ACT Math

Algebra

Functions

Geometry

Statistics & Probability

Number & Quantity

100

Which of the following gives all solutions of the equation ∣x−3∣=8 ?

A. x = -5 or x = 11

B. x = -11 or x = 5

C. x = 5 or x = 11

D. x = 11 only

A. x = -5 or x = 11

100

If f(x)=3(2)^x, what is the value of f(4) ?

A. 24

B. 48

C. 81

D. 1296

B. 48

100

Angles ∠PQR and ∠RQS form a linear pair. If the measure of ∠PQR is 47°, what is the measure of ∠RQS?

A. 43°

B. 47°

C. 133°

D. 313°

C. 133°

100

A beekeeper recorded the amount of honey, in kilograms, collected from each of 5 hives: 14, 19, 11, 23, and 18. What is the mean amount of honey, in kilograms, per hive?

A. 12

B. 17

C. 18

D. 21.25

B. 17

100

A bakery mixes flour and sugar in the ratio 7 : 3 by weight for its shortbread dough. If one batch uses 2.1 kilograms of sugar, how many kilograms of flour does the batch use?

A. 0.9

B. 4.9

C. 6.3

D. 14.7

B. 4.9

200

Which of the following is a solution to the equation (x-6)(x+2)=0 ?

A. -2

B. 2

C. 4

D. 12

A. -2

200

A lab culture starts with 200 bacteria, and the number of bacteria doubles every hour. Which function gives the number of bacteria B(t) after t hours?

A. B(t) = 200 + 2t

B. B(t) = 200(2t)

C. B(t) = 2(200)^t

D. B(t) = 200(2)^t

200

In isosceles triangle DEF, DE=DF and the measure of ∠D is 40∘. What is the measure of ∠E?

A. 40∘

B. 70∘

C. 100∘

D. 140∘

B. 70∘

200

The histogram below shows how long it took each of 35 students to finish a logic puzzle. Each interval includes its left endpoint but not its right endpoint. How many students took at least 30 minutes?

A. 3

B. 7

C. 10

D. 22

C. 10

200

For the imaginary unit i, where i²=−1, what is the value of i²⁷ ?

A. -i

B. -1

C. 1

D. i

A. -i

300

When (2x−3)(x²+4x−5) is written in the form ax³+bx²+cx+d, what is the value of b ?

A. -3

B. 5

C. 8

D. 11

B. 5

300

For real numbers x, the function f(x)=3x²+18x+20 reaches a least value. What is that least value?

A. -7

B. -3

C. 20

D. 101

A. -7

300

A tile designer works with a regular polygon in which each interior angle is 5 times as large as each exterior angle. What is the measure of each exterior angle of the polygon?

A. 30∘

B. 36∘

C. 72∘

D. 150∘

A. 30∘

300

A school's website runs on two servers that work independently. Server A is working 95% of the time, and Server B is working 98% of the time. The website is available whenever at least one of the servers is working. What is the probability that the website is available at a randomly chosen moment?

A. 0.001

B. 0.931

C. 0.965

D. 0.999

300

On a hiking map, 1.5 centimeters represents 4 kilometers. Two campsites are 10.2 centimeters apart on the map. What is the actual distance, in kilometers, between the campsites?

A. 3.8

B. 15.3

C. 27.2

D. 40.8

C. 27.2

400

In the polynomial 2x³+kx²−5x−10, k is a constant. If x+2 is a factor of the polynomial, what is the value of k ?

A. -4

B. -1

C. 1

D. 4

400

A hiking club has 50 members and gains 30 members each week, so it has A(w)=50+30w members after w weeks. A cycling club has 5 members, and its membership doubles each week, so it has B(w)=5(2)^w members after w weeks. What is the least whole number of weeks w for which the cycling club has more members than the hiking club?

A. 4

B. 5

C. 6

D. 7

C. 6

400

A solid wooden cone has a base radius of 5 centimeters and a height of 12 centimeters. Every surface of the cone, including the circular base, will be painted. What is the total surface area to be painted, in square centimeters?
A. 60π

B.65π

C. 85π

D. 90π

400

A school's library has two printers. Printer P handles 65% of all print jobs and jams on 4% of its jobs. Printer Q handles the other 35% of print jobs and jams on 10% of its jobs. If a print job that jammed is chosen at random, what is the probability that it was sent to Printer Q?

A. 0.035

B. 0.061

C. 0.350

D. 0.574

400

A model car is built at a scale of 1 : 24, so every length on the model is 1/24 of the matching length on the real car. The painted surface of the model has an area of 150 square centimeters. What is the area, in square meters, of the matching painted surface on the real car? (1 meter = 100 centimeters)

A. 0.36

B. 3.6

C. 8.64

D. 86.4

C. 8.64

500

A lab technician mixes a 20% salt solution with a 50% salt solution to make 30 liters of a 30% salt solution. How many liters of the 50% solution does the technician use?

A. 10

B. 12

C. 15

D. 20

A. 10

500

A community theater sells 300 tickets per show at $20 each. For each $1 increase in the ticket price, it expects to sell 10 fewer tickets. If the price is increased by x dollars, the revenue is R(x)=(20+x)(300−10x) dollars. What ticket price gives the greatest revenue?

A. $5

B. $20

C. $25

D. $50

C. $25

500

In the figure below, equilateral triangle ABC is inscribed in a circle with center O and radius 8. What is the area of △ABC?

A. 16sqrt3

B. 24sqrt3

C. 32sqrt3

D. 48sqrt3

500

A one-year protection plan for a tablet costs $90. Without the plan, the owner estimates a 0.15 probability that the screen will crack during the year, which would cost $280 to repair, and a 0.25 probability that the battery will need to be replaced, which would cost $70. Assume these are the only possible repairs and each can happen at most once. By how much does the cost of the plan exceed the expected repair cost without the plan?

A. $30.50

B. $48.00

C. $59.50

D. $72.50

A. $30.50

500

Juice blend A is concentrate and water in the ratio 2 : 3, and blend B is concentrate and water in the ratio 1 : 4. If 10 liters of blend A are mixed with 15 liters of blend B, what percent of the mixture is concentrate?

A. 20%

B. 28%

C. 30%

D. 32%

B. 28%