Name: ____________________ Math 8 Period: _____________

Unit 1 - Square Roots and the Pythagorean Theorem Test

Part A: Multiple Choice: Identify the choice that best completes the statement or answers the question.

____ 1. What is the square of 7?

a. 1 c. 14

b. 7 d. 49

____ 2. Which number is not a perfect square?

a. 49 c. 81

b. 64 d. 86

____ 3. What is the square root of 225?

a. 12 c. 15

b. 13 d. 16

____ 4. Which number is not a prime factor of 210?

a. 2 c. 7

b. 3 d. 13

____ 5. What is the area of a square with sides of 9 m?

a. 18 m2

c. 81 m2

b. 3 m2

d. 89 m2

____ 6. Use the Pythagorean relationship to find the unknown area of the square.

a. 26 cm

2 c. 104 cm

2

b. 25 cm2

d. 2535 cm2

____ 7. Determine the missing side length.

a. 5 cm c. 7 cm

b. 6 cm d. 8 cm

____ 8. Between which two consecutive numbers is found?

a. 8 and 9 c. 6 and 7

b. 7 and 8 d. 5 and 6

____ 9. A square has an area of 30 cm2. Find the approximate side length of the square. Round your answer to

the nearest tenth.

a. 4.5 cm c. 5.5 cm

b. 5 cm d. 6 cm

____ 10. Where on this number line is the value of located?

a. A c. C

b. B d. D

____ 11. The length of the hypotenuse, to the nearest tenth of a centimetre, is

a. 11.5 cm c. 19.0 cm

b. 14.3 cm d. 20.5 cm

____ 12. The length of the missing side is

a. 21.9 cm c. 27.7 cm

b. 24.9 cm d. 37.0 cm

____ 13. Where on this number line is the value of 3 98 located?

a. A c. C

b. B d. D

____ 14. Estimate the value of 3 50 located?

a. 7.1 c. 3.7

b. 7.3 d. 49

Part B: Extended Answers: Please place your answer in the box provided and show all your work. Full marks will be given for correct answers placed in the box.

1. Use prime factorization to find

2. Estimate using the number line below.

_______

5 6 7 8

3. The hypotenuse of the triangle cuts the circle in half. What is the diameter of the circle? Round your

answer to the nearest tenth of a centimeter.

4. What is the approximate value of x? Express your answer to the nearest tenth of a centimeter.

.

==

5. (a) What is the side length of the tilted square?

(b) What is the area of the tilted square?

6. Show how you could determine if a triangle with side lengths 5, 12 and 13 is a right triangle.

7. The roof of the bird house is 14 cm wide and the distance up the slope of the roof is 9 cm. What is the

height x of the roof to the nearest tenth of a cm.

8. The volume of a Rubik’s cube is 216 cm3, what is the length of one of its sides?

9. Find the volume of a cube if the side length is 4 feet.

10. Randy plots the points in the following graph.

a) Find the lengths of AB , BC , and AC .

b) What kind of triangle is ABC ? Explain.

__________________________________________________________________________________

__________________________________________________________________________________

x9cm

14cm

MATH 8 - CHAPTER 3 Test

Answer Section

MULTIPLE CHOICE

1. ANS: D PTS: 1 DIF: Easy OBJ: Section 3.1

NAT: N1 TOP: Squares and Square Roots KEY: square

2. ANS: D PTS: 1 DIF: Average OBJ: Section 3.1

NAT: N1 TOP: Squares and Square Roots KEY: perfect square

3. ANS: C PTS: 1 DIF: Average OBJ: Section 3.1

NAT: N1 TOP: Squares and Square Roots KEY: square root

4. ANS: D PTS: 1 DIF: Average OBJ: Section 3.1

NAT: N1 TOP: Squares and Square Roots KEY: prime factorization | factors

5. ANS: C PTS: 1 DIF: Average OBJ: Section 3.1

NAT: N1 TOP: Squares and Square Roots KEY: square

6. ANS: A PTS: 1 DIF: Average OBJ: Section 3.2

NAT: M1 TOP: Exploring the Pythagorean Relationship

KEY: Pythagorean relationship | Pythagorean triple

7. ANS: D PTS: 1 DIF: Average OBJ: Section 3.2

NAT: M1 TOP: Exploring the Pythagorean Relationship

KEY: Pythagorean relationship | Pythagorean triple

8. ANS: A PTS: 1 DIF: Average OBJ: Section 3.3

NAT: N2 TOP: Estimating Square Roots KEY: estimation | square root | benchmark

9. ANS: C PTS: 1 DIF: Average OBJ: Section 3.3

NAT: N2 TOP: Estimating Square Roots KEY: estimation | square root | benchmark

10. ANS: C PTS: 1 DIF: Average OBJ: Section 3.3

NAT: N2 TOP: Estimating Square Roots

KEY: number line | square root | benchmark

11. ANS: B PTS: 1 DIF: Average OBJ: Section 3.4

NAT: M1 TOP: Using the Pythagorean Relationship

KEY: Pythagorean relationship | unknown hypotenuse

SHORT ANSWER

16. ANS:

a) , 4.7, , , 7

b) Answers will vary, but the number line should generally look as follows:

PTS: 1 DIF: Average OBJ: Section 3.3 NAT: N2

TOP: Estimating Square Roots KEY: estimation | square root

PROBLEM

17. ANS:

The diameter of the circle is 11.4 cm.

18. ANS:

In the smaller triangle the hypotenuse (call it a) is

Use this value with the known length of the larger triangle to calculate x:

The approximate value of x is 8.2 cm.

PTS: 1 DIF: Difficult+ OBJ: Section 3.2 NAT: M1

TOP: Applying the Pythagorean Relationship KEY: Pythagorean relationship

19. ANS

The distance between the two cars is 20 km.

20. ANS:

The distance is approximately 120.4 m.

PTS: 1 DIF: Average OBJ: Section 3.4 NAT: M1

TOP: Exploring the Pythagorean Relationship KEY: Pythagorean relationship

21. ANS:

The highway forms a right triangle with Prince Albert and Red Deer.

The length of the highway is approximately 505 km.

22. ANS:

w = 1.82h

Substitute w = 1.82h and d = 81 into the Pythagorean relationship.

Since h = 39, then w = 1.82 39 = 70.99

The TV screen is approximately 39 cm high and 71 cm wide.