# Free ACT Sample Questions with Answers

Feb 22, 2022 | Turito Team USA The ACT is a college entrance exam utilized by most colleges and universities to determine admissions choices. ACT, Inc. administers a multiple-choice, pencil-and-paper exam. High school students take the ACT and SAT in the spring of their junior year or the fall of their senior year. Therefore, it’s crucial to provide enough time to retake the test to improve your score before applying to college.

ACT, Inc. releases ACT sample questions every year, containing genuine questions administered to students in the past. No matter how you prepare for the ACT, access to these tests is crucial. ACT sample questions can tell you how prepared you are and reduce anxiety. Although ACT sample questions will help you achieve a good score, make sure you aren’t taking them too close to your exam date.

We have provided a few ACT sample questions with answers below:

## Sample ACT Math Questions

Here, we will discuss important sample ACT Math questions with answers.

Q1. If f (x) = x3  – kx2 + 2x and f (2) = 6. What is the value of k?

Options:

1. 3/2
2. 5/2
3. 3
4. 6
5. 15

Solution- 1

f (x) = x³−kx² + 2x

=>f(2) = 8 − 4k + 4

=>12 − 4k = 6

=>k = 3/2

Hence, the correct option for this sample ACT Math question is a:  3/2.

Q2. On a bus trip from city A to city B, the fare is \$3.60, while from city B to city C, the fare is \$4.50. If John makes a total of n trips from city A to city B and m trips from city B to city C, with the total number of trips not exceeding 10, what is the correct range of total fare, f, he had to pay for all the trips?

Options:

1. f ≤ 36 – 0.9 n
2. f ≤ 36 + 0.9 n
3. f ≤ 36 – 0.9 m
4. f ≤ 36 + 0.9 m
5. f ≥36 – 0.9 n

Solution:

We know that: m+n≤10

Total fare = \$(3.6n+4.5m)

=>f=3.6n + 3.6m + 0.9m = 3.6 (n+m)+0.9m

=>f≤36+0.9m; replacing the value of n+m

Note that m + n ≤10, thus, the equality  f = 3.6 (n+m) + 0.9m will change to inequality f ≤36+0.9m

Alternatively, the answer could also be

f ≤ 45−0.9n

Let’s see how.

We have, total fare = \$(3.6n+4.5m)

=>f = 4.5n − 0.9n + 4.5m = 4.5 (n+m)−0.9n

=>f ≤ 45 − 0.9n

Since there is no such option, option d:  f ≤ 36 + 0.9 m is the only correct choice.

Q3. Abe takes nutrition supplements of either vitamins or proteins every day. His daily protein consumption is 50 g, and his vitamin intake is 120 mg. Which of the following shows the relationship between the number of days and nutrition supplement if, after N days, his total protein consumption is P grams and his total vitamin intake is V grams?

Options:

1. N = 50P + 0.12/V
2. N = 50/P + 120/V
3. N = P/50 + V/120
4. N = P/150 + 100V/12
5. N = P/50 + 5V/6

Solution:

A3. As Abe consumes 50 g of proteins per day, the number of days required to consume P grams = P/50

Also, as Abe consumes 120 mg of vitamins per day, the number of days required to consume V grams (1000V mg) = 1000V/120 = 100V/12

Since he consumes only one supplement in a day, we have N = P/150 + 100V/12.

Hence, the correct option for this sample ACT Math question is d:  N = P/150 + 100V/12

## Sample ACT Science Questions

Here, we will discuss important sample ACT Science questions with answers.

Q1. A student who learns how to disperse gases has received the following formula: Subsequent tests were performed to test his formula and to study the factors that affect the rate at which gases are distributed.

Experiment #1

When vapors of hydrogen chloride (HCl) and ammonia (NH3) combine, solid ammonium chloride (NH4Cl) is formed:

HCl(G)+NH3(g) → NH4Cl(s)

He inserted the HCl solution into one part of the glass tube (1 cm wide) and the NH3 solution into the other, separating the swabs 10 cm apart. As the NH4Cl ring develops, the distances traveled by each vapor can be calculated (see Figure 1). Reactions are carried out at various temperatures. In each test, the time it took for the ring to develop and its distance from the HCl swab were noted.

Table 1

 Trial Temperature (°C) Time (sec) Distance of ring from HCl swab (cm) 1 20 33 4.0 2 30 30 4.1 3 40 26 4.1 4 50 23 4.0

The student projected that the distance between the ring and the HCl swab would be 4.06 cm using the formula; thus, he determined that his formula was right. Experiment # 2

The first experiment was repeated, except that the temperature was maintained at 20°C and the tube diameter was varied for each trial.

Table 2

 Trial Tube diameter      (cm) Time (sec) Distance of ring from HCl swab (cm) 5 1.0 33 4.0 6 1.2 33 4.0 7 1.4 33 4.1 8 1.6 33 4.0

Experiment # 3

Experiment 2 was repeated, but the tube diameter was kept constant at 1 cm, and longer tubes were used to vary the distance between the swabs.

Table 3

 Trial Distance between swabs (cm) Time (sec) Range from HCl swab (cm) 9 10 33 4.0 10 20 67 8.1 11 30 101 12.2 12 40 133 16.2

A. Which option best describes the difference between the methods used in Experiments 1 and 2? In Experiment 1:

1. The temperature varied; in Experiment 2, the diameter of the tube varied.
2. Tube diameters varied; in Experiment 2, the temperature varied.
3. The distance between the swabs varied; in Experiment 2, the temperature varied.
4. The temperature varied; in Experiment 2, the distance between the swabs varied.

The correct answer to this sample ACT science question is A – In Exp. 1, the temperature varied; in Exp. 2, the diameter of the tube varied.

B. In Experiments 1, 2, and 3, which trials were completed using identical sets of conditions?

1. Trials 2, 3, and 4
2. Trials 1, 5, and 9
3. Trials 4, 7, and 9
4. Trials 10, 11, and 12

The correct answer for this sample ACT science question is B- Trials 1, 5, and 9.

C. The student concluded that NH3 diffuses faster than HCl. Do the results of Experiments 1–3 support her conclusion?

1. No, the HCl fumes traveled further than NH3.
2. No, the NH3 fumes traveled further than HCl.
3. Yes, the HCl fumes traveled further than NH3.
4. Yes, the NH3 fumes traveled further than HCl.

The correct answer for this sample ACT science question is D- Yes, the NH3 vapors traveled further than HCl.

### ACT Aspire Sample Math Questions

ACT Aspire Sample Math Questions are available online to assess what pupils have learned in Math. ACT Aspire scores forecast how a student will do on the ACT in 11th grade.

Q1. Arthur wants to arrive at soccer practice at 5:30 PM. He knows it takes him 45 minutes to walk to practice from his house. Estimate the time Arthur should leave his house to practice on time?

1. 5:00 PM.
2. 4:45 PM.
3. 4:30 PM.
4. 3:45 PM.

The correct answer for this ACT Aspire Sample Math question is b – 4:45 PM.

Q2. Find the sum 3/12 + 2/12

1. 5/24
2. 6/12
3. 5/12
4. 3/5

The correct answer for this ACT Aspire Sample Math question is b- 5/12.

Q3. In the number 913,87, which digit is in the ten thousand’s place?

1. 8
2. 1
3. 9
4. 3

The correct answer for this ACT Aspire Sample Math question is b- 1.

With the help of these ACT sample questions, it becomes easier for the candidates to understand the pattern of the questions that can be expected in the exam and practice them regularly.

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