Review Answer Sheet

Types of Files

Question 1:
What type of file does the ".doc" or ".docx" extension indicate?

Answer:
A Word file

Question 2:
What type of file does the ".txt" extension indicate?

Answer:
A text file

Question 3:
What are three file extensions used for image files?

Answer:
Any three of the following: .jpg, .png, .tif, .gif, .bmp, .psd

Question 4:
What is the most common extension for an executable file?

Answer:
.exe

Order of Operations

Question 1:
1 + 2 * 3 - 4

Answer: 3
1 + 2 * 3 - 4
1 + 6 - 4
7 - 4 = 3

Question 2:
(1 + 2) * 3 - 4

Answer: 5
(1 + 2) * 3 - 4
3 * 3 - 4
9 - 4 = 5

Question 3:
8 - 4 / 2 + 1

Answer: 7
8 - 4 / 2 + 1
8 - 2 + 1
6 + 1 = 7

Question 4:
8 - 6 / (2 + 1)

Answer: 6
8 - 6 / (2 + 1)
8 - 6 / 3
8 - 2 = 6

Question 5:
8 + 7 * 4 / 2

Answer: 22
8 + 7 * 4 / 2
8 + 28 / 2
8 + 14 = 22

Question 6:
(8 + 7) * 4 / 2

Answer: 30
(8 + 7) * 4 / 2
15 * 4 / 2
60 / 2 = 30

Question 7:
((20 + 10) - (6 * 2))

Answer: 18
((20 + 10) - (6 * 2))
(30 - 12) = 18

Question 8:
9 - 2 * (14 - 10) + 6

Answer: 7
9 - 2 * (14 - 10) + 6
9 - 2 * 4 + 6
9 - 8 + 6
1 + 6 = 7

Question 9:
((2 + 1) + (7 - 3) * (4 / 2))

Answer: 11
((2 + 1) + (7 - 3) * (4 / 2))
(3 + 4 * 2)
3 + 8 = 11

Exponents Part 1

Question 1:
2 ^ 4

Answer: 16
2 ^ 4
2 * 2 * 2 * 2
4 * 4 = 16

Question 2:
4 ^ 1

Answer: 4

Question 3:
6 ^ 0

Answer: 1
Any number raised to the 0 power equals 1.

Question 4:
-2 ^ 3

Answer: -8
(-2) * (-2) * (-2)
4 * (-2) = -8

Question 5:
-3 ^ 3

Answer: -27
(-3) * (-3) * (-3)
9 * (-3) = -27

Question 6:
3 ^ 3 ^ 3

Answer: 19,683
3 ^ 3 ^ 3
(3 * 3 * 3) ^ 3
27 ^ 3
27 * 27 * 27 = 19,683

Question 7:
0 ^ 0

Answer: 1
Any number raised to the 0 power equals 1, even if that number is 0.

Exponents Part 2

Question 1:
12 ^ -2

Answer: 1 / 144
12 ^ -2
(1 / 12) * (1 / 12) = 1 / 144

Question 2:
5 ^ -3

Answer: 1 / 125
(1 / 5) * (1 / 5) * (1 / 5) = 1 / 125

Question 3:
8 ^ -1

Answer: 1 / 8

Question 4:
3 / 5 ^ -2

Answer: 25 / 9
(5 / 3) ^ 2
(5 / 3) * (5 / 3) = 25 / 9

Exponents Part 3

Question 1:
144 ^ 1 / 2

Answer: 12
√144 = 12
Because 12 * 12 = 144, therefore 12 is the square root of 144

Question 2:
64 ^ 1 / 3

Answer: 4
3√64 = 4
Because 4 * 4 * 4 = 64, therefore 4 is the cube root of 64

Question 3:
9 ^ 3 / 2

Answer: 27
(9 ^ 1 / 2) ^ 3
3 ^ 3 = 27

Linear Equations

Note: For all of these problems, the goal is to isolate the variable "n" on one side
Question 1:
8 + n = 13

Answer: 5
(8 + n) - 8 = 13 - 8
n = 5

Question 2:
n / 5 = 12

Answer: 60
(n / 5) * 5 = 12 * 5
n = 60

Question 3:
6n = 24

Answer: 4
(6n) / 6 = 24 / 6
n = 4

Question 4:
36 = 48 - n

Answer: 12
36 = 48 + (-n)
36 - 48 = -n
-12 = -n
-12 / -1 = -n / -1
12 = n

Logarithms

Question 1:
log2 (4)

Answer: 2
log2(4) is asking what power to we need to raise 2 to, in order to get an answer of 4.

Question 2:
log10 (100)

Answer: 2
log10(100) is asking what power we need raise 10 to, in order to get an answer of 100.

Question 3:
4 log2 (2)

Answer: 4
4 log2 (2)
4 * log2(2)
4 * 1 = 4

Question 4:
log4(64) + 2

Answer: 5
log4(64) + 2
3 + 2 = 5

Question 5:
log5(1)

Answer: 0
You can raise any number to the 0 power to get 1.

Averages

Question 1:
Over the course of 4 games, a basketball player scores 12, 20, 36, and 8 points. What is her average score per game?

Answer: 19
Let x represent the average score.
(12 + 20 + 36 + 8) / 4 = x
76 / 4 = x
19 = x

Question 2:
Aidan received the following scores on his Chemistry tests: 80, 90, 70, 100, 70, 100. What is his average test score?

Answer: 85
(80 + 90 + 70 + 100 + 70 + 100) / 6 (number of tests taken) = x
510 / 6 = x
85 = x

Question 3:
Sally has an average exam score of 87 based on 3 Algebra exams taken so far. What score would Sally need to get on her next Algebra exam to bring her average score up to 90?

Answer: 99
Her sum for the last 4 exams was 261 (87 * 3), so we need to add that to x (her potential score on the next exam), and divide by 4 (the total number of exams including the next one), and this must equal 90.
(261 + x) / 4 = 90
((261 + x) / 4 ) * 4 = 90 * 4
261 + x = 360
x = 360 - 261
x = 99

Percentages

Question 1:
There are 36 students in a class and 9 of these students failed their History test. What percentage of these students failed their test?

Answer: 25%
Reframe question: 9 is what percent of 36? Let x = "what percent" and solve for x.
9 = x * 36
9 / 36 = (x * 36) / 36
.25 = x
(and .25 = 25%)

Question 2:
Paula spends $600 per month on rent. If that amount of money is 40% of her monthly income, then how much money does Paula make per month?

Answer: $1500
Reframe question: 600 is 40% of what number? Let x = "what number" and solve for x.
40% of x = 600
.4 * x = 600
(.4x) / .4 = 600 / .4
x = 1500

Question 3:
What is 55% of 40?

Answer: 22
40 * .55 = 22

Question 4:
What is .1% of 3000?

Answer: 3
3000 * .001 = 3

Question 5:
A football team played 52 games in one season. They won nearly 90% of their games. About how many games did they win? (Round to the nearest whole number.)

Answer: 47
Reframe question: What number is 90% of 52? Let x = "what number" and solve for x.
x = 52 * .90
x = 46.8 (round up to 47, so x = 47)

Perimeter and Area of Rectangles

Calculate the Area and Perimeter for each rectangle.

Question 1:
A square with sides that are 4 in long.

Answer: Area: 16 in^2, Perimeter: 16 in
For the area, multiply 2 of the sides of the square and make sure the answer is marked inches squared.
4 * 4 = 16 in^2
For the perimeter, add all sides of the square.
4 + 4 + 4 + 4 = 16 in

Question 2:
A rectangle with a length of 5 ft and a width of 3 ft.

Answer: Area: 15 ft^2, Perimeter: 16 ft
For the area, multiply the length and width and make sure the answer is marked feet squared.
5 * 3 = 15 ft^2
For the perimeter, add all sides of the rectange (so 2 lengths and 2 widths).
(2 * 5) + (2 * 3)
10 + 6 = 16 ft

Question 3:
A rectangle with a length of 12 ft and a width of 6 ft.

Answer: Area: 72 ft^2, Perimeter: 36 ft
For the area, multiply the length and width and make sure the answer is marked feet squared.
12 * 6 = 72 ft^2
For the perimeter, add all sides of the rectange (so 2 lengths and 2 widths).
(2 * 12) + (2 * 6)
24 + 12 = 36 ft

Circles Part 1

Use 3.14 for pi.
Question 1:
Given a circle with a diameter of 12 ft, what is its circumference?

Answer: 37.68 ft
The circumference is the diameter times pi (shortened to 3.14 here), so:
12 * 3.14 = 37.68

Question 2:
Given a circle with a diameter of 8 ft, what is its radius?

Answer: 4 ft
The radius is half the diameter, so:
8 / 2 = 4

Question 3:
Given a circle with a circumference of 87.92 ft, what is its radius?

Answer: 14 ft
The circuference is 2 times the radius times pi, so if x represents the radius:
2 * 3.14 * x = 87.92
(6.28 * x) / 6.28 = 87.92 / 6.28
x = 14

Question 4: 69.08 ft
Given a circle with a radius of 11 ft, what is its circumference?

Answer:
11 * 2 * 3.14 = 69.08

Circles Part 2

Use 3.14 for pi.
Question 1:
Given a circle with a diameter of 12 ft, what is its area?

Answer: 113.04 ft^2
area = pi * radius^2 (and the radius is half the diameter) so:
area = 3.14 * 6^2
area = 3.14 * 36 = 113.04

Question 2:
Given a circle with a diameter of 8 ft, what is its area?

Answer: 50.24 ft^2
area = 3.14 * 4^2
area = 3.14 * 16 = 50.24

Question 3:
Given a circle with a radius of 14 ft, what is its area?

Answer: 615.44 ft^2
area = 3.14 * 14^2
area = 3.14 * 196 = 615.44

Question 4:
Given a circle with a radius of 11 ft, what is its area?

Answer: 379.94 ft^2
area = 3.14 * 11^2
area = 3.14 * 121 = 379.94

Number Types

For each number, identify which categories it belongs to.
The categories are: Natural, Whole, Integer, Rational, Irrational, and Real.
Question 1:
-6.06

Answer: Rational, Real

Question 2:
-9 / 37

Answer: Rational, Real

Question 3:
10

Answer: Natural, Whole, Integer, Rational, Real

Question 4:
-198

Answer: Integer, Rational, Real

Question 5:
3.05005050005...

Answer: Irrational, Real

Number Systems

Question 1:
Convert this binary number into decimal notation:
11001011

Answer: 203

Question 2:
Convert this binary number into decimal notation:
00010010

Answer: 18

Question 3:
Convert this decimal number into hexadecimal notation:
228

Answer: E4

Question 4:
Convert this hexadecimal number into decimal notation:
CC

Answer: 204

Question 5:
Convert this binary number into hexadecimal notation:
00111111

Answer: 3F