ACT Math Practice Questions

ACT Math practice questions
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ACT Math Practice Questions

Solve each problem and choose the correct answer. Do not linger over problems that take too much time. Solve as many as you can; then return to the others in the time you have left for this test. On the real ACT test, you'll have 60 minutes to answer 60 math questions. So, since there are twenty questions here, give yourself 20 minutes to complete these. Scroll down after the questions for solutions and explanations.

1. In the Cartesian plane, a line runs through points (1,-5) and (5,10). What is the slope of that line?

A.  4/15

B.  4/5

C. 1

D. 5/4

E. 15/4

2. If y = 0.25(100-y), what is the value of y?

F. 200

G. 75

H. 25

J. 20

K. 18

3. If y = 4, what does |1-y| = ?

A.  -5

B.  -3

C.  3

D.  4

E. 5

4. For what value of q is the equation 9/q = 6/10 true?

F. 3

G. 5

H. 13

J. 15

K. 19

5. If the first day of the year is a Monday, what is the 260th day?

A.  Monday

B. Tuesday

C. Wednesday

D. Thursday

E. Friday

6. All the following statements about rational and/or irrational numbers must be true EXCEPT:

F. the sum of any two rational numbers is rational

G. the product of any two rational numbers is rational

H. the sum of any two irrational numbers is irrational

J. the product of a rational and an irrational number may be rational or irrational

K. the product of any two irrational numbers is irrational.

7. What is the sum of the two solutions of the equation xsquared +5x minus 24 = 0?

A.  -24

B. -8

C. -5

D. 0

E. 5

8. In triangle XYZ, angle Y is a right angle and angle Z measures less than 52 degrees. Which of the following phrases best describes the measure of angle X?

F. Greater than 38 degrees

G. Equal to 38 degrees

H. Equal to 45 degrees

J. Equal to 142 degrees

K. Less than 38 degrees

9. Which of the following expressions must be an even integer if x is an integer?

A. x + 5

B. x/4

C. x to the fourth power

D. 4x

E. 5 to the x power

10. In the fall semester of her math class, Alissa's test scores were 108, 81, 79, 99, 85, and 82. What was her average test score?

F.  534

G. 108

H. 89

J. 84

K. 80

11. Point X is located at negative 15 on the real number line. If point Y is located at negative 11, what is the midpoint of line segment XY?

A.  -13

B. -4

C. -2

D. 2

E. 13

12. What is the least common multiple of 25, 16, and 40?

F.  4

G. 32

H. 320

J. 400

K. 16,000

13. A 16-piece orchestra wants to choose one of its members to speak at performances. They decide that this member CANNOT be one of the 4 soloists in the group. What is the probability that Jonah, who is NOT a soloist, will be chosen as the speaker?

A.  0

B. 1/16

C. 1/12

D. 1/4

E. 1/3

14. While working on a lengthy problem on his calculator, Matt had meant to multiply a number by 3, but accidentally divided the number 3 instead. Which of the following calculations could he do on his calculator to obtain the result he originally wanted?

F.  Multiply by 3

G. Multiply by 9

H. Divide by 3

J. Divide by 9

K. Add the original number

15. If a sphere is intersected by two different planes NOT occupying the exact same space, how many sections is it possible to end up with?

A. only 2

B. only 2 or 4

C. only 3

D. only 3 or 4

E. only 2, 3, or 4

16. For the imaginary number i, which of the following is a possible value of i to the nth power if n is an integer less than 5?

F.  0

G. -1

H. -2

J. -3

K. -4

17. A dress that usually sells for $60 is on sale for 30% off. Shondra has a store credit card that gives her an additional 10% off the reduced price of any item. Excluding sales tax, what is the price she pays for the dress?

A.  $22.20

B. $24.75

C. $34.00

D. $36.00

E. 37.80

18. Two similar triangles have perimeters in the ratio of 5:6. The sides of the larger triangle measure 12 in, 7 in and 5 in. What is the perimeter in inches of the smaller triangle?

F.  18

G. 20

H. 22

J. 24

K. 32

19. A hamster is running on his wheel when the wheel breaks free of its axis due to a mechanical error. The hamster remains in the wheel, running in a straight line until the wheel has rotated exactly 15 times. If the diameter of the wheel is 10 inches, how many inches has the wheel rolled?

A.  75

B. 150

C. 75pi

D. 150pi

E. 1,500pi

20. Janie has 5 novels and 7 memoirs on the bookshelf in her dorm room. As she randomly selects a book to read at the end of the night, what is the probability that the book she selects is a novel?

F. 1/5

G. 5/7

H. 1/12

J. 5/12

K. 7/12


 Solutions to the ACT Math Practice Questions

1. The correct answer is "E". Don't panic. The Cartesian plane is the same old (x,y) plane you're used to. Slope = rise/run, so use the two points given in the slope formula: y2 minus y1/x2 minus x1 = 10 minus (-5) / 5-1 = 10 + 5 / 4 = 15/4 

2. The correct answer is "J". Solve for y, people! Get rid of the .25 by dividing both sides by it, and you get 4y = 100-y. Add y to both sides to get 5y = 100. Divide by 5 on both sides to isolate the y and you get y = 20. Ta-da!

3. The correct answer is "C". Remember, those two lines indicate absolute value. So, it must always be greater than or equal to zero, you can get rid of choices A and B. Substitute y = 4 into the expression and you get this: |1-y| = |1-4| =|-3| =3. 

4. The correct answer is "J". Basic cross-multiplication gets you to 90 = 6q. Divide both sides by 6 to isolate the q and you get 15. Easy cheesy.

5. The correct answer is "A". Here, draw out a mini-calendar until you see a pattern develop: Day 1 is Mon. 2 is Tues, all the way until you realize that Sundays fall on multiples of 7. So, pick a multiple of 7 close to 260, such as 259. If Day 259 has to be a Sunday because it's a multiple of 7, then day 260 has to be a Monday.

6. The correct answer is "K". Remember: on a "Must be" type of question, the relationships must be true in all cases. If there is one case in which a relationship is not true, that answer choice may be wrong. In this case, that one wrong instance is what you're looking for, and since answer K is often true, but not always, it's the one you'd choose.

7. The correct answer is "C". First, simplify the expression, and you get (x + 8)(x - 3). Now, find the solutions by setting each of them equal to 0. If x + 8 = 0, then x = -8. If x - 3 = 0, then x = 3. But the question asks us to find the SUM of the two solutions. Add them together: -8 + 3 = -5, or answer C.

8. The correct answer is "F". The sum of the measures of all angles in a triangle is 180 degrees. If Y, a right angle is 90 degrees (by definition), The other two angles must add up to 90 degrees to total 180. If angle Z measures less than 52, then angle X has to be greater than 90-52. It can't be equal to 38 degrees because angle Z is described as less than 52 degrees. Hence, F is the correct answer. 

9. The correct answer is "D". Only D can be correct because the product of an even number multiplied by either an even or an odd number will always be even. That's the only instance in the above samples where it will be true. Don't believe me? Plug in a smattering of numbers in the other equations and see what you get. 

10. The correct answer is "H". To find the average test score, add up all the numbers and divide by the total, which would be 534/6 = 89, choice H. You could immediately eliminate choices F and G because the average score has to be less than the highest test score.

11. The correct answer is "A". The midpoint of the line is the average of the two numbers, so add them up and divide by two. Negative 15 + -11/2 = -13. Or in this case, you could simply draw out the line and plot the numbers on it, counting toward the middle.

12. The correct answer is "J". First, you have to remember that a least common multiple is the smallest number that will divide evenly by 25, 16, and 40. That gets rid of answer choice A. Then, you just choose one of the larger numbers that's divisible by all three. Can't figure it out in your head? Take a guess and do the math - it's easy enough. Answer K is wrong because although it's a multiple of all three, it's not the smallest.

13. The correct answer is "C". Basic probability laws indicate that you have to figure out the part to whole ratio. The question you have to ask yourself is "How many people have a shot as the speaker?" The answer = 12, because the 4 soloists weren't included in those with a shot. So Jonah, being 1 of those 12 people with a shot has a 1 in 12 chance of being selected. Hence, 1/12.

14. The correct answer is "G". Matt needs to get back to his original place by canceling the division by multiplying by 3. Then, he needs to multiply by 3 again to get the correct answer, which in essence, is just multiplying by 9. Answer G.

15. The correct answer is "D". Imagine cutting an orange. There is no way you can cut an orange with two different planes and get two pieces, so eliminate any choice that has "2" in it. Bye-bye to A, B and E. That leaves choices C and D. We know, easily, that you can get four slices of an orange by cutting it twice (slice the orange in half lengthwise, put the halves back together, slice it in half width-wise) so that eliminates choice C, which leaves only D as the correct answer.

16. The correct answer is "G." Because i is defined as the square root of negative 1, its range of possibility when raised to certain powers is limited, and B is the only possibility if you figure out the square root of i to every power under 5.

17. The correct answer is "E". Take it step by step. $60 x .30 = $18, which means the dress is discounted to $42. Shondra's second discount: $42 x .10 = $4.20 off the discounted price, which comes to $37.80. Choice D is the distracter here, because it discounts the dress at 40%, but that's wrong because Shondra gets 10% off the reduced price. Read carefully.

18. The correct answer is "G". First, find the perimeter of the first triangle by adding up the sides = 24 inches. Since you know the ratio, you can set up this ratio and solve for x: 5/6 = x/24. x = 20. 

19. The correct answer is "D". Since the wheel's diameter is 10, you can find the circumference of the hamster's wheel C = pi x d = 10pi. This means the hamster's wheel travels 10pi inches in one rotation. Since his wheel rotated 15 times, multiply it by 15. 150pi.y 15. 150pi.

20. The correct answer is "D". Here, you just make a fraction. The total number of novels goes on top and the total number of books goes on the bottom: 5/12, choice D.