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.