Name: ______________________

Class: _________________

Date: _________

ID: A

Algebra 1 Spring Semester Final Exam Review What is the simplified form of each expression? ____

1.

(1 point)

( −5.1 ) a. 1 ____

____

2.

3.

0

b.

0

b.

−

c.

–5.1

d.

–1

c.

–32

d.

1 32

d.

1 648

d.

64

d.

−12x y

8

d.

t

−60

d.

y

(1 point)

(−2)

−5

a.

10

1 32

(1 point) −2

−2

What is the value of 2x y for x = 3 and y = –2? 1 −4 a. b. 72 c. 2 ( −6 ) 18 What is each expression written using each base only once? ____

4.

(1 point) 8

3

4 ⋅4 11 a. 4

b.

12

11

c.

4

24

11

What is the simplified form of each expression? ____

5.

(1 point) 8

9

(−2x ) ⋅ 3y ⋅ 2x a.

12

3x y

9

4

b.

72

−12x y

9

c.

−12xy

21

12

What is the simplified form of the expression? ____

6.

(1 point)

t

8

a. ____

7.

0 ÁÊÁ t 10 ˜ˆ˜ ÁÁ ˜˜ Ë 

t

80

80

c.

t

60

c.

y

b.

t

b.

y

−8

(1 point)

ÊÁ −5 ˆ˜ −10 10 ÁÁ y ˜˜ y ÁË ˜ a.

y

−60

1

−150

9

Name: ______________________

ID: A

What is the simplified form of each expression? ____

8.

(1 point) 2

4 3

5

8 3

(3c d ) (2c d ) a.

21

216c d

36

b.

21

−216c d

36

c.

13

216c d

18

21

d.

8c d 27

36

What is the simplified form of each expression? ____

9.

(1 point)

c d

8

−12

−4

−8

c d a.

12

c d

4

b.

−4

c d

−4

c.

d d

−4

−12

d.

c

12

d

4

What is the simplified form of the expression? ____ 10.

(1 point)

ÊÁ 2 ÁÁ m ÁÁ ÁÁ Á 10j 5 Ë a. ____ 11.

ˆ˜ 2 ˜˜ ˜˜ ˜˜ ˜  4 10

10m j

b.

m

4

100j

10

c.

m

4

20j

10

4

d.

m 10j

(1 point)

Does the table represent an exponential function?

____ 12.

x y

1 –1

a.

yes

2 –8

3 –27

4 –64 b.

no

(1 point) 5

Does the rule y = −3x represent an exponential function? a. yes b. no ____ 13.

(1 point) x

Suppose a population of 160 crickets doubles in size every month. The function f(x) = 160 ⋅ 2 gives the population after x months. How many crickets will there be after 2 years? a. 2,684,354,560 crickets c. 7,680 crickets b. 640 crickets d. 640 crickets

2

Name: ______________________

ID: A

What is the graph of the function? ____ 14.

(1 point)

y = −2 ⋅ 5

____ 15.

x

a.

c.

b.

d.

(1 point)

Suppose the population of a town is 4,400 and is growing 2% each year. Predict the population after 7 years. a. b. c. d.

about about about about

31416 people 61,600 people 5,054 people 563,200 people

Find the balance in the account. ____ 16.

(1 point)

$1,000 principal earning 6.25%, compounded quarterly, after 7 years a. $29,750.00 c. $1,543.60 b. $1,114.64 d. $1,528.63

3

Name: ______________________ ____ 17.

ID: A

(1 point)

A boat costs $11,850 and decreases in value by 10% per year. How much will the boat be worth after 8 years? a. $5,101.04 b. $11,770.00 c. $4,590.93 d. $25,401.53 What is the sum or difference? ____ 18.

(1 point)

6x7 + 8x7 a. 14x7 ____ 19.

b.

–2x7

c.

14x1 4

d.

48x7

b.

–21x8

c.

–4x8

d.

10x8

c. d.

15 – 7u + 2u 2 + 11 u 3 5u 3 + 2u 2 – 7u + 15

c. d.

–3w2 – 7w – 6 –3w2 – w – 10

c. d.

2n 3 + 6n + 8 n 2 + 5n + 4

(1 point)

3x8 – 7x8 a. –4x1 6 Simplify the sum. ____ 20.

(1 point)

(8u 3 + 2u 2 + 7) + (3u 3 – 7u + 8) a. b.

5u 3 – 7u 2 + 2u – 15 11u 3 + 2u 2 – 7u + 15

Simplify the difference. ____ 21.

(1 point)

(2w2 – 4w – 8) – (5w2 + 3w – 2) a. 7w2 – w – 10 b. 7w2 + 7w + 6 Simplify the product. ____ 22.

(1 point)

2n(n 2 + 3n + 4) a. 2n 3 + 6n 2 + 8n b. 2n 3 + 3n + 4

Find the GCF of the terms of the polynomial. ____ 23.

(1 point)

30x3 + 16x5 a.

16x

b.

2x3

c.

4

2x5

d.

x3

Name: ______________________

ID: A

Factor the polynomial. ____ 24.

(1 point)

42w1 0 + 24w6 a. w6 (42w4 + 24) b. 6w6 (7w4 + 4)

c. d.

6(7w1 0 + 4w6 ) 6w5 (7w5 + 4w)

Simplify the product using the distributive property. ____ 25.

(1 point)

(5h − 3)(3h + 7) a. b. ____ 26.

2

15h − 44h + 21 2 15h − 26h − 21

2

c. d.

15h + 44h + 21 2 15h + 26h − 21

c. d.

−10h − 29h − 10 2 −10h + 29h − 10

c. d.

12x + 4x − 16 2 12x + 28x + 16

(1 point)

(−2h + 5)(5h − 2) a. b.

2

−10h − 21h + 10 2 −10h + 21h + 10

2

Simplify the product using FOIL. ____ 27.

(1 point)

(4x − 4)(3x − 4) a. b.

2

12x − 28x + 16 2 12x − 4x − 16

2

What is a simpler form of the expression? ____ 28.

(1 point)

(2n 2 + 5n + 4)(2n – 4) a. b.

4n 3 – 2n 2 + 28n – 16 4n 3 + 12n 2 – 2n – 16

c. d.

4n 3 + 2n 2 – 12n – 16 4n 3 + 18n 2 – 28n – 16

c. d.

64m + 16m + 1 2 64m + 16m − 1

What is a simpler form of each product? ____ 29.

(1 point)

(8m + 1)

2

a. b.

2

64m − 16m + 1 2 64m + 8m − 1

5

2

Name: ______________________

ID: A

What is a simpler form of the following expressions? ____ 30.

(1 point)

(7p – 8)(7p + 8) a. 49p 2 + 112p + 64 b. 49p 2 – 112p – 64

c. d.

49p 2 + 64 49p 2 – 64

What is the factored form of the following expressions? ____ 31.

(1 point)

d 2 + 12d + 32 a. (d + 8)(d + 4) b. (d – 8)(d – 4) ____ 32.

c. d.

(d – 8)(d + 4) (d + 8)(d – 4)

c. d.

(d – 8)(d – 10) (d + 8)(d – 10)

(1 point)

d 2 – 18d + 80 a. (d – 8)(d + 10) b. (d + 8)(d + 10)

What is the factored form of the expression? ____ 33.

(1 point)

10x2 + 41x + 40 a. (2x + 5)(5x – 8) b. (2x + 5)(5x + 8)

c. d.

(2x – 5)(5x + 8) (2x – 5)(5x – 8)

What is the factored form of the expression? ____ 34.

(1 point)

8g 2 + 6g – 9 a. (4g + 3)(2g + 3) b. (4g – 3)(2g – 3) ____ 35.

(4g + 3)(2g – 3) (4g – 3)(2g + 3)

c. d.

(3x – 2)(4x + 3) (3x + 2)(4x – 3)

(1 point)

12x2 + x – 6 a. (3x + 2)(4x + 3) b. (3x – 2)(4x – 3) ____ 36.

c. d.

(1 point)

The area of a rectangular pool is given by the trinomial 8y2 + 4y – 12. What are the possible dimensions of the pool? Use factoring. a. – 2y – 2 and –4y – 6 c. 2y – 2 and 4y + 6 b. 2y – 2 and 4y + 6 d. 2y + 2 and 4y – 6 What is the factored form of the expression? ____ 37.

(1 point)

60y2 – 51y – 72 a. (5y + 8)(4y – 3) b. 3(5y – 8)(4y + 3)

c. d.

6

3(5y + 8)(4y + 3) (5y – 8)(12y + 9)

Name: ______________________

ID: A

What is the factored form of the expression? ____ 38.

(1 point)

s2 – 16 a. (s – 4)(s – 4) b. (s + 4)(s + 4)

c. d.

(s – 4)(s + 4) (s – 4)(s + 6)

What is the factored form of the expression? ____ 39.

(1 point)

15g 3 + 20g 2 – 18g – 24 a. (5g 2 + 4)(3g – 6) b. (5g 2 – 6)(3g + 4)

c. d.

(5g 2 + 6)(3g – 4) (5g 2 – 4)(3g + 6)

What are the coordinates of the vertex of the graph? Is it a maximum or minimum? ____ 40.

(1 point)

a. b.

(2, 0); minimum (0, 2); minimum

c. d.

(2, 0); maximum (0, 2); maximum

Order the group of quadratic functions from widest to narrowest graph. ____ 41.

(1 point) 2

2

y = −5x , y = −x , y = −4x

____ 42.

2

2

2

2

c.

y = −5x , y = −4x , y = −x

2

2

2

d.

y = −4x , y = −x , y = −5x

a.

y = −x , y = −5x , y = −4x

b.

y = −x , y = −4x , y = −5x

2 2

2

2

2 2

(1 point)

How is the graph of y = –2x2 – 5 different from the graph of y = –2x2 ? a. It is shifted 5 unit(s) up. c. It is shifted 5 unit(s) left. b. It is shifted 5 unit(s) down. d. It is shifted 5 unit(s) right. 7

Name: ______________________ ____ 43.

ID: A

(1 point) 2

If an object is dropped from a height of 144 feet, the function h(t) = −16t + 144 gives the height of the object after t seconds. When will the object hit the ground? a. 1.5 s c. 6 s b. 3 s d. 9 s Graph the function. Identify the vertex and axis of symmetry. 44.

(1 point) 2

f(x) = x + 4x + 1

Solve the equation using square roots. ____ 45.

(1 point) 2

x − 81 = 0 a. − 9 , 9 b. –81, 81

c. d.

–9, 9 no real number solutions

Solve the equation using the Zero-Product Property. ____ 46.

____ 47.

(1 point)

(x − 9)(x + 7) = 0 a. 9, 7 b. –9, −7

c. d.

–1,1 9,−7

(1 point)

−9n(5n − 5) = 0 1 a. − , 1 9 b. 0, 1

d.

1 − , −1 9 0, −1

c. d.

–3, 9 –3, –9

c. d.

3, –2 3, 2

c.

What are the solutions of the equation? ____ 48.

(1 point) 2

z − 6z − 27 = 0 a. 3, 9 b. 3, –9 ____ 49.

(1 point) 2

3z + 3z − 6 = 0 a. 1, –2 b. 1, 2

8

Name: ______________________ ____ 50.

ID: A

(1 point) 2

x + 3x = 18 a. 3, –6

b.

–3, 6

c.

4.42, –4.42

d.

18.75, –21.75

Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. ____ 51.

(1 point) 2

x + 3 = −4x a. 1, 3 ____ 52.

b.

–1, –3

c.

1, –3

d.

1, –3

b.

–0.35, –8.65

c.

0.35, 8.65

d.

–0.35, 8.65

(1 point) 2

x + 3 = 9x a. 0.35, –8.65

How many real-number solutions does the equation have? ____ 53.

(1 point) 2

−7x + 6x + 3 = 0 a. one solution b. two solutions ____ 54.

c. d.

no solutions infinitely many solutions

c. d.

no solutions infinitely many solutions

c. d.

no solutions infinitely many solutions

(1 point) 2

−8x − 8x − 2 = 0 a. one solution b. two solutions ____ 55.

(1 point) 2

7x + 8x + 5 = 0 a. one solution b. two solutions

What is the length of the hypotenuse of the right triangle shown? ____ 56.

(1 point)

a.

28

b.

4

c.

9

20

d.

5.3

Name: ______________________

ID: A

What is the side length b in the triangle below? ____ 57.

(1 point)

a.

16

b.

8

c.

2.8

d.

23.3

Can the set of lengths be the side lengths of a right triangle? ____ 58.

(1 point)

8 f t, 15 f t, 17 f t a. no

b.

yes

c.

6

c.

5h k

d.

5

10h k

c.

12

30

c.

9

Simplify the radical expression. ____ 59.

(1 point)

72 a. ____ 60.

2

b.

2

2

d.

12

d.

6

(1 point) 4

250h k

____ 61.

6

5

a.

hk

125

b.

5

10h k

4

5

2

2

10k 4

5

(1 point)

2

10 ⋅ 3

a.

12

60

12 b.

5

120

120

Simplify the radical expression. ____ 62.

(1 point)

10 81 a.

10 9

b.

10 41

10

10

d.

10 9

Name: ______________________

ID: A

Simplify the expression. ____ 63.

____ 64.

(1 point)

2

6 +3

a.

14

96 6

b.

14

b.

−16

96

c.

5

96

c.

−52

d.

50

d.

−16

d.

6

6

(1 point)

2

6 −6

a.

−4

54 54

54

6

6

Solve the equation. Check your solution. ____ 65.

____ 66.

(1 point)

4=

p −2

a.

6

b.

36

c.

3

(1 point)

The number of eagles observed along a certain river per day over a two week period is listed below. What is a frequency table that represents the data? 1 3 2 5 10 8 9 15 0 7 12 13 6 18

a.

b.

Eagle s

Fre que ncy

Eagle s

Fre que ncy

0−4

2

0−4

4

5−9

3

5−9

5

10 − 14

4

10 − 14

3

15 − 19

5

15 − 19

2

Eagle s

Fre que ncy

Eagle s

Fre que ncy

0−4

4

0−4

5

5−9

5

5−9

4

10 − 14

2

10 − 14

2

15 − 19

3

15 − 19

3

c.

d.

11

Name: ______________________ ____ 67.

ID: A

(1 point)

The data below shows the average number of text messages a group of students send per day. What is a histogram that represents the data? 20 5 8 22 10 1 7 15 16 12 15 6 13 8

a.

c.

b.

d.

12

Name: ______________________

ID: A

Is the histogram uniform, symmetric, or skewed? ____ 68.

(1 point)

a. b. c. ____ 69.

uniform symmetric skewed

(1 point)

a. b. c.

uniform symmetric skewed

13

Name: ______________________ ____ 70.

ID: A

(1 point)

a. b. c.

uniform symmetric skewed

14

Name: ______________________ ____ 71.

ID: A

(1 point)

The data below shows the number of kilowatt hours of electricity used by the tenants of a small apartment building in a given month. What is a cumulative frequency table that represents the data? 80 85 86 90 96 75 66 70 99 65 70 99 70 73 64 92 72 81 88 91 93 69 77 82 Kilowatt

Fre que ncy

Fre que ncy

Hours

a.

60 − 69

7

24

70 − 79

4

24

80 − 89

5

24

90 − 99

6

24

Kilowatt

Fre que ncy

Cumulative Fre que ncy

Hours

b.

60 − 69

4

4

70 − 79

6

10

80 − 89

7

17

90 − 99

7

24

Kilowatt

Fre que ncy

Cumulative Fre que ncy

Hours

c.

60 − 69

7

7

70 − 79

4

11

80 − 89

7

18

90 − 99

6

24

Kilowatt

Fre que ncy

Cumulative Fre que ncy

Hours

d.

Cumulative

60 − 69

4

4

70 − 79

7

11

80 − 89

6

17

90 − 99

7

24

15

Name: ______________________

ID: A

Find the mean, median, and mode of the data set. Round to the nearest tenth. ____ 72.

(1 point)

test scores on a math exam: 88, 89, 65, 62, 83, 63, 84, 63, 74, 64, 71, 82, 66, 88, 79, 60, 86, 63, 93, 99, 60, 85 a. mean = 75.8, b. mean = 75.8, c. mean = 69.5, d. mean = 69.5, median = 79.5, median = 76.5, median = 76.5, median = 76.5, mode = 63 mode = 63 mode = 63 mode = 79.5 ____ 73.

(1 point)

Suppose that to make the golf team you need to scored 75, 74, 100, and 69 in your first 4 games game and still make the team? a. 88 c. b. 85 d. ____ 74.

score no more than 81 on average over 5 games. If you what is the highest score you can shoot in your 5th 87 89

(1 point)

The salaries of seven employees of a small company are $41,000, $50,000, $42,500, $35,000, $50,000, $44,000, and $48,500. Each of the employees receives a 4% raise. What are the mean, median, mode, and range of their new salaries? a. mean = 46,205.71 c. mean = 52,000 median = 45,760 median = 45,760 mode = 52,000 mode = 46,205.71 range = 15,600 range = 15,600 b. mean = 45,760 d. mean = 46,205.71 median = 46,205.71 median = 45,760 mode = 52,000 mode = 52,000 range = 445.71 range = 445.71 What are the minimum, first quartile, median, third quartile, and maximum of the data set? ____ 75.

(1 point)

60, 50, 130, 200, 180, 150, 100, 140 a. minimum 50; first quartile 80; median 135; third quartile 165; maximum 200 b. minimum 50; first quartile 107.5; median 150; third quartile 182.5; maximum 200 c. minimum 50; first quartile 80; median 135; third quartile 182.5; maximum 200 d. minimum 50; first quartile 65; median 150; third quartile 165; maximum 200

16

Name: ______________________

ID: A

Make a box-and-whisker plot of the data. ____ 76.

(1 point)

average daily temperatures in Tucson, Arizona, in December: 67, 57, 52, 51, 64, 58, 67, 58, 55, 59, 66, 50, 57, 62, 58, 50, 58, 50, 60, 63 a.

b.

c.

d.

Is each data set qualitative or quantitative? ____ 77.

(1 point)

favorite sports teams a. qualitative

b.

quantitative

Is each data set univariate or bivariate? ____ 78.

(1 point)

the number of hours surfing the web by students at your school a. univariate b. bivariate Identify the sampling method. ____ 79.

(1 point)

You want to determine the number of text messages students at your school make in a month. You randomly ask everyone in each of your classes. a. random c. stratified b. systematic d. none of these ____ 80.

(1 point)

You want to find how many students use public transportation. You interview every fifth teenager you see exiting a movie theater. a. random c. stratified b. systematic d. none of these

17

ID: A

Algebra 1 Spring Semester Final Exam Review Answer Section 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42.

ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS:

A B A A D C B A D B B B A C C C A A C B C A B B D D A C C D A C B D C B B C B D B B

PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS:

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

ID: A 43. ANS: B 44. ANS:

PTS: 1

axis of symmetry: x = −2 vertex: (–2, –3)

45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70.

PTS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS:

1 C D B C A A B C B A C C A B C C C D A D B C A A C B

PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS:

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2

ID: A 71. 72. 73. 74. 75. 76. 77. 78. 79. 80.

ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS:

D B C A A A A A C B

PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS:

1 1 1 1 1 1 1 1 1 1

3