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Chapter 4 Test
Another unit finished! You folks are amazing young people.
Show all work or full credit may not be given. Please show all
work on loose-leaf and staple to this test page. Provide all final
answers on this page.
Short Answer
[1pt.]1. Evaluate
.
Final Answer:
[2pt.]2. Evaluate
Final Answer:
[2pt.]3. Evaluate
without using a calculator.
Final Answer:
[2pt.]4. Evaluate
without using a calculator.
Final Answer:
[4pt.]5. Simplify
Final Answer:
[4pt.]6. Simplify
Final Answer:
[3pt.]7. Evaluate
Final Answer:
[3pt.]8. Evaluate
Final Answer:
Write using powers with positive exponents.
Problem
[2pt.]9. This diagram shows a cube with volume V cubic units and edge length s units.
s
V cubic units
Provide a value of V for which s is rational.
Final Answer:
[1pt.]10. Determine whether the perimeter of a square with area 92 m is a rational number or an irrational number.
Final Answer:
[2pt.]11. In isosceles ABC, what is the length of BC? Write your answer as a mixed radical.
A
10ft.
|
5 ft.
|
B
D
C
Final Answer:
[3pt.]12. At a distance of 1 m from a light source, the intensity of the light is 2 mW/m2 (milliwatts per square metre).
The intensity, I, at a distance d metres from the source is given by the formula: I = 2d–2 .
Determine the intensity of the light 3 m from the source.
Final Answer:
CHAPTER 4 TEST
Answer Section
SHORT ANSWER
1. ANS:
PTS: 1
LOC: 10.AN2
2. ANS:
81
DIF: Easy
REF: 4.1 Estimating Roots
TOP: Algebra and Number
KEY: Conceptual Understanding
PTS: 1
LOC: 10.AN3
3. ANS:
DIF: Moderate
REF: 4.4 Fractional Exponents and Radicals
TOP: Algebra and Number
KEY: Conceptual Understanding
PTS: 1
LOC: 10.AN3
4. ANS:
9
4
DIF: Easy
REF: 4.5 Negative Exponents and Reciprocals
TOP: Algebra and Number
KEY: Conceptual Understanding
PTS: 1
LOC: 10.AN3
5. ANS:
DIF: Moderate
REF: 4.5 Negative Exponents and Reciprocals
TOP: Algebra and Number
KEY: Conceptual Understanding
PTS: 1
LOC: 10.AN3
6. ANS:
DIF: Easy
REF: 4.6 Applying the Exponent Laws
TOP: Algebra and Number
KEY: Conceptual Understanding
PTS: 1
LOC: 10.AN3
7. ANS:
1
DIF: Moderate
REF: 4.6 Applying the Exponent Laws
TOP: Algebra and Number
KEY: Conceptual Understanding
PTS: 1
LOC: 10.AN3
8. ANS:
1
0.0016 or
625
DIF: Moderate
REF: 4.6 Applying the Exponent Laws
TOP: Algebra and Number
KEY: Conceptual Understanding
PTS: 1
LOC: 10.AN3
DIF: Moderate
REF: 4.6 Applying the Exponent Laws
TOP: Algebra and Number
KEY: Conceptual Understanding
PROBLEM
9. ANS:
The formula for the volume, V, of a cube with edge length s units is:
V = s3
To determine the value of s, take the cube root of each side.
For s to be rational, V must be a positive number that is a perfect cube.
For example, V = 125
PTS: 1
DIF: Moderate
REF: 4.2 Irrational Numbers
LOC: 10.AN1
TOP: Algebra and Number
KEY: Problem-Solving Skills | Communication
10. ANS:
The formula for the area, A, of a square with side length s units is:
To determine the value of s, take the square root of each side.
Since 92 is not a perfect square,
is irrational.
So, the side length of the square is irrational.
The perimeter of a square is: P = 4s
Since the product of 4 and an irrational number is irrational, the perimeter of the square is irrational.
PTS: 1
DIF: Difficult
REF: 4.2 Irrational Numbers
LOC: 10.AN2
TOP: Algebra and Number
KEY: Problem-Solving Skills
11. ANS:
Use the Pythagorean Theorem in ABD to determine BD.
So,
The length of BC is
PTS: 1
LOC: 10.AN2
12. ANS:
Use the formula
ft.
DIF: Moderate
REF: 4.3 Mixed and Entire Radicals
TOP: Algebra and Number
KEY: Problem-Solving Skills
. Substitute: d = 3
0.22
At a distance of 3 m, the intensity of light is about 0.22 mW/m2.
PTS: 1
LOC: 10.AN3
DIF: Moderate
REF: 4.5 Negative Exponents and Reciprocals
TOP: Algebra and Number
KEY: Problem-Solving Skills