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Unit D Review for Test
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Date:
NON-CALCULATOR SECTION
1. Which of the following have a value between 4 and 5?
3
A. √8
3
B. √74
3
C. √64
D.
3
125
2. √67 is between which of the following consecutive whole numbers?
A. Between 8 and 10
B. Between 8 and 9
C. Between 66 and 68
D. Between 33 and 34
3. Which of the following points on the number line best approximates the value of −√12
A. Point A
B. Point B
C. Point C
D. point D
4. In the equation y = 𝑥 2 which of the following are possible values of x when y = 7. (Circle all that apply.)
A. √49
B. -√7
C. −√49
D. √7
E. √3
5. Which of the following are irrational numbers? (Circle all that apply).
A. √2
3
F. √343
B. √3
3
G. √−216
C. √16
D. √
1
9
E.
12
7
6. Anne claims that the solutions to the equation 𝑥 2 = 5 are rational numbers. Do you agree or disagree with Anne’s
statement? Explain your reasoning in the space below.
__________________________________________________________________________________________________
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7. Describe and correct the errors
Problem A
Error:
2
𝑥 = 169
Problem B
Error(s):
3
𝑥 = 64
3
√𝑥 2 = √169
𝑥 = 13
3
√𝑥 3 = √64
𝑥 = ±8
Correction:
Correction:
8. Determine between which two consecutive whole numbers each square root lies.
a.
√20 _____ and _______
c.
√3 ________ and ________
b.
d.
√94
_______ and ________
√50 ________ and ________
9. In the box below circle all the RATIONAL NUMBERS.
3
5
53
-786
0
8.7
-6.28
√49
-3
 2
𝜋
6.4132…
10. Place each of the values below the number line, use leader lines to indicate location on the line
𝜋
3
-4
-3
31
,
9
,
-2
 15 ,
-3.9,
-1
0
1.2 ,
1
1
1 ,
3.5,
4
2
3
13 ,
4
11. For each inequality, list TWO values of x that would make the inequality true.
13  x  14
11  x  12
7 x 8
x  _____
x  _____
x  _____
12. Determine if a right triangle can be formed use each of the following sets of side lengths:
a. 8, 10, 12
b. 5, 13, 12
13. In ABC , BD is perpendicular to AC. BD is 6 inches. AC is 16 inches. What is the perimeter of ABC
Write your answer in the box
B
A
C
D
14. The right triangle pictured below side BC = 6 cm and side AB = 15 cm. Find the exact and estimated
length of side AC. Write your answers in the boxes.
Exact Length:
Estimated Length:
15. What is the distance between the points (2, 5) and (6, 15) on the coordinate grid? Write the exact and
estimated lengths in the boxes below. Show your work.
Exact Length:
16. If t 2 
Estimated Length:
25
, what are the solutions of the equation?
64
CALCULATOR SECTION
17. How can you use your calculator to demonstrate that √5 is an IRRATIONAL NUMBER?
18. A rectangle has a width of 7.25 inches and a length of x inches. If the diagonal of the rectangle is 16.5
inches, what is the value of x ? Round your answer to the nearest tenth of an inch.
Solve each equation below.
19. 4 x 3  864
20. 𝑥 3 = −6859
21.  7 x 3  1367
3
22. 5 x  300  3945
3
23. 2 x  300  543.75
24.
4 y 2  600
25.
20  y 2  101
26.
6w 2  30  400
27. Starting from the California, Zachary drove 300 miles due east, then turned and drove 250 miles south.
When he saw how beautiful the National Park was he called his friend Ian to come backpacking with him.
Ian stopped at Zachary’s house to pick up his pack and then drove directly to the national park site where
Zachary was staying. How many more miles did Zachary drive than Ian? Round your answer to the
nearest whole mile.
Write your answer in the box. Show your work.
28. The area of a square park is 9 square miles. How long is one side of the park?
A.
36 miles
B. 81 miles
C. 3 miles
D. 18 miles
29. Find the exact distance between each pair of points. Show your work and circle your answers in the box.
A to D:
B to C:
D to C:
256
 square meters. What is the length of the radius? Show
289
your work. Then enter your answer in the box.
30. The area of the circle pictured below is A 
31. The following polygon has segment lengths as follows: AD = 10 cm, AB = 15 cm, segment AC = 30 cm.

Label each side of the triangle pictured above with the correct measurement.

Find the length of ̅̅̅̅
𝐶𝐷. Show all your work.

Find the length of ̅̅̅̅
𝐷𝐵. Show all your work.

Find the area of the triangle of triangle ABC.

Find the length of ̅̅̅̅
𝐵𝐶 .

Find the perimeter of triangle ABC
32. Tell whether each triangle is a right triangle. Show your work then enter your answer in the box.
33. Find the edge length of each cube. Show your work then enter your answer in the box.
a.
Volume = 83375 𝑐𝑚3
1
b. Volume = 343 𝑚3