Download Grade 8 Mathematics Test #1 Square Roots and the Pythagorean

Grade 8 Mathematics Test #1
Square Roots and the Pythagorean Theorem
October 7, 2014
Name:___________
No calculators are permitted for PART A and PART B of the test. Submit the
answer sheet for two parts after completion and then continue with PART C
for which you may use a calculator.
PART 1 - Multiple Choice. Write the letter of the correct response on the answer
sheet provided.
(10 points)
1.
How would the equation 42 = 16 be read?
a) four squared is sixteen
b) the sum of four and itself is sixteen
c) the square root of four is sixteen
d) two to the exponent four is sixteen
2.
Which is a square number?
a) 3
3.
c) 9
d) 12
A perfect square has an __________ number of factors.
a) even
4.
b) 6
b) infinite
c) imaginary
What is a square root?
a) one of two equal factors of a particular number
b) one of two unequal factors of a particular number
c) the product of a number and itself
d) a square shaped thing that grows below the ground
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d) odd
5.
Which of the following proves that 3 is the square root of 9?
a) 3 x 3 = 3
6.
If
b) 8 and 9
8.1
c)
d) 23042 = 48
48  2304
c) 49 and 64
b) 8.4
c) 8.6
d) 64 and 81
65 ?
d) 8.9
A ladder leans against a brick wall. Which is the hypotenuse?
a)
b)
c)
d)
10.
b) 482 = 2304
Which number would be a reasonable estimate for
a)
9.
d) 3 + 3 = 9
The square root of 53 lies between which two whole numbers? (think numberline!)
a) 7 and 8
8.
c) 3 + 3 = 6
2304  48, which statement is also true?
a) 48 + 48 = 2304
7.
b) 3 x 3 = 9
The
The
The
The
distance between the ladder and wall
height of the wall
length of the ladder
width of the ladder
Which is true for ∆ABC?
a) a2 + b2 = c2
b) a2 x b2 = c2
c) a2 + c2 = b2
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d)
b2 x c2 = a2
PART 2 - Completion. Write the answer to each question on the answer sheet
provided.
(10 points)
1.
Write a mathematical equation for the phrase “two squared is four”.
2.
Simplify (i.e. show final answer):
3.
Simplify:
4.
If the area of a square is 81 cm2, what is the length of each side?
5.
What number has a square root of 6?
6.
Simplify:
144
7.
Simplify:
72
8.
If the factors of a perfect square are {1, 2, 4, 7, 14, 28, 49, 98, 196},
what is the square root of the number?
9.
What number is the perfect square in #8 above?
10.
In the diagram below, find the missing area.
12
82
2704 cm
2
?
900 cm
2
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PART 3 - Show all workings to receive full credit. Use of a calculator is
permitted for this section.
1.
Calculate the missing side.
Round your answers to the nearest tenth.
(i)
(i)
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(10 points)
Draw a diagram to show that 49 is a perfect square.
Show how you would write this with symbols.
State this in words.
2.
(i)
(ii)
(iii)
(4 points)
3.
Find the square root of 36 by using Division of primes OR by listing factors.
(4 points)
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4.
Use benchmark perfect squares to estimate
75 to the nearest tenth. You
may use a number line if you wish. BE SURE TO SHOW ALL WORKINGS!
(4 points)
5.
Use the Pythagorean theorem to determine if the numbers 7, 24, 26 form a
Pythagorean triple. SHOW WORKINGS! EXPLAIN!
(4 points)
6.
Use the Pythagorean theorem to determine if the triangle is a right
triangle. SHOW ALL WORKINGS!
(4 points)
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7.
The G.P.S. in a car gives directions in a busy city to travel 8 km toward the
north, then turn left at the intersection and travel 5 km toward the west.
If you had Luke Skywalker’s landspeeder and could rise above the buildings,
how far would your shortest route be? Give your answer to the nearest tenth.
INCLUDE A DIAGRAM! SHOW ALL WORKINGS!
(5 points)
7.
You’ve just bought an awesome new Samsung flat screen T.V. that is 61” wide
and 34” high. It was advertised according to the diagonal length. What ‘size’
T.V. are we watching the habs beat the leafs on Wednesday night? (5 pts)
MTL
5
TOR
0
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Bonus
(10 pts)
1. The measurements of a triangle have been given as :
48 cm – 52 cm – 91 cm
Classify the triangle according to its sides and according to its angles. Show
your work as proof.
34
2.
Construct the line segment of the length:
3.
A woodstove has the dimensions: 30 cm by 40 cm by 60 cm. What is the
longest piece of wood that can be put in the stove? Justify with
workings.(think of the stove shape as the room you’re in)
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Test marked out of 50 points
Grade 8 Math Test #1 - Answer Sheet
Square Roots and the Pythagorean Theorem
October 7, 2014
PART A – Multiple
Choice
ANSWER
Name:__________
PART B Completion
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ANSWER