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How close are you to a 21 on the math portion of the ACT?
Take this 10 question quiz to see how you are doing. Students who score over 21 on the math
portion of the ACT usually get at least 8 out of these 10 questions correct.
1. Bill wants to make 3 gallons of punch for a party. He mixes 2 gallons of cranberry juice with 1 gallon of orange
juice. Later Bill finds out he actually need 9 gallons of punch instead of 3. How much cranberry juice does he need
for the 9 gallon mixture?
A. 3
B. 4
C. 5
D. 6
E. 7
2. Which of the following equations does not represent a line when graphed in a coordinate (x,y) plane?
F. y= -6
G. x+2y=4
H. 3x=2y
J. 5y=2x-7
2
2
K. x +y = 3
3. Samantha wants to tile the floor of her bathroom that measures 20 inches long and 9 inches wide. She
determines that she will need 1 tile for every 4 inch by 3 inch area. What is the minimum number of tiles that she
will need to cover the entire bathroom floor?
A. 12
B. 15
C. 21
D. 26
E. 31
4. If 14x= 6(-4+x), then x=?
F. -6/14
G. 13/24
H. 1
J. -6
K. -3
5. How many positive integers can be divided into 8 while leaving a remainder of 2?
A. 1
B. 2
C. 3
D. 4
E. 5
3
2
3
2
3
2
6. (x + 2x - 6x +5) - (2x + 4x - 5x +10) is equivalent to
F. 3x + 6x - 11x +15
3
2
G. –x + 6x -11x +15
3
2
3
2
H. –x - 2x - x - 5
J. -2x - 2x + x + 5
3
2
K. x + 6x – 2x + 15
7. The cost of a bagel and a cup of coffee is $2.35. The cost of 2 bagels and a cup of coffee is $4.20. What is the
cost of one cup of coffee?
A. $0.50
B. $0.65
C.$1.25
D. $1.85
E. $2.00
8. Which of the following represents the midpoint of a line segment with end points of (1,5) and (3,9)?
F. (2,2)
G. (3,4)
H. (4,14)
J. (2,7)
K. (4,3)
9. The five integers in a set are 121, 118, 133, 142 and x. Which of the following could be equal to x if x is the
median number in this set?
A. 120
B. 129
C. 135
D. 133
E. 144
10. There are 18 boys and 10 girls in Mr. Smith’s class. If Mr. Smith chooses a student at random, what is the
probability that the student is a girl?
F. 5/9
G. 5/14
H. 9/5
J. 9/14
K. 4/5
ANSWERS
1. D
2. K
3. B
4. K
5. B
6. H
7. A
8. J
9. B
10. G
Explanations
1. The correct answer is (D). The punch was originally 2 parts cranberry and 1 part Orange juice. This
can also be expressed as 2/1, or 2:1 (a ratio). Since the total mixture went from 3 gallons to 9 gallons
that means it was multiplied by 3. Since the actual ratio of cranberry to orange juice does not change all
we need to do is multiply each part by 3. So if we originally had 2 gallons of cranberry juice for every 3
gallon mixture, then we have 6 gallons of cranberry juice for a 9 gallons mixture.
Each time you see a question concerning a mixture make sure to remember that the ratios will remain
constant no matter how much larger or smaller the mixture becomes.
-----------------------------------------------------------------------------------------------------------2. Answer choice K is correct. A linear equation is one that contains an x or a y (or both) without any
exponents. We see in the answer choices that answer choice E has an x with an exponent. Therefore,
that equation will not graph as a line.
-----------------------------------------------------------------------------------------------------------3. Answer choice B is correct. We can figure out the area of the bathroom floor by multiplying the
length times the width (20x9=180). Then, we can figure out how much area 1 tile covers by multiplying
the length and width of the area that 1 tile covers (4x3=12). So 1 tile covers 12 square inches of area. If
we are trying to cover 180 square inches, we can divide 180/12 to figure out how many tiles are needed.
180/12=15.
4. Answer choice K is correct. Distribute the 6 on the right side of equation to make it -24+6x. Subtract
the 6x from both sides so now you have 8x= -24. Divide both sides by 8 and you get -3.
-----------------------------------------------------------------------------------------------------------5. The correct answer is (B). All we need to do is divide 8 by each number from 1 to 8 and see which
ones leave us with a remainder of 2.
1 goes into 8- eight times, no remainder
2 goes into 8- four times, no remainder
3 goes into 8- two times, remainder 2
4 x 2 = 8, no remainder
5 x 1 = 5, remainder 3
6 x 1 = 6, remainder 2
7 x 1 = 7, remainder 1
8 x 1 = 8, no remainder
-----------------------------------------------------------------------------------------------------------6. Answer choice H is correct. The key to this question is to make sure to switch the signs of every term
in the second set of parenthesis, because of the negative sign outside of it. Once the signs are switched,
combine like terms from both sets of parenthesis.
-----------------------------------------------------------------------------------------------------------7. Answer choice A is correct. We can solve this question algebraically by writing equations. We will let
b=bagel and c=coffee. For the first sentence, b+c=2.35. For the second sentence, 2b+c=4.20. If we
subtract the first equation from the second, we get b=1.85. If we plug 1.85 into the first equation for b,
then we can solve for c: 1.85+c=2.35. Subtract 1.85 from both sides of the equation and you will get
$0.50.
8. Answer choice J is correct. Use the midpoint formula to solve this problem.
Midpoint formula = (X1 + X2) / 2 , (Y1 + Y2) / 2.
Plug the given points into the formula.
Midpoint formula = (1 + 3) / 2 , (5 + 9) / 2
Midpoint formula = 4/2 , 14/2
Therefore, the midpoint of this line segment is (2,7).
-----------------------------------------------------------------------------------------------------------9. When solving median questions you should put the numbers in order from smallest to greatest. If x
is the median number it should be in the middle with two numbers on either side (118, 121, x, 133, 142).
In order for x to be the median the number has to be greater than 121 and less than 133. The only
answer that is greater than 121 and less than 133 is 129 (choice B).
-----------------------------------------------------------------------------------------------------------10. Probability = Part/ Whole (part is what the question is asking for and the whole is the total amount).
For this question the part is the amount of girls (10) and the whole is 28 because there are 28 total
students in the class.
Part / Whole = 10 / 28 = 5/14