Free Printable DP SL UNIT 1 - Summative Review Test

1.

Simplify the following radical: √32

a)

3√2

b)

4√8

c)

16√2

d)

4√2

2.

√24

a)

4√6

b)

2√6

c)

6√2

d)

2√12

3.

√125

a)

5√5

b)

25√5

c)

5√25

d)

5√2

4.

Add: 4√7 - 10 √7 + 7√7

a)

-6√7

b)

14√7

c)

-3√14

d)

√7

5.

a)

7√3

b)

Can't Simplify

c)

6√15

d)

6√3

6.

Simplify:
√6 ⋅√6

a)

√36

b)

2√3

c)

12

d)

6

7.

(-2√7)(3√28)

a)

-6√14

b)

6√13

c)

-84

d)

-78

8.

Simplify:
√10 ⋅ √45

a)

3√50

b)

8√2

c)

√450

d)

15√2

9.

$4\sqrt{6}\cdot\sqrt{3}$

a)

$4\sqrt{9}$

b)

$\sqrt{72}$

c)

$4\sqrt{18}$

d)

$12\sqrt{3}$

10.

$5\sqrt{2}\cdot4\sqrt{10}$

a)

$20\sqrt{20}$

b)

$10\sqrt{40}$

c)

$40\sqrt{5}$

d)

$9\sqrt{13}$

11.

$\sqrt{5}\left(3-\sqrt{6}\right)$

a)

$\sqrt{15}-\sqrt{30}$

b)

$3\sqrt{5}-\sqrt{30}$

c)

$-\sqrt{15}$

d)

$\sqrt{15}-\sqrt{18}$

12.

$3\sqrt{6}\left(\sqrt{6}-2\sqrt{10}\right)$

a)

$18-12\sqrt{15}$

b)

$6\sqrt{15}$

c)

$-3\sqrt{24}$

d)

$3\sqrt{36}-6\sqrt{60}$

13.

$\sqrt{2}\left(4\sqrt{10}-6\sqrt{6}\right)$

a)

$8\sqrt{10}-6\sqrt{12}$

b)

$4\sqrt{12}-6\sqrt{8}$

c)

$4\sqrt{20}-6\sqrt{12}$

d)

$8\sqrt{5}-12\sqrt{3}$

14.

$\left(4\sqrt{2}-2\sqrt{3}\right)\left(5\sqrt{2}-\sqrt{3}\right)$

a)

$20\sqrt{2}-14\sqrt{6}+2\sqrt{3}$

b)

$46-14\sqrt{6}$

c)

$32\sqrt{6}$

d)

$40-14\sqrt{6}+6\sqrt{3}$

15.

$\left(3-4\sqrt{10}\right)\left(\sqrt{5}+2\sqrt{3}\right)$

a)

$3\sqrt{5}+6\sqrt{3}-20\sqrt{2}-8\sqrt{30}$

b)

$\sqrt{15}+18-4\sqrt{50}-8\sqrt{30}$

c)

$-3\sqrt{88}$

d)

$3\sqrt{5}+6\sqrt{3}-4\sqrt{50}-8\sqrt{30}$

16.

$\left(10-3\sqrt{2}\right)\left(10+3\sqrt{2}\right)$

a)

$82-\sqrt{2}$

b)

$20-6\sqrt{2}$

c)

$100-60\sqrt{2}$

d)

82

17.

Find the area of the rectangle

a)

11

b)

$22\ -3\sqrt{6}$

c)

$22+\sqrt{42}-2\sqrt{6}$

d)

$34+11\sqrt{6}$

18.

Divide:

a)

√12

b)

(4√3)/3

c)

√3

d)

(2√3)/3

19.

a)

A

b)

B

c)

C

d)

D

20.

a)

A

b)

B

c)

C

d)

D

21.

a)

A

b)

B

c)

C

d)

D

22.

a)

A

b)

B

c)

C

d)

D

23.

a)

A

b)

B

c)

C

d)

D

24.

a)

A

b)

B

c)

C

d)

D

25.

a)

A

b)

B

c)

C

d)

D

26.

a)

A

b)

B

c)

C

d)

D

27.

a)

A

b)

B

c)

C

d)

D

28.

Multiply. Be sure to simplify your answer: $-2\sqrt{8}\cdot5\sqrt{8}$

a)

$-10\sqrt{8}$

b)

$-64$

c)

$-80$

d)

$-640$

29.

a)

b)

c)

d)

30.

a)

b)

c)

d)

31.

a)

b)

c)

d)

32.

a)

b)

c)

d)

33.

a)

b)

c)

d)

34.

a)

b)

c)

d)

35.

How many significant figures are in this number: 0.00258

a)

2

b)

3

c)

4

d)

5

36.

How many significant figures are in this number: 47.00

a)

2

b)

3

c)

4

d)

5

37.

How many significant figures are in this number: 250,000

a)

2

b)

3

c)

5

d)

6

38.

How many significant figures are in this number: 0.0008

a)

1

b)

2

c)

4

d)

5

39.

How many significant figures are in this number: 10,002.000

a)

2

b)

3

c)

5

d)

8

40.

How many significant figures are in this number: 0.0005

a)

1

b)

3

c)

4

d)

5

41.

How many significant figures are in this number: 8.0

a)

1

b)

2

c)

3

d)

8

42.

Which of the following has 5 significant figures?

a)

0.000 5 cm

b)

0.000 05 cm

c)

10 005 cm

d)

1 005 550 cm

43.

How many significant figures are in the number? 4.06 x 10^-5 m

a)

3

b)

7

c)

5

d)

unknown

44.

What is the correct answer for: 12.00 m +15.001m =

a)

27.001 m

b)

27.00 m

c)

27.0 m

d)

27 m

45.

What is the correct answer for: 1.31 cm x 2.3 cm

a)

3.013 square cm

b)

3.01 square cm

c)

3.02 square cm

d)

3.0 square cm

46.

Give the answer to the correct number of significant figures to

3.419 + 3.912 + 7.0518 + 0.00013

a)

14.383

b)

14.382

c)

14.3829

d)

14.38293

47.

Give the answer to the correct number of significant figures to

145.63 - 28.9

a)

116.73

b)

116.7

c)

116.70

d)

117

48.

Give the answer to the correct number of significant figures to

247.89 ÷ 43.5

a)

5.70

b)

5.7

c)

5.699

d)

5.69

49.

Express 23400 in proper scientific notation.

a)

2.34 x 10⁴

b)

2.3 x 10³

c)

2.30 x 10⁵

d)

2.34 x 10³

50.

Write 0.000972 in scientific notation.

a)

9.72 x 10^-4

b)

9.72 x 10^-3

c)

972 x 10^-4

d)

9.72 x 10⁴

51.

Write 0.037 in scientific notation.

a)

3.7 x 10^-2

b)

3.7 x 10²

c)

37 x 10^-3

d)

37 x 10³

52.

Write 2.08 x 10²in standard form.

a)

208

b)

0.0208

c)

20,800

d)

0.208

53.

Write 46.3 x 10⁴in scientific notation.

a)

It is in scientific notation.

b)

.463 x 10⁶

c)

4.63 x 10⁵

d)

4.63 x 10⁴

54.

What is the correct answer for: 20.2 cm ÷ 7.41 s

a)

2.726045884

b)

2.72604

c)

2.73

d)

2.7

55.

3.05 + 0.013

a)

3.063

b)

3.06

c)

3.1

d)

3

56.

Which number is correctly written in scientific notation?

a)

5.67 x 10⁵

b)

56.7 x 10³

c)

0.567 x 10⁶

57.

How would you write 4.3756 x 10⁴in standard form?

a)

437,560,000

b)

0.00043756

c)

43,756

58.

What is the standard form?
1.245 x 10³

a)

0.001245

b)

12.45

c)

1245

59.

How many sig figs are there?
100.00

a)

1

b)

3

c)

4

d)

5

60.

How many sig figs are there?
4004

a)

1

b)

2

c)

3

d)

4

61.

Calculate: (2.5 x 10⁵) x (3 x 10⁴)

a)

7.5 x 10⁹

b)

7,600,000,000

c)

7.5 x 10^-9

62.

Calculate: (2.2 x 10⁶) x (4 x 10^-2)

a)

1.155 x 10⁶

b)

115500

c)

1.155 x 10⁴

63.

Calculate: (4.23 x 10⁶) ÷ (7.5 x 10^-3)

a)

5.64 x 10⁸

b)

3.1725 x 10⁴

c)

5 x 10⁶

64.

A full grown adult female blue whale weighs about 1.65 x 10⁵ kilograms. This is 60 times as heavy as a newborn blue whale calf. Calculate the weight of a newborn blue whale calf.

a)

3.64 x 10^-4 kg

b)

9.9 x 10⁶ kg

c)

2.75 x 10³ kg

65.

Multiply:
(3.4 x 10⁵)(1.2 x 10^-3)

a)

4.08 x 10^-8

b)

4.8 x 10²

c)

4.08 x 10²

d)

4.08 x 10^-15

66.

Divide:
(6.9 x 10⁷) / (2.3 x 10^-3)

a)

3 x 10¹⁰

b)

3 x 10⁴

c)

3 x 10^-4

d)

3 x 10^-11

67.

Multiply:
(9.4 x 10⁶)(3.2 x 10⁵)

a)

30.08 x 10¹¹

b)

3.8 x 10¹

c)

3.008 x 10¹²

d)

2.9375 x 10¹

68.

Solve:
(2.1×10²) × (3.0×10⁴)

a)

5.1 x 10²

b)

6.3 x 10⁶

c)

5.1 x 10⁶

d)

6.3 x 10⁸

69.

Solve:
(6 x 10⁶) / (2 x 10³)

a)

12 x 10³

b)

3 x 10⁹

c)

1.2 x 10⁴

d)

3 x 10³

70.

Solve:
(9 x 10^-6) / (3 x 10^-3)

a)

27 x 10^-9

b)

3 x 10^-3

c)

3 x 10^-9

d)

27 x 10^-3

71.

Write the answer in scientific notation.
4.1 x 10⁵ + 5.5 x 10⁶ =

a)

5.91 x 10⁶

b)

9.6 x 10⁵

c)

9.6 x 10¹¹

d)

4.65 x 10⁵

72.

Write the answer in scientific notation.
4.1 x 10⁵ + 5.5 x 10⁶ =

a)

5.91 x 10⁶

b)

9.6 x 10⁵

c)

9.6 x 10¹¹

d)

4.65 x 10⁵

73.

What is the simplified version of

a)

3.9 x 10⁶

b)

4 x 10²⁰

c)

4 x 10⁶

d)

3.9 x 10²⁰

74.

Find the common difference of the arithmetic sequence 14, 20, 26, ...

(a)

75.

Find the common difference of the arithmetic sequence -19, -14, -9, ...

(a)

76.

What is a formula for the nth term in the sequence 12, 20, 28, ...?

a)

$a_n=20+8\left(n-1\right)$

b)

$a_n=-4+8\left(n+1\right)$

c)

$a_n=12+8\left(n+1\right)$

d)

$a_n=12\left(8\right)^n$

77.

What is a formula for the nth term in the sequence -4, -9, -14, ...?

a)

$a_n=-4-5\left(n-1\right)$

b)

$a_n=a_{n-1}+5$

c)

$a_n=-5-4\left(n-1\right)$

d)

$a_n=-4+5\left(n-1\right)$

78.

Find the 75th term of the arithmetic sequence -17, -13, 9, ...

(a)

79.

Find the 63rd term of the arithmetic sequence -1, 5, 11, ...

(a)

80.

Given the sequence:
25, 21, 17, 13,...
Write the explicit equation that models the sequence.

a)

a_n = 4n + 29

b)

a_n = -4n + 25

c)

a_n= -4n + 29

d)

a_n = 4n + 25

81.

What is the rule (explicit equation) for the n^th term given
60, 55, 50, 45, ...

a)

a_n= -5+60n

b)

a_n= -5n+55

c)

a_n= -5n+65

d)

a_n= 5n+55

82.

Write the explicit rule for the arithmetic sequence
12, 10, 8, 6, ...

a)

a_n = 12n - 14

b)

a_n= 2n - 14

c)

a_n= -2n + 14

d)

a_n= -12n + 14

83.

Find the first term of the given sequence:
a₁₄=68
d=3

a)

14

b)

20

c)

26

d)

29

84.

What sequence follows the formula a_n=4n+11

a)

4, 15, 26, 37...

b)

15, 19, 23, 27...

c)

15, 26, 37, 48...

d)

11,15, 19, 23...

85.

This summation is the same as which series?

a)

1 + 2 + 3 + 4 + 5 + 6

b)

(1 - 2) + (2 - 2) + (3 - 2) + (4 - 2) + (5 - 2) + (6 - 2)

c)

(1 - 2) + (6 - 2)

d)

(1 - 2) + (2 - 2) + (3 - 2) + (4 - 2)

86.

Is this summation finite or infinite?

a)

Finite, because there are only 6 terms to add up.

b)

Infinite, because there are an infinite number of terms to add up.

87.

The summation is the same as which series?

a)

(4+10) + (4+20) + (4+30) + (4+40) + (4+50) + (4+60) + (4+70) + (4+80) + (4+90) + (4+100) + (4+110)

b)

1+2+3+4+5+6+7+8+9+10+11

c)

4 + 110

d)

4 + 10

88.

a)

196

b)

392

c)

49

d)

254

89.

Evaluate the series.

a)

36

b)

85

c)

35

d)

86

90.

Find the sum of the 1st 20 terms: 2+5+8+......

a)

1220

b)

610

c)

600

d)

612

91.

Find the sum of the 1st 100 terms: 100+98+96+......

a)

100

b)

1000

c)

50

d)

-98

92.

Find the sum: 11 + 15 + 19 + .......+ 83

a)

19

b)

83

c)

893

d)

624

93.

Find the sum: 50 + 48 + 46 + ..... + 10

a)

630

b)

21

c)

210

d)

1260

94.

Find the sum: 50 + 33 + 16 + ..... -18

a)

162

b)

9

c)

-150

d)

-162

95.

Find the sum: 400 + 394 + 388 + .... - 32

a)

400

b)

13432

c)

432

d)

73

96.

Given the following: $a_1=−3,\ d=2,\ S_n=21$ , how many terms do the arithmetic sequence have?

a)

11

b)

9

c)

7

d)

5

97.

A theater has 32 rows of seats. If there are 26 seats in the 1st row, 30 in the 2nd, 34 in the 3rd, and so on, how many seats are there in all? Assume the pattern continues.

a)

2,791 seats

b)

2,803 seats

c)

2,816 seats

d)

2.829 seats

98.

A grocer is creating a display of cans. There are 40 cans on the 1st (bottom) row, 38 cans on the 2nd row, 36 cans on the 3rd row, and so on. How many cans will be on the 15th row?

a)

32 cans

b)

10 cans

c)

12 cans

d)

68 cans

99.

Determine the number of terms in the arithmetic sequence given the following: $a_1=19,\ a_n=96,\ S_n=690$ .

a)

9

b)

10

c)

11

d)

12

100.

You are sitting in row 23 and notice there are 65 seats in your row. The row in front of you has 63 seats and the row behind you has 67 seats. There are 42 rows in the auditorium. How many seats does the auditorium contain? (Hint: Find the number of seats in the first and last rows)

a)

2,604

b)

2,163

c)

2,422

d)

2,803

101.

A construction company will be penalized each day of delay in construction for bridge. The penalty will be $4000 for the first day and will increase by $10000 for each following day. How much total money in fines will they pay in 15 days?

(a)

102.

What is the sum of the first ten terms of the sequence 4, -12, 36, -108 . . . ?

a)

59,050

b)

-59,048

c)

-78,732

d)

118,096

103.

What is the twelfth term in the sequence 3, -6, 12, . . . ?

a)

-2,048

b)

6,144

c)

-6,144

d)

-531,441

104.

The next two terms of the sequence 8,4,2,1, 1/2 are

a)

1/3 and 1/4

b)

1/4 and 1/8

c)

1/8 and 1/6

d)

1/5 and 1/7

105.

Find the 13th term:
2, 6, 18, 54, ….

a)

1,000,000

b)

1,062,882

c)

123,587

d)

5 bazillion

106.

Find the sum of the first 9 terms: -2 + -6 + -18 + ...

a)

-59,048

b)

-39,366

c)

-19,682

d)

-4,374

107.

Find the common ratio: 16, 8, 4, 2, ...

a)

r = 2

b)

r = 8

c)

r = 1/4

d)

r = 1/2

108.

Find the 10th term of the following geometric sequence

5, 20, 80, 320, ...

a)

81,920

b)

327,680

c)

1,310,720

d)

5,242,880

109.

$a_n=a_1r^{n-1}$

Find the 7th term in the sequence when the first term is 2, and the common ratio is 4

a)

8192

b)

32768

c)

2048

d)

512

110.

Find the common ratio of the geometric sequence:
$2,\ \frac{1}{2},\ \frac{1}{8},\ \frac{1}{32},\ ...$

a)

$\frac{1}{3}$

b)

$\frac{1}{12}$

c)

$\frac{1}{16}$

d)

$\frac{1}{4}$

111.

Find the sum of the infinite geometric series:

200 - 100 + 50 - 25 + ...

a)

525 / 2

b)

400 / 3

c)

3 / 400

d)

2 / 525

112.

In a geometric sequence, the 4th term is -12 and the 5th term is -24. Find the common ratio.

a)

2

b)

-2

c)

$\frac{1}{2}$

d)

$-\frac{1}{2}$

113.

The sixth term of a geometric sequence is 1215 and the third term is 45. Find the first term.

a)

5

b)

6

c)

7

d)

8

114.

Find the sum of the geometric series

7 + 14 + 28 + 56 + ... + 7168.

a)

14,327

b)

14,329

c)

14,331

d)

14,333

115.

Evaluate.

a)

5461

b)

800

c)

4095

d)

6241

116.

Evaluate the geometric series, if possible.

a)

3/2

b)

2/3

c)

6

d)

Does not exist

117.

Evaluate the geometric series

1-2+4-8..., n=8

a)

1/3

b)

-87

c)

-86

d)

-85

118.

a₁=2, r=−2, Sn = 22

Determine the number of terms n in the series

a)

6

b)

8

c)

7

d)

5

119.

Evaluate $\sum_{k\ =\ 1}^7\left(-2\right)^{k\ -1\ }$

a)

44

b)

$\frac{1}{3}$

c)

43

d)

49

120.

Write the explicit formula for the geometric sequence.

a)

a_n = 4(3)^n-1

b)

a_n = 3(4)^n-1

c)

a_n = -4(3)^n-1

d)

a_n = 3(-4)^n-1

121.

Find an explicit rule for the nth term of the sequence.

a)

a_n= -2(4)^n-1

b)

a_n= -2(4)ⁿ

c)

a_n= 2(-4)^n-1

d)

a_n= 2(4)^n-1

122.

What is the rule for the nth term of the geometric sequence with third term –12 and common ratio 3

a)

–(⁴/₃)(3)^n-1

b)

–(³/₄)(3)^n-1

c)

–4(3)^n-1

d)

–(¹/₃)(3)^n-1

123.

What is the explicit rule for the sequence:
11, 22, 44, 88...

a)

a_n = 2(11)^n-1

b)

a_n = 11x2

c)

a_n = 11(2)^n-1

124.

Neisha's salary for her first year was $44,000. She earned raises of 3% each year. What was her salary in her 10th year at the company? Round to the nearest dollar.

a)

$44,001

b)

$55,080

c)

$57,410

d)

$59,132

125.

$\left(\frac{2x^4}{5y^5}\right)^{-2}$

a)

$\left(\frac{25y^{10}}{4x^8}\right)$

b)

$\left(\frac{-4x^8}{-25y^{10}}\right)$

c)

$\left(\frac{2y^{10}}{5x^8}\right)$

d)

$\left(\frac{2x^8}{5y^{10}}\right)$

126.

$\left(\frac{4^{-2}x^3y^4z^{-5}}{20y^5z^2}\right)$

a)

$\frac{16x^3y}{20z^7}$

b)

$\frac{x^3}{320yz^7}$

c)

$\frac{16x^3}{20yz^7}$

d)

$\frac{320x^3}{yz^3}$

127.

$\left(8x^3\right)\left(-7x^4y^3\right)$

a)

$\frac{8x^3}{7x^4y^3}$

b)

$x^7y^3$

c)

$-56x^7y^3$

d)

$\frac{8}{7xy^3}$

128.

$\frac{15x^9}{3x^6}$

a)

$12x^3$

b)

$5x^3$

c)

$5x^{15}$

d)

$\frac{1}{12x^{15}}$

129.

Simplify $16^{\frac{3}{2}}$

a)

64

b)

4

c)

8

d)

32

130.

$\frac{\left(x^{\frac{1}{2}}\cdot x^{\frac{5}{12}}\right)^{\frac{1}{3}}}{x^{\frac{2}{3}}}$ Simplify the expression. Assume that all variables are positive.

a)

$\frac{1}{x^{\frac{7}{12}}}$

b)

$x^{\frac{12}{36}}$

c)

$\frac{1}{x^{\frac{13}{36}}}$

d)

$x^{\frac{7}{12}}$

131.

a)

1 / (t² √r³)

b)

r⁹ / t¹²

c)

1/(r⁹t³⁶)

d)

√r³ / t³⁶

132.

a)

a⁶/ b¹²

b)

b¹²/ a⁴

c)

a¹²/ b⁶

d)

1 / a⁶b¹⁰

133.

Simplify:

a)

(∛4) / 3

b)

2 / 3

c)

3 / (∛4)

d)

3/2

134.

Simplify:

a)

∛121

b)

121

c)

√11

d)

1331

DP SL UNIT 1 - Summative Review Test

Total questions: 134

Worksheet time: 12hrs 6mins

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