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
Lulita pays $65 a month for cable. How much does she pay for cable over the course of 12 months?
What is the operation?
What is the expression used to solve?
Solve.
ANSWER:
Operation is multiplication
Expression is 65 x 12
Solution is 780
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
At Finson’s Fine Furniture, a dining room table costs $550 and the chairs cost $95 each. Write an expression and solve to show the amount you would pay for a table and eight chairs.
ANSWER:
Expression: $550 + ($95 x 8)
Solution: $1310
EXPLANATION:
First, solve for the cost of the chairs. There are 8 chairs costing $95 each. Therefore, 95 x 8, which equals $760. Then, add in the cost of the table since there is only one. $760 + $550 = $1310
200
A red house is made from red bricks. A blue house is made from blue bricks. A yellow house is made from yellow bricks. What is a greenhouse made from?
ANSWER: Glass
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
What is the value of m2n + mn – mn2 when
m = 3 and n = -5?
ANSWER: -135
EXPLANATION: First plug in numbers for variables.
32(-5) + 3(-5) - 3(-52)
Multiply.
9(-5) -15 -3(25)
-45-15-75
Subtract.
-60-75 = -135
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
Monroe is 7 years younger than his brother Cedric and 3 years older than his sister Kate. Cedric is 13 years old. How old is Kate?
What is the expression?
Solve?
ANSWER:
Expression: (13 - 7) - 3
Solution: Kate is 3 years old.
EXPLANATION:If Cedric is 13 and Monroe is 7 years younger, then 13 - 7 = 6.
If Monroe is 6 and he is 3 years older than his sister, or his sister is 3 years younger than him, then 6 - 3 =3.
300
What is harder to catch the faster you run?
ANSWER:
Your breath
or
Your shadow
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
32+3[(2+6/2]
ANSWER: 21
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
What five-letter word becomes shorter when you add two letters to it?
ANSWER: Short
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 = −5p3 + 22
ANSWER: p = 1
EXPLANATION:
Isolate the variable to one side.
17 = -5p3 + 22
Using inverse operation, subtract 22 from both sides:
17 - 22 = -5p3 + 22 - 22
-5 = -5p3
Using inverse operation, divide -5 from both sides:
-5/-5 = -5p3/-5
1 = p3
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
Barney’s Burger Barn is a seasonal beachfront snack shack that is open each year from May to September. It occupies a 22 foot by 32 foot space on the boardwalk which rents for $2,200 a month and employs 4 people who make $13 an hour. The sales tax rate in town is 5.4%.
What is the rent per square foot?
BONUS: What is the total monthly business cost and profit if he sells $12000 worth of product in one month and his employees working a total of 576 hours?
ANSWER: $3.13/ft2
BONUS:
Cost: $10,336
Profit: $1,664
EXPLANATION:
Cost per square foot is determined by dividing the monthly rent by the area of the shack. So, the expression is $2,200 / (22 x 32)
2200 / 704 = 3.125
Round 3.125 to the nearest cent = $3.13.
BONUS:
Expression:$12,000 - [(12000/5.4%) + $2,200 + (576 x $13)]
12000 - (648 + 2200 + 7488)
12000 - (10336)
1664
Therefore, cost is $10,336 and profit is $1,664.
500
During which month do people sleep the least?
ANSWER: February because it has less days