Download Math 9 Unit 1 Powers and Roots Practice Exam Fall 2014

Math 9
Fall 2014
Unit 1 Powers and Roots
Practice Exam
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Write the quotient of
B. 2
A.
____
as a single power.
C.
D.
2. Which square roots are correct to the nearest tenth?
i)
ii)
iii)
iv)
v)
A. i, iii
____
B. i, iii, v
C. ii, iv, v
D. i, ii, v
C. i, ii, and iv
D. iii and iv
3. Which power is positive?
i)
ii)
iii)
iv)
A. i and iv
B. i and ii
____
4. State which operation you would do first to evaluate
.
A. Subtract 5 from 6
C. Add 8 and 9
B. Multiply 9 and 6
D. Square 6
____
5. Evaluate:
A. 100
B. 1 000 000 001 000
____
____
____
6. Write
A.
B.
C. 10 001 000
D. 10 000 000 000
as a product of powers.
C.
D.
7. Write
as a power.
A. 8
B.
8. Write
A.
C.
D.
as a power.
B.
C.
D.
____
9. A square has an area of 24.1 cm2.
Determine the perimeter of the square, to the nearest tenth of a centimeter.
A. 19.6 cm
B. 4.9 cm
C. 24.0 cm
D. 6.1 cm
____
10. Name the two whole numbers whose squares (areas) are closest to 52.5.
A. 49, 64
B. 4, 9
C. 7, 8
D. 16, 25
____
11. Write
A.
____
B.
C.
D.
C. iii
D. ii
C. i and ii
D. i and iv
C. 35 741
in standard form.
D. 35 740
12. Which number is the greatest?
i)
ii) 5645
iii)
iv) 5780
A. iv
____
as a quotient of powers.
B. i
13. Which expressions have positive values?
i)
ii)
iii)
iv)
A. ii and iv
B. ii and iii
____
14. Write 1 000 000 as a power of 10.
A.
B. 105
C.
D. 106
____
15. Write
A. 35 746
B. 3574
____
16. List all the whole numbers between 63 and 101 that are perfect squares.
A. 64, 81, 96
C. 64, 81, 100
B. 64, 81
D. 64, 72, 81, 100
____
17. Which fraction is a perfect square?
i)
ii)
iii)
iv)
A. ii
____
18. Use benchmarks to determine the value of
A.
____
B. iii
B.
C. iv
D. i
.
C.
D.
19. The lengths of the two legs of a right triangle are 6.5 cm and 3.4 cm.
Determine the length of the hypotenuse to 1 decimal place.
A. 53.8 cm
B. 7.3 cm
C. 5.5 cm
D. 3.1 cm
Numeric Response
1. Determine the value of
, to the nearest tenth.
2. The lengths of the two legs of a right triangle are 6.5 cm and 3.4 cm.
Determine the length of the hypotenuse to 1 decimal place.
3. Evaluate:
4. Evaluate:
5. Correct the errors in the work below and then record the correct answer.
6. Express
in the form
. Place the value of n in the numerical response box.
Short Answer
1. Use benchmarks to estimate
2. To estimate the value of
to the nearest tenth.
, determine the two whole number perfect squares closest to 159.5 and
their square roots.
3. Write 50 986 using powers of 10.
4. Write
as a product of powers.
5. Simplify, then evaluate.
6. A field measures 105 m by 104 m.
a) Write an expression for the area of the field, using powers of 10.
b) Write an expression for the perimeter of the field, using powers of 10.
7. Insert brackets to make each statement true.
a)
b)
8. Write the number of unit cubes in the large cube as a power.
9. Calculate the number whose square root is
10. Replace
.
with a fraction to make this statement true.
Problem
1. Simplify, then evaluate. Show your work.
2. Identify, then correct, any errors in the work shown.
3. a) Write 128 as a power of 2.
b) Write 243 as a power of 3.
4. Write the expression
so that the powers have the same base.
Simplify, then evaluate.
5. Where possible, replace
with a “+” or “” sign to make each product positive.
a)
b)
c)
d)
Can all products be made positive? Explain.
6. The side length of square PQRS is half the side length of square ABCD.
Square ABCD has area 121 cm2.
a) What is the area of square PQRS?
b) What is the length of each side of square PQRS?
D
S
C
R
P
A
Q
B
7. Determine the value of
.
Math 9
Fall 2014
Answer Section
Unit 1 Powers and Roots
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
C
C
A
D
C
B
C
D
A
C
B
A
D
D
A
C
A
D
B
NUMERIC RESPONSE
1.
2.
3.
4.
5.
ANS:
ANS:
ANS:
ANS:
ANS:
8.8
7.3
29
0.3
261
6. ANS:
DIF:
SHORT ANSWER
1. ANS:
Moderate
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
DIF:
Easy
Moderate
Moderate
Easy
Moderate
Easy
Easy
Easy
Moderate
Easy
Easy
Moderate
Moderate
Easy
Moderate
Easy
Easy
Moderate
Moderate
Practice Exam
Between 4 and 5 but closer to 5
DIF: Moderate
2. ANS:
144 and 169
DIF: Easy
3. ANS:
DIF: Easy
4. ANS:
DIF: Easy
5. ANS:
DIF: Moderate
6. ANS:
a) Area of the field:
b) Perimeter of the field:
DIF: Difficult
7. ANS:
a)
b)
DIF: Moderate
8. ANS:
As a power, the number of unit cubes is
DIF: Easy
9. ANS:
DIF: Easy
10. ANS:
.
Between
DIF:
and
Moderate
PROBLEM
1. ANS:
DIF: Difficult
2. ANS:
Errors:
In line 1, the exponents of 3 should be added instead of multiplied.
In line 3, the exponents of 3 should be multiplied instead of added.
Correction:
DIF: Moderate
3. ANS:
a)
b)
DIF: Difficult
4. ANS:
DIF: Difficult
5. ANS:
a) Replace
with a “” sign.
b) Replace
with a “+” sign.
c)
is always negative.
d) Replace
with a “” sign.
Not all products can be made positive.
In part c, there is an even number of factors in the power
is always positive, which means
DIF: Difficult
6. ANS:
a) Area of PQRS =
b) PQ =
DIF: Moderate
7. ANS:
DIF:
Difficult
 area of ABCD
cm = 5.5 cm
.
is always negative.