evaluate ax
− (b + c)y for a = 4, b = 2, c = 8, x = –1, and y = –2.
a.1
24c. –96
b.3
25d.
6
25
____ 8. Simplify 6w
0r
−5
t−7
.
a.6r
5
t7
b.6t
7
r5
c. 6wr5t
7d.
6
r5t
7
____ 9. Multiply. Write the product as a power.
125• 122
a. 1210c. 127
b. Cannot combine d. 123
Name: ________________________ ID: A
2
____ 10. Divide. Write the quotient as a power.
139
135
a. 134c. 1314
b. Cannot combine d. 52
____ 11. Simplify (99 )−8.
a. 91c. 81−8
b. 9−72d. 917
____ 12. Simplify (x2 )−4x
4.
a.1
x−4
b. x−32
c. x−4
d. x−8
____ 13. Write the number 6.54 × 107 in standard notation.
a. 0.000000654 c. 65,400,000
b. 6,540,000 d. 654,000,000
____ 14. Write the number 9.91 × 10−6 in standard notation.
a. 0.0000991 c. 0.00000991
b. 9,910,000 d. 0.000000991
____ 15. Write the number 230,000 in scientific notation.
a. 0.230 × 106c. 2.3 × 105
b. 2.30 × 106d. 23.0 × 104
____ 16. Write the number 0.000000001 in scientific notation.
a. 0.01 × 10−6c. 0.001 × 10−6
b. 00.1 × 10−8d. 1.0 × 10−9
____ 17. Suppose a sheet of 100 stamps is 0.77 millimeters thick. If a stack of sheets contains 100,000 stamps, how
many millimeters thick is the stack? Write the answer in scientific notation.
a. 7.7 × 104 mm c. 77.0 × 101
mm
b. 7.7 × 102 mm d. 0.77 × 103
mm
____ 18. If an average grape weighs 4.87 grams and a company purchases 1,000,000 grapes, how much will the grape
shipment weigh in kilograms? Write the answer in scientific notation.
a. 4.87 × 106 kg c. 4.87 × 103
kg
b. 48.7 × 102 kg d. 0.487 × 104
kg
____ 19. The attendance at a parade was 6.73 × 104 people. The attendance at a rally was 6.75 × 104
people. Which event had the higher attendance?a. rally b. parade
Name: ________________________ ID: A
3
____ 20. The attendance at a college football game was 1.27 × 105 people. The attendance at a World Cup soccer
match was 1.22 × 105 people. Which event had the higher attendance?
a. soccer match b. football game
____ 21. Find the two square roots of the number 144.
a. 36, –36 c. 11, –11
b. 72, –72 d. 12, –12
____ 22. A square room has a tiled floor with 81 square tiles. How many tiles are along an edge of the room?
a. 9 tiles c. 40 tiles
b. 11 tiles d. 20 tiles
____ 23. A square mosaic is made of small glass squares. If there are 196 small squares in the mosaic, how many are along an edge?
a. 98 squares c. 14 squares
b. 49 squares d. 16 squares
____ 24. Evaluate the expression −4 −14 + 50 . If necessary, round your answer to the nearest tenth.
a. 50 c. 32
b. –24 d. –28.3
____ 25. The square root 103 is between two integers. Name the integers.
a. 102, 104 c. 10, 11
b. 15, 16 d. 25, 26
____ 26. Elena needs to cut a square piece of wood with an area of 69 square inches. How long should the sides of the square be, rounded to the nearest tenth of an inch?
a. 7 in. c. 34.5 in.
b. 8.3 in. d. 17.3 in.
____ 27. A chessboard is made of 64 small squares. Suppose a single square on a chessboard has an area of 6 square
centimeters. How long is one side of the entire board, rounded to the nearest tenth of a centimeter?
a. 2.4 cm c. 9.8 cm
b. 156.8 cm d. 19.6 cm
____ 28. Use a calculator to find 304 . Round your answer to the nearest tenth.
a. 17.44 c. 17.02
b. 13.2 d. 17.4
____ 29. Classify the number 16
2 as rational or irrational.
a. irrational b. rational
____ 30. Classify the number 43
8 as rational, irrational, or not a real number.
a. irrational b. not a real number c. rational
Name: ________________________ ID: A
4
____ 31. Graph the numbers 5 , 1.7, 25 , 1
2, and π on a number line. Then, order the numbers from least to
greatest.
a.
25 , 5 , 1
2, π , and 1.7
b.
1
2, 1.7, 5 , π , and 25
c.
25 , π , 5 , 1.7, and 1
2
d.
1
2, 5 , 25 , 1.7, and π
____ 32. Harry and Selma start driving from the same location. Harry drives 42 miles north while Selma drives 144 miles east. How far apart are Harry and Selma when they stop?
a. 1,764 mi c. 22,500 mi
b. 150 mi d. 20,736 mi
____ 33. A community is building a square park with sides that measure 80 meters. To separate the picnic area from
the play area, the park is split by a diagonal line from opposite corners. Determine the approximate length of the diagonal line that splits the square. If necessary, round your answer to the nearest meter.
a. 12,800 m c. 160 m
b. 80 m d. 113 m
____ 34. Combine like terms.
2z + 9 – z + 3
a. –2z + 27 c. z + 12
b. 3z + 6 d. z + 6
____ 35. Combine like terms.
8x + 5z – 4x + 3z + 6.
a. 4x + 8z c. 4x + 8z + 6
b. –32x + 15z + 6 d. 12x + 2z + 6
Name: ________________________ ID: A
5
____ 36. Simplify.
9(4t + 6) + 3t
a. 33t + 54 c. 39t – 54
b. 39t + 54 d. 39t + 6
____ 37. Solve.
10y – 2y = 64
a. y = 56 c. y = 51
3
b. y = 8 d. y = 72
____ 38. Simplify and solve.3(9 − 8x − 4x) + 8(3x + 4) = 11
a. x = 3 c. x = 24b. x = 4 d. x = 5
____ 39. Solve.
–2z + 3 + 7z = –12
a. z = –3 c. z = 1
b. z = –15 d. z = –1.8
____ 40. Solve.z
32+
5
8=
13
16
a. z = 13 c. z = 46
b. z = 6 d. z = 1
4
____ 41. The Sanchez family had dinner at their favorite restaurant. A 9% sales tax was added to their bill. Amy paid
the bill with a $10 gift certificate plus $30.60. How much did the family’s dinner cost before tax? Round your answer to the nearest penny.
a. $43.25 c. $35.95
b. $37.25 d. $36.95
____ 42. Carlos works part time as a salesperson for an electronics store. He earns $7.50 per hour plus a percent
commission on all of his sales. Last week Carlos worked 15 hours and earned a gross income of $270.63. If
his total sales for the week were $2,750, what percent commission does Carlos earn? If necessary, round your answer to the nearest hundredth of a percent.
a. 0.06% c. 6.75%
b. 5.75% d. 1.04%
____ 43. Solve 3.8y +4
7x + 2 = 0 for y.
a. y = −4
7x − 2 c. y = −
76
35x −
38
5
b. y = −20
133x −
10
19d. y = −
10
19
____ 44. Solve.
8a – 10 = 6a
a. a = –0.3 c. a = 2
b. a = 5 d. a = 0
Name: ________________________ ID: A
6
____ 45. Solve.
4v – 13 – 10v = 12 – 24v + 5
a. v = 12
3c. v =
18
29
b. v = 18
31d. v =
3
5
____ 46. Solve.
y
3+
8y
4−
3
6= y +
7
2
a. y = 16
49c. y = 3
b. y = 1
3d. y =
17
48
____ 47. A local water park has two types of season passes. Plan A costs a one-time fee of $142 for admission plus
$10 for parking every trip. Plan B costs a one-time fee of $48 for parking plus $22 for admission every trip.
How many visits must a person make for plan A and plan B to be equal in value?
a. 8 c. 16
b. 7 d. 3
____ 48. Solve the system of equations.
y = 5x + 4
y = 7x + 6
Ï
ÌÓ
ÔÔÔÔÔÔÔÔÔÔ
a. (–1, 11) c. (–1, –1)
b. (–1, –1) d. (–4, –1)
____ 49. Solve the system of equations.
−x + 2y = 2
−x + y = −1
Ï
ÌÓ
ÔÔÔÔÔÔÔÔÔÔ
a. −4,−3ÊËÁÁ ˆ
¯˜̃ c. 4,3Ê
ËÁÁ ˆ
¯˜̃
b. −4,3ÊËÁÁ ˆ
¯˜̃ d. 4,−3Ê
ËÁÁ ˆ
¯˜̃
ID: A
1
Q4 Week 2 HW Exponents and Equations
Answer Section
MULTIPLE CHOICE
1. ANS: BIdentify how many times (b) is a factor.
(b)(b)(b)(b)(b) = b5
Feedback
A Check that you are not using the base as the exponent.
B Correct!
C Check the sign on the exponent.
D The exponent tells the number of times the base is used as a factor.
PTS: 1 DIF: Basic REF: Page 162 OBJ: 4-1.1 Writing ExponentsNAT: 8.5.3.c TOP: 4-1 Exponents KEY: exponent | write
2. ANS: D
Identify how many times (? ? ) is a factor.
2 × 2 × 2 × 2 = 24
Feedback
A Check that you are not using the base as the exponent.
B The exponent tells the number of times the base is used as a factor.
C Count the factors.
D Correct!
PTS: 1 DIF: Basic REF: Page 162 OBJ: 4-1.1 Writing ExponentsNAT: 8.5.3.c TOP: 4-1 Exponents KEY: exponent | write
3. ANS: C
Identify how many times (3) is a factor.
3 = 31
Feedback
A Use the correct exponent.
B Check that you are not using the base as the exponent.
C Correct!
D The exponent represents how many times the base is used as factor.
PTS: 1 DIF: Average REF: Page 162 OBJ: 4-1.1 Writing ExponentsNAT: 8.5.3.c TOP: 4-1 Exponents KEY: exponent | write
ID: A
2
4. ANS: D
The exponent tells the number of times to multiply the base by itself.
(−2)2 = 4
Feedback
A Multiply the base by itself instead of adding.
B Multiply the base to find the answer. The exponent tells how many times to multiply the base by itself.
C The exponent tells the number of times to multiply the base by itself.
D Correct!
PTS: 1 DIF: Average REF: Page 162 OBJ: 4-1.2 Evaluating PowersNAT: 8.5.3.c TOP: 4-1 Exponents KEY: exponent | power | evaluate
5. ANS: B
First, substitute a = 7, b = 3, c = 2, d = 6, and x = 2.Then, multiply inside the parentheses. Next, evaluate the exponent.Then, divide from left to right. Finally, subtract from left to right.
72− (3 • 2) ÷ 6
= 72− 6 ÷ 6
= 49 − 6 ÷ 6= 48
Feedback
A First, substitute the given values. Then, use the order of operations and simplify.
B Correct!
C Use the order of operations.
D Multiply and divide before subtracting.
PTS: 1 DIF: Average REF: Page 163 OBJ: 4-1.3 Using the Order of OperationsNAT: 8.5.3.c TOP: 4-1 Exponents
6. ANS: BAny number except 0 with a negative exponent equals its reciprocal with the opposite exponent. A power with a negative exponent equals 1 divided by that power with its opposite exponent.
Feedback
A Check the sign of the exponent.
B Correct!
C First, write the reciprocal, and change the sign of the exponent. Then, find the product and simplify.
D The reciprocal of a number is 1 divided by that number.
PTS: 1 DIF: Average REF: Page 167 OBJ: 4-2.2 Evaluating Negative Exponents NAT: 8.5.3.cTOP: 4-2 Look for a Pattern in Integer Exponents KEY: negative exponent | evaluate
ID: A
3
7. ANS: D
First, substitute a = 4, b = 2, c = 8, x = –1, and y = –2.Then, add inside the parentheses. Next, evaluate the exponents. Finally, subtract from left to right.
4−1− (2 + 8)−2
= 4−1− (10)−2
= 1
4−
1
100
= 6
25
Feedback
A Use the order of operations.
B First, substitute the given values. Then, use the order of operations and simplify.
C Write the number with a negative exponent as the reciprocal with an opposite exponent.
D Correct!
PTS: 1 DIF: Average REF: Page 167 OBJ: 4-2.3 Using the Order of OperationsNAT: 8.5.3.c TOP: 4-2 Look for a Pattern in Integer Exponents
8. ANS: B
6w0r
−5
t−7
= 6 • 1 • r−5
•1
t−7 Rewrite
6w0r
−5
t−7
without negative or zero exponents.
= 6 • 1 •1
r5
•1
t−7
Simplify each part of the expression. r−5
=1
r5
.
= 6 • 1 •1
r5
• t7 1
t−7
= t7.
= 6t
7
r5
Feedback
A Any number to the zero power is equal to 1. A negative exponent in the numerator becomes positive in the denominator.
B Correct!
C Any number to the zero power is equal to 1. A negative exponent in the numerator becomes positive in the denominator.
D A negative exponent in the denominator becomes positive in the numerator.
PTS: 1 DIF: Advanced NAT: 8.1.3.a TOP: 4-2 Look for a Pattern in Integer Exponents
ID: A
4
9. ANS: C
To multiply powers with the same base, keep the base and add the exponents.
Feedback
A To multiply powers with the same base, keep the base and add the exponents.
B Check whether the bases are the same.
C Correct!
D To multiply powers with the same base, keep the base and add the exponents.
PTS: 1 DIF: Basic REF: Page 170 OBJ: 4-3.1 Multiplying Powers with the Same Base NAT: 8.5.3.cTOP: 4-3 Properties of Exponents KEY: exponent | power | multiplication | base
10. ANS: A
To divide powers with the same base, keep the base and subtract the exponents.
Feedback
A Correct!
B Check whether the bases are the same.
C To divide powers with the same base, keep the base and subtract the exponents.
D To divide powers with the same base, keep the base and subtract the exponents.
PTS: 1 DIF: Basic REF: Page 171 OBJ: 4-3.2 Dividing Powers with the Same Base NAT: 8.5.3.cTOP: 4-3 Properties of Exponents KEY: exponent | power | division | base
11. ANS: B
(99 )−8
= 99 • −8 Multiply the exponents.
= 9−72
Feedback
A Multiply the exponents, not add.
B Correct!
C To raise a power to a power, keep the base and multiply the exponents.
D Multiply the exponents, not subtract.
PTS: 1 DIF: Average REF: Page 171 OBJ: 4-3.3 Raising a Power to a PowerNAT: 8.5.3.c TOP: 4-3 Properties of Exponents
ID: A
5
12. ANS: C
(x2 )−4x
4
= x2 −4( )
x4 Multiply the exponents.
= x−8
x4
= x−8 + 4 Add the exponents.
= x−4
Feedback
A When you write the reciprocal, the sign of the exponent changes.
B To raise a power to a power, keep the base and multiply the exponents.
C Correct!
D To multiply powers with the same base, keep the base and add the exponents.
PTS: 1 DIF: Advanced NAT: 8.5.3.c TOP: 4-3 Properties of Exponents
13. ANS: CA positive exponent means move the decimal point to the right. A negative exponent means move the decimal point to the left.
Feedback
A A positive exponent means move the decimal point to the right.
B Move the decimal point the correct number of places.
C Correct!
D Move the decimal point the correct number of places.
PTS: 1 DIF: Average REF: Page 174 OBJ: 4-4.1 Translating Scientific Notation to Standard Notation NAT: 8.1.1.f TOP: 4-4 Scientific Notation KEY: scientific notation | standard notation
14. ANS: C
A positive exponent means move the decimal point to the right. A negative exponent means move the decimal point to the left.
Feedback
A Move the decimal point the correct number of places.
B A negative exponent means move the decimal point to the left.
C Correct!
D Move the decimal point the correct number of places.
PTS: 1 DIF: Average REF: Page 174 OBJ: 4-4.1 Translating Scientific Notation to Standard Notation NAT: 8.1.1.f TOP: 4-4 Scientific Notation KEY: scientific notation | standard notation
ID: A
6
15. ANS: C
To write a number in scientific notation, write it as the product of a power of ten and a number greater than or equal to 1 but less than 10.
Feedback
A The first part is a number greater than or equal to 1 but less than 10.
B Count how many places the decimal point is moved.
C Correct!
D The first part is a number greater than or equal to 1 but less than 10.
PTS: 1 DIF: Average REF: Page 175 OBJ: 4-4.2 Translating Standard Notation to Scientific Notation NAT: 8.1.1.f TOP: 4-4 Scientific Notation KEY: scientific notation | standard notation
16. ANS: DTo write a number in scientific notation, write it as the product of a power of ten and a number greater than or equal to 1 but less than 10.A number less than 1 will have a negative exponent when written in scientific notation.
Feedback
A Count how many places the decimal point is moved.
B The first part is a number greater than or equal to 1 but less than 10.
C The first part is a number greater than or equal to 1 but less than 10.
D Correct!
PTS: 1 DIF: Average REF: Page 175 OBJ: 4-4.2 Translating Standard Notation to Scientific Notation NAT: 8.1.1.f TOP: 4-4 Scientific Notation KEY: scientific notation | standard notation
17. ANS: BTo write a number in scientific notation, write it as the product of a power of ten and a number greater than or equal to 1 but less than 10.
The stack will be 7.7 × 102 mm thick.
Feedback
A There are 100 stamps per sheet. Calculate the thickness correctly.
B Correct!
C The first part is a number greater than or equal to 1 but less than 10.
D The first part is a number greater than or equal to 1 but less than 10.
PTS: 1 DIF: Average REF: Page 175 OBJ: 4-4.3 ApplicationNAT: 8.1.1.f TOP: 4-4 Scientific Notation KEY: scientific notation | standard notation | expression | evaluate
ID: A
7
18. ANS: C
To write a number in scientific notation, write it as the product of a power of ten and a number greater than or equal to 1 but less than 10.
The shipment would weigh 4.87 × 103 kg.
Feedback
A There are 1000 grams in a kilogram. Calculate the weight correctly.
B The first part is a number greater than or equal to 1 but less than 10.
C Correct!
D The first part is a number greater than or equal to 1 but less than 10.
PTS: 1 DIF: Average REF: Page 175 OBJ: 4-4.3 ApplicationNAT: 8.1.1.f TOP: 4-4 Scientific Notation KEY: scientific notation | standard notation | expression | evaluate
19. ANS: ACompare the powers of 10. Then compare the values between 1 and 10.
6.73 × 104 < 6.75 × 104
Feedback
A Correct!
B First, compare the powers of 10. Then, compare the values between 1 and 10.
PTS: 1 DIF: Basic REF: Page 176 OBJ: 4-4.4 ApplicationNAT: 8.1.1.f TOP: 4-4 Scientific Notation
20. ANS: BCompare the powers of 10. Then compare the values between 1 and 10.
1.27 × 105 > 1.22 × 105
Feedback
A First, compare the powers of 10. Then, compare the values between 1 and 10.
B Correct!
PTS: 1 DIF: Basic REF: Page 176 OBJ: 4-4.4 ApplicationNAT: 8.1.1.f TOP: 4-4 Scientific Notation
ID: A
8
21. ANS: D
The square root of a number is another number that, when multiplied by itself, equals the first number.12 is a square root, since 12 • 12 = 144.
–12 is also a square root, since −12 • −12 = 144.
Feedback
A Multiply these numbers by themselves to see if they equal the original number.
B The square root of a number is another number that, when multiplied by itself, equals the first number.
C Check your calculations.
D Correct!
PTS: 1 DIF: Basic REF: Page 182 OBJ: 4-5.1 Finding the Positive and Negative Square Roots of a NumberNAT: 8.5.3.b TOP: 4-5 Squares and Square Roots KEY: square | square root | positive | negative
22. ANS: A
Find the square root of 81.
81 = 9, since 9 • 9 = 81.
There are 9 tiles along the edge.
Feedback
A Correct!
B Check your calculations.
C Find the square root of the number of tiles in the room.
D Multiply this number by itself to check your answer.
PTS: 1 DIF: Average REF: Page 183 OBJ: 4-5.2 ApplicationNAT: 8.5.3.b TOP: 4-5 Squares and Square Roots KEY: square | square root | perfect square
23. ANS: C
Find the square root of 196.
196 = 14, since 14 • 14 = 196.
There are 14 squares along the edge.
Feedback
A Find the square root of the number of glass squares in the mosaic.
B Multiply this number by itself to check your answer.
C Correct!
D Check your calculations.
PTS: 1 DIF: Average REF: Page 183 OBJ: 4-5.2 ApplicationNAT: 8.5.3.b TOP: 4-5 Squares and Square Roots KEY: square | square root | perfect square
ID: A
9
24. ANS: B
First, evaluate the square root. Use the order of operations, and add the numbers under the square root symbol. Then, take the square root of the sum, and multiply the result by the number outside the square root.
Feedback
A Use the order of operations, and evaluate everything under the square root symbol first.
B Correct!
C Evaluate everything under the square root symbol first.
D Use the order of operations.
PTS: 1 DIF: Average REF: Page 183 OBJ: 4-5.3 Evaluating Expressions Involving Square Roots NAT: 8.5.3.cTOP: 4-5 Squares and Square Roots KEY: square | square root | expression | evaluate
25. ANS: C
Find two perfect squares close to 103.
102= 100
112= 121
So, 103 is between 10 and 11.
Feedback
A Think of two perfect squares close to the number.
B Check your calculations.
C Correct!
D Think of two perfect squares close to the number.
PTS: 1 DIF: Basic REF: Page 186 OBJ: 4-6.1 Estimating Square Roots of Numbers NAT: 8.1.2.dTOP: 4-6 Estimating Square Roots KEY: square | square root | estimate
26. ANS: BUse the square root of the area to find the length of the sides.
69 ≈ 8.3
The sides should be 8.3 inches long.
Feedback
A Check your calculations.
B Correct!
C Find the square root of the area.
D Use the square root of the area to find the length of the sides.
PTS: 1 DIF: Average REF: Page 186 OBJ: 4-6.2 Problem-Solving ApplicationNAT: 8.1.2.d TOP: 4-6 Estimating Square Roots KEY: square | square root | estimate
ID: A
10
27. ANS: D
Take the square root of the area to get the length of a single square. There are 64 = 8 squares along the
side of a chessboard, so multiply the side length of a single square by 8.
6 ≈ 2.4495
2.4495 × 8 ≈ 19.6
The sides are 19.6 cm long.
Feedback
A Include all of the squares along the edge of a chessboard.
B Check your calculations.
C First, take the square root of the area to get the length of a single square. Then, multiply the result by the side length of a single square.
D Correct!
PTS: 1 DIF: Average REF: Page 186 OBJ: 4-6.2 Problem-Solving ApplicationNAT: 8.1.2.d TOP: 4-6 Estimating Square Roots KEY: square | square root | estimate
28. ANS: D
304 ≈ 17.435596 ≈ 17.4
Feedback
A Round your answer to the correct place.
B Use a calculator to help you.
C Use a calculator to help you.
D Correct!
PTS: 1 DIF: Basic REF: Page 187 OBJ: 4-6.3 Using a Calculator to Estimate the Value of a Square Root NAT: 8.1.2.d TOP: 4-6 Estimating Square Roots KEY: square | square root | estimate | calculator
29. ANS: BA rational number can be written as a fraction. Rational numbers include integers, fractions, terminating decimals, and repeating decimals.An irrational number can only be written as decimals that do not terminate or repeat.
Feedback
A A rational number will terminate or repeat, but an irrational number will not.
B Correct!
PTS: 1 DIF: Basic REF: Page 191 OBJ: 4-7.1 Classifying Real NumbersNAT: 8.1.1.b TOP: 4-7 The Real Numbers KEY: real number | classify | rational number | irrational
ID: A
11
30. ANS: A
Fractions with a denominator of 0 and square roots of negative numbers are not real numbers.A rational number can be written as a fraction with a non-zero denominator. Rational numbers include integers, fractions, terminating decimals, and repeating decimals.An irrational number cannot be expressed as a terminating decimal or repeating decimal.
Feedback
A Correct!
B Irrational numbers cannot be expressed with a finite number of digits.
C Dividing by a 0 or taking the square root of a negative number will not produce a real number.
PTS: 1 DIF: Average REF: Page 192 OBJ: 4-7.2 Determining the Classification of All Numbers NAT: 8.1.1.bTOP: 4-7 The Real Numbers KEY: real number | classify | rational number | irrational
31. ANS: BWrite all the numbers in decimal form, and then graph them. From left to right on the number line, the numbers appear from least to greatest.
Feedback
A Write all the numbers in decimal form, and then graph them.
B Correct!
C Order the numbers from least to greatest, not greatest to least.
D Write all the numbers in decimal form, and then graph them.
PTS: 1 DIF: Advanced NAT: 8.1.1.b TOP: 4-7 The Real Numbers
32. ANS: B
Use the Pythagorean Theorem: a2
+ b2
= c2.
First, substitute for a and b. Then, simplify the powers, and add. Finally, find the square root.
a2
+ b2
= c2
422+ 1442
= c2
22,500 = c2
22,500 = c
150 = c
Harry and Selma are 150 miles apart.
Feedback
A Substitute for a and b in the Pythagorean Theorem, and then simplify.
B Correct!
C There is one more step before the getting the answer. Take the square root of this number.
D Use the Pythagorean Theorem.
PTS: 1 DIF: Average REF: Page 197 OBJ: 4-8.3 Using the Pythagorean Theorem for Measurement NAT: 8.3.3.dTOP: 4-8 The Pythagorean Theorem
ID: A
12
33. ANS: D
Since the park is square and the diagonal line stretches between opposite corners, the length of the diagonal line is the hypotenuse of a right triangle. Use the Pythagorean Theorem, a2 + b2 = c2, to solve this problem.Let c = the length of the diagonal.
802+ 802
= c2
12,800 = c2
113 ≈ cThe diagonal is about 113 meters long.
Feedback
A Take the square root after you add the squares of the lengths of the legs.
B Use the Pythagorean Theorem to find the length of the diagonal.
C Use the Pythagorean Theorem to find the length of the diagonal.
D Correct!
PTS: 1 DIF: Advanced NAT: 8.3.3.d TOP: 4-8 The Pythagorean TheoremKEY: Pythagorean Theorem | right triangle | diagonal
34. ANS: C
Example:7k + 5 – k – 2
(7k – k) + (5 – 2) Group like terms.6k + 3 Add or subtract the coefficients.
Feedback
A Did you multiply the numbers together, rather than adding them?
B Did you use the proper signs for all the numbers?
C Correct!
D Did you use the proper signs for the terms with no variables?
PTS: 1 DIF: Basic REF: Page 584 OBJ: 11-1.1 Combining Like Terms to Simplify NAT: 8.5.3.cTOP: 11-1 Simplifying Algebraic Expressions KEY: like terms | simplify | combine
ID: A
13
35. ANS: C
Example:Simplify 8a + 5t – 4a – 4t – 2(8a – 4a) + (5t – 4t) – 2 Group like terms.
4a + t – 2 Add or subtract the coefficients.
Feedback
A Did you forget to put one of the terms in your answer?
B Did you multiply the coefficients together, rather than adding them?
C Correct!
D Did you use the proper signs for all the coefficients?
PTS: 1 DIF: Basic REF: Page 585 OBJ: 11-1.2 Combining Like Terms in Two-Variable Expressions NAT: 8.5.3.c TOP: 11-1 Simplifying Algebraic Expressions KEY: like terms | simplify | combine | two-variable expression
36. ANS: BExample:Simplify 9(10a – 7) + 5a.
90a – 63 + 5a Multiply.(90a + 5a) – 63 Group like terms.
95a – 63 Add or subtract the coefficients.
Feedback
A After grouping like terms did you add and subtract the coefficients correctly?
B Correct!
C Did you use the proper sign for the number that has no variable?
D Did you multiply through for all the terms in the parentheses?
PTS: 1 DIF: Average REF: Page 585 OBJ: 11-1.3 Using the Distributive Property to Simplify NAT: 8.1.5.eTOP: 11-1 Simplifying Algebraic Expressions KEY: like terms | simplify | combine | algebraic expression
ID: A
14
37. ANS: B
Example:Solve 9x + 2x = 77
11x = 77 Combine like terms.
11x
11 =
77
11Divide both sides by 11 to isolate x.
x = 7
Feedback
A Did you use division to solve this problem?
B Correct!
C Should you be adding or subtracting the coefficients?
D How do you undo multiplication?
PTS: 1 DIF: Average REF: Page 585 OBJ: 11-1.4 Combining Like Terms to Solve Algebraic Equations NAT: 8.5.3.c TOP: 11-1 Simplifying Algebraic Expressions KEY: like terms | simplify | combine | equation
38. ANS: B
3(9 − 8x − 4x) + 8(3x + 4) = 11
27 − 24x − 12x + 24x + 32 = 11 Distributive Property
59 − 12x = 11Combine Coefficients.27 + 32 = 59−24 − 12 + 24 = −12
59 − 12x = 11 Subtract 59 from both sides.−59 −59
− 12x = –48 Simplify.
−12x
12=
−48
12Divide both sides by 12.
x = 4 Simplify.
Feedback
A After removing the parenthesis and combining like terms, isolate the variable x.
B Correct!
C A negative number minus a negative number is the sum of two negative numbers.
D First use the distributive property to remove the parentheses.
PTS: 1 DIF: Advanced NAT: 8.5.4.a TOP: 11-1 Simplifying Algebraic Expressions
ID: A
15
39. ANS: A
To solve this equation, combine like terms and use the inverse operation to isolate the variable from the addition/subtraction. Then use division as the inverse operation to isolate the variable from the multiplication.
Feedback
A Correct!
B How do you combine like terms?
C Did you use inverse operations to solve?
D How do you solve multi-step equations?
PTS: 1 DIF: Basic REF: Page 588 OBJ: 11-2.1 Solving Equations That Contain Like Terms NAT: 8.5.4.aTOP: 11-2 Solving Multi-Step Equations KEY: equation | like terms | solving
40. ANS: BTo solve this equation, multiply both sides of it by the least common denominator to clear the fraction. Use the inverse operation to isolate the variable from the addition/subtraction. Then use division as the inverse operation to isolate the variable from the multiplication.
Feedback
A How do you solve multi-step equations?
B Correct!
C Did you use inverse operations to solve the equation?
D Did you clear the fractions?
PTS: 1 DIF: Average REF: Page 588 OBJ: 11-2.2 Solving Equations That Contain Fractions NAT: 8.5.4.aTOP: 11-2 Solving Multi-Step Equations KEY: fraction | multi-step equation | solving
ID: A
16
41. ANS: B
price of dinner + (price of dinner • % sales tax) = amount of gift certificate + amount paidSubstitute values and solve. Example: The family paid 8% sales tax and paid with a $25 gift certificate plus $39.30.
Let p represent the price of the dinner.
p + p • 0.08ÊËÁÁ ˆ
¯˜̃ = 25.00 + 39.30
1.08p = 64.30
1.08p
1.08=
64..30
1.08
p = 59.53703 ≈ 59.54
Feedback
A How do you find the percent?
B Correct!
C Did you remember to account for the gift certificate?
D Did you account for the sales tax?
PTS: 1 DIF: Average REF: Page 589 OBJ: 11-2.3 ApplicationNAT: 8.5.4.a TOP: 11-2 Solving Multi-Step Equations KEY: multi-step equation | solving
ID: A
17
42. ANS: B
Sample:Aaron earns $5.25 per hour. Last week he worked 25 hours, had sales of $1,700, and earned a gross income of $195.
Set up an equation relating the hourly income, the commission, and the total income:
hourly income + commission = total income
Let p represent the percent commission and substitute known values:
5.25(25) + 1,700p = 195
131.25 + 1,700p = 195
1,700p = 63.75
p = 0.0375
p = 3.75%
He earns a 3.75% commission on sales.
Feedback
A How do you convert a decimal to a percent?
B Correct!
C How are the hourly income, the amount of commission, and the gross income related?
D Did you remember to check your addition?
PTS: 1 DIF: Average REF: Page 589 OBJ: 11-2.3 ApplicationNAT: 8.5.4.a TOP: 11-2 Solving Multi-Step Equations KEY: multi-step equation | solving
ID: A
18
43. ANS: B
3.8y +4
7x + 2 = 0
3.8y +4
7x = −2 Subtract 2 from both sides.
3.8y = −4
7x − 2 Subtract the
4
7x term from both sides.
38
10y = −
4
7x − 2 Rewrite 3.8 as
38
10.
y =10
38−
4
7x − 2
Ê
ËÁÁÁ
ˆ
¯˜̃˜ Multiply by
10
38.
y = −40
266x −
20
38 Distribute.
y = −20
133x −
10
19 Simplify.
Feedback
A Divide all terms by 3.8.
B Correct!
C Multiply by the reciprocal of 3.8.
D Keep the x term in the equation.
PTS: 1 DIF: Advanced NAT: 8.5.4.a TOP: 11-2 Solving Multi-Step Equations
44. ANS: BUse inverse operations to group terms with variables on the same side of the equation, and simplify by using addition/subtraction. After the like terms are on one side of the equation and the equation is simplified, divide by the like terms to get the correct value for the variable.
Feedback
A Did you combine like terms?
B Correct!
C Did you divide the like terms correctly?
D Did you use the correct inverse operations to solve?
PTS: 1 DIF: Basic REF: Page 593 OBJ: 11-3.1 Solving Equations with Variables on Both Sides NAT: 8.5.4.aTOP: 11-3 Solving Equations with Variables on Both Sides KEY: equation | solving
ID: A
19
45. ANS: A
Use inverse operations to group terms with variables on the same side of the equation and to group the constant values on the opposite side of the equation. Then use division as the inverse operation to isolate the variable from the multiplication.
Feedback
A Correct!
B Should your first step be to combine like terms?
C Did you combine like terms properly?
D Did you use the correct inverse operations to solve?
PTS: 1 DIF: Average REF: Page 594 OBJ: 11-3.2 Solving Multi-Step Equations with Variables on Both SidesNAT: 8.5.4.a TOP: 11-3 Solving Equations with Variables on Both SidesKEY: multi-step equation | solving
46. ANS: CTo solve multi-step equations with variables on both sides, clear the fractions by multiplying the entire equation by the Least Common Denominator. Combine the like terms. Add or subtract variable terms to both sides of the equation so the variable occurs on only one side of the equation. Use division as the inverse operation to isolate the variable from the multiplication.
Feedback
A Did you combine the like terms correctly?
B Did you correctly isolate the variable?
C Correct!
D Did you combine the fractions correctly?
PTS: 1 DIF: Average REF: Page 594 OBJ: 11-3.2 Solving Multi-Step Equations with Variables on Both SidesNAT: 8.5.4.a TOP: 11-3 Solving Equations with Variables on Both SidesKEY: multi-step equation | solving
ID: A
20
47. ANS: A
Let n represent the number of trips to the park.
admission + (parking • n) = parking + (admission • n)
Use inverse operations to group terms with variables on the same side of the equation and to group the constant values on the opposite side of the equation. Then use division as the inverse operation to isolate the variable from the multiplication.
Feedback
A Correct!
B Should your first step be to combine like terms?
C Did you combine like terms properly?
D Did you use the correct inverse operations to solve?
PTS: 1 DIF: Average REF: Page 595 OBJ: 11-3.3 ApplicationNAT: 8.5.4.a TOP: 11-3 Solving Equations with Variables on Both SidesKEY: multi-step equation | solving
48. ANS: BTo solve a system of equations that are already simplified, you must substitute the first equation into the second equation. Then you can simplify the resulting equation by combining the like terms. Once the value of x has been found, you can substitute it into either of the two original equations in order to determine the y-value. Once you have an x- and y-value determined, you then put the values in the form (x, y).
Feedback
A Did you combine the like terms correctly?
B Correct!
C Did you insert the x-value into an original equation to solve for y?
D Did you combine the two equations correctly?
PTS: 1 DIF: Basic REF: Page 608 OBJ: 11-6.1 Solving Systems of Equations TOP: 11-6 Systems of EquationsKEY: solving | system of equations
ID: A
21
49. ANS: C
Solve the first equation for either variable x or y. Then substitute the result into the second equation, thus eliminating one of the variables, and simplify. Once the value of x or y has been found, you can substitute it into either of the two original equations in order to determine the other value. Then write the solution in the form (x, y).
Feedback
A Did you use the correct equation?
B Are you paying attention to the signs?
C Correct!
D Does the ordered pair solve both equations?
PTS: 1 DIF: Average REF: Page 609 OBJ: 11-6.2 Solving Systems of Equations by Solving for a Variable TOP: 11-6 Systems of Equations KEY: solving | system of equations
MATCHING