GEOMETRY
ALGEBRA
FRACTIONS
PERCENTS
WORD PROBLEMS
MISC
100
Find the area, to the nearest hundredth, of the circle below.
ANSWER: 78.5 mm2
EXPLANATION: Area of a circle is
A=pi r^2
First, find the radius be dividing the diameter in half: 10/2 = 5
A = 3.14 x 52
A = 3.14 x 25
A = 78.5
100
Evaluate -4x2y for x=-6, y=1.
ANSWER: 48
EXPLANATION: If x = -6 and y = 1, then plug in numbers for variables:
-4(-6) x 2(1)
Therefore, 24 x 2 = 48
100
What is
2 1/4 + 3 2/5 ?
ANSWER:
4 4/5
EXPLANATION: Turn mixed numbers into improper fractions, find the common denominator, add, then divide to turn back into a mixed number.
2 1/4 + 3 2/5
Turn into improper fraction
9/4 + 17/5
Find common denominator, add, and reduce
45/20 + 68/20 = 113/20
Divide to change back into mixed number
113/20 or 113 divide 20 = 5 13/20
100
What is 75% of 40?
ANSWER: 30
EXPLANATION: Write the equation using terms in word problem.
What = unknown (X)
is = (=)
of = multiply (x)
Then change percent to a decimal by dividing by 100, or moving decimal point 2 places to the left.
So, the equation is X = .75 x 40
.75 x 40 = 30
100
Lisa earns $8.10 an hour and worked 40 hours. Jamie earns $10.80 an hour. How many hours would Jamie need to work to equal Lisa’s earnings over 40 hours?
ANSWER: 30
Begin by calculating Lisa’s total earnings after 40 hours:
40 hours × $8.10 an hour = $324
Next, divide this total by Jamie’s hourly rate to find the number of hours Jamie would need to work:
$324 ÷ $10.80 = 30 hours
100
Passing score on all GEDs
145
200
A box of cereal is 11 ½ inches tall, 7 ½ inches long, and 2 inches wide. How many cubic inches of cereal can the box hold?
ANSWER: 172.5 in2
EXPLANATION: V=lwh
7.5 x 2 x 11.5=V
15 x 11.5 = 172.5
200
Simplify (2y-5z)(y+3z)
ANSWER: 2y2 + zy -15z2
EXPLANATION: Using the FOIL method (First, Outer, Inner, Last) use distributive property of multiplication.(2y-5z)(y+3z)
To distribute:
First: 2y x y = 2y2
Outer: 2y x 3z = 6yz
Inner: -5z x y = -5zy
Last: -5z x 3z = -15z2
Put it together, 2y2+6yz-5zy-15z2
Therefore, 2y2 + yz -15z2
200
2/3/11
2/33
200
35 is what percent of 235?
Round to the nearest tenth
ANSWER: 14.9%
EXPLANATION:
35 = X (235)
35/235 = X235/235
X=.1489361
X=14.9%
200
In Kingsport School, 46% of students are female. If the total number of students is 1250, then how many male students are attending this high school?
ANSWER: 675
If 46% of the total number of students is female, then 100% − 46% = 54% of the students are male. Calculate 54% of the total to find the number of male students.
Recall that 54% is equivalent to 54 ÷ 100, or 0.54:
0.54 * 1250 = 675.
200
What occurs once in every minute, twice in every moment, yet never in a thousand years?
ANSWER:
The letter "m"
300
A rectangle has an area of 42 square inches. If the width of the rectangle is 8 inches, what is the length?
ANSWER: 5.25 inches
EXPLANATION: The area of a rectangle is A=lw. Therefore, the equation for this rectangle is
42 = l(8)
42/8 = l8/8
dividing 42 by 8 the answer is 5.25.
300
Which of the following equations represents y in terms of x for all ordered pairs listed?
A. y = 4x ÷ 3
B. y = 2x + 3
C. y = x + 5
D. y = 3x2
ANSWER: B
The answer must be y = 2x + 3. This answer can be further verified by substituting each ordered pair into the equation, for example:
11 = 2(4) + 3
11 = 8 + 3
11 = 11
300
write .65 as a fraction in lowest terms.
13/20
300
45 is 15% of what number?
ANSWER: 300
EXPLANATION: 45 = .15X
45/.15 = .15X/.15
300 = X
300
Lily wants to buy as many bags of mulch as possible with her $305, and she would like them to be delivered to her house. The cost is $7.50 per bag and there is a $35.75 delivery charge. The mulch is only sold in full bags. How many bags can Lily buy?
ANSWER: 35 bags
EXPLANATION:charge is deducted:
$305 − $35.75 = $269.25.
We can then divide this amount by the cost per bag to find the total number of bags that Lily can buy:
$269.25 ÷ $7.50 = 35.9 bags. However, the question states that the mulch can only be sold in full bags, so we must round our answer down to ensure that Lily does not exceed his budget.
300
Sam’s mother had 4 children in all. The first one was named May. The second and third were called June and July respectively. What was the fourth child’s name?
ANSWER:
Sam
400
What is the perimeter of the polygon shown below?
ANSWER: 108 ft
EXPLANATION: Add up all the sides of this shape, however, notice that there are no measurements given for one 12ft side and one 7ft side.
Starting with the longest side:
34 + 20 + 12 + 12 + 8 + 8 + 7 + 7 = 108
400
What is the slope of the line that passes through points (0,5) and (7,0) on the coordinate plane shown below?
ANSWER:
-5/7
Substitute the given points (0,5) and (7,0) into the equation to calculate the slope:
400
It snowed 3/8 inches on Monday and 5/8 inches on Tuesday. How much more it snowed on Tuesday than Monday?
1/4
400
Janice works from home about 75% of the time. In an average month, how many of the 22 work days would she probably be at home?
Round answer
ANSWER: about 17 days
EXPLANATION: 75% of 22 days
.75 x 22 = 16.5
Round up = 17 days
400
In a bag there are a variety of marbles: 5 red, 6 blue, 3 yellow, and 2 green. If you pick one marble and put it back and then choose another marble, what is the probability that both marbles will be red?
First figure total marbles:
There are 16 marbles total
Next, what are the chances of choosing red on your first try:
5/16
Next, what are the chances of choosing red on the second try:
5/16
Then, multiply them together:
5/16 x 5/16 =25/256
400
ANSWER:
Space Invaders
500
A 15 foot ladder is leaning against a building. Its base is 2.5 feet from the base of the building. How far up the wall, to the nearest tenth of a foot, will the ladder reach?
ANSWER: 14.8 feet
EXPLANATION: Using Pythagorean Theorem a2 + b2 = c2, the leaning ladder would be the longest side (c). Therefore, the equation would be:
152 = 2.52 + b2
225=6.25 + b2
225-6.25 = 6.25 -6.25 + b2
218.75 = b2
sqrt 218.75
b = 14.8
500
Solve for p.
17 = −5p2 + 22
ANSWER: p = 1
EXPLANATION:
Isolate the variable to one side.
17 = -5p2 + 22
Using inverse operation, subtract 22 from both sides:
17 - 22 = -5p2 + 22 - 22
-5 = -5p2
Using inverse operation, divide -5 from both sides:
-5/-5 = -5p2/-5
1 = p2
square root 1 = p
1 = p
500
(1 8/2)(1 3/9)
6 2/3
500
A shoe store is offering 29% off in honor of the store’s 29th year in business.
How much will a person save off of a pair of boots marked at $59.99?
What will be the cost of the shoes after the discount?
ANSWER: Save $17.40
New Cost $42.59
EXPLANATION: First find 29% of $59.99 then subtract the saving from the original cost.
59.99 - (.29 x 59.99)
59.99 - 17.40
$42.59
500
A toy manufacturer makes 15,000 toys a year. The company randomly selects 300 of the toys to sample for inspection. The company discovers that there are 5 faulty toys in the sample. Based on the sample, how many of the 15,000 total toys are likely to be faulty?
ANSWER: 250
The sample indicates that 5 out of every 300 randomly selected toys will be faulty. Consequently, a proportion can be set up that relates the unknown number of faulty toys in the total number of toys to the ratio of faulty toys to the sample. Stated otherwise:
T is the unknown number of faulty toys in the total. Multiply both sides by 15,000 and then divide the left side by 300 to solve for T:
500
ANSWER:
