Free ACT practice test — 171 questions, full length, real timing 🇺🇸

8 original practice questions written by Myndaq in the ACT style. They are not taken from this mock paper or from official past papers. Try each one, then open the answer.

1. Question 1MathematicsOne correct answer

   The function f is defined by f(x) = 3x² − 7x + k, where k is a constant. If f(2) = 9, what is the value of f(−1)?

   1. A. 7
   2. B. 17
   3. C. 21
   4. D. 27
   Show answer and explanation

   Answer: C

   First find k. f(2) = 3(4) − 7(2) + k = 12 − 14 + k = k − 2. Setting k − 2 = 9 gives k = 11.

   Then f(−1) = 3(−1)² − 7(−1) + 11 = 3 + 7 + 11 = 21.

   7 comes from treating −7(−1) as −7 (3 − 7 + 11). 17 comes from solving k − 2 = 9 as k = 7 instead of k = 11. 27 comes from forgetting to square: computing f(2) as 3(2) − 7(2) + k = k − 8 gives k = 17, and then 3 + 7 + 17 = 27.

2. Question 2MathematicsOne correct answer

   A jar contains 5 red, 4 blue and 3 green marbles. Two marbles are drawn at random, one after the other, without replacement. What is the probability that the two marbles are the same color?

   1. A. 5/33
   2. B. 25/72
   3. C. 1/3
   4. D. 19/66
   Show answer and explanation

   Answer: D

   There are 12 marbles, so the number of possible pairs is 12 × 11 / 2 = 66.

   Same-color pairs: red 5 × 4 / 2 = 10, blue 4 × 3 / 2 = 6, green 3 × 2 / 2 = 3, for a total of 19. The probability is 19/66.

   5/33 (= 10/66) counts only the red pairs. 25/72 is the answer if the first marble were put back before the second draw: (25 + 16 + 9)/144 = 50/144. 1/3 is simply the chance of picking any one given color class from three, which ignores the different counts.

3. Question 3EnglishOne correct answer

   The underlined portion of the sentence below is shown in square brackets.

   The ferry to Halvard Island, [which had run every morning since 1962, were] canceled for the winter after the town lost its only licensed mechanic.

   Which choice is the best version of the bracketed portion?

   1. A. NO CHANGE
   2. B. which had run every morning since 1962, was
   3. C. which had run every morning since 1962 was
   4. D. that had ran every morning since 1962, was
   Show answer and explanation

   Answer: B

   The subject of the sentence is the singular noun 'ferry', so the verb must be 'was', not 'were'. The clause 'which had run every morning since 1962' is nonessential and already opens with a comma, so it must also close with one before the verb.

   Choice B does both. NO CHANGE keeps the agreement error. Choice C fixes the verb but drops the closing comma, leaving the clause half set off. Choice D uses the incorrect form 'had ran' (the past participle is 'run') and sets off a 'that' clause with commas.

4. Question 4EnglishOne correct answer

   (1) Maribel Ortega opened the seed library in a corner of the Eastbrook public library in 2019. (2) Patrons borrow packets of tomato, squash and bean seeds, grow the crops at home, and bring back a portion of the seeds they save at the end of the season. (3) Over five seasons, the collection has slowly filled with varieties suited to the valley's short summers and cold nights.

   The writer is considering adding the following sentence between sentence 2 and sentence 3:

   Seeds saved this way come from plants that have already survived a full growing season in the valley.

   Should the writer make this addition?

   1. A. Yes, because it explains how the borrow-and-return cycle produces seeds adapted to the valley's climate.
   2. B. Yes, because it shows that Ortega grows most of the library's seeds in her own garden.
   3. C. No, because it repeats the point of sentence 2 that patrons return the seeds they save.
   4. D. No, because it interrupts the paragraph's account of how the library was founded.
   Show answer and explanation

   Answer: A

   Sentence 3 claims the collection now suits the valley's climate but never says why. The added sentence supplies the missing link: returned seeds come from plants that have already coped with local conditions, so each season's returns are better adapted. That makes the addition useful, as choice A says.

   Choice B misreads the sentence, which says nothing about Ortega's own garden. Choice C is wrong because sentence 2 describes the returning of seeds, not the fact that those plants survived the local season. Choice D is wrong because the paragraph has already moved past the founding to how the library works.

5. Question 5ReadingOne correct answer

   Most people step over the thin green mats of moss that grow in sidewalk cracks without a second glance. To a small group of environmental chemists, however, those mats are a record book. Mosses have no roots; they take in water and nutrients directly through their leaves, and in doing so they also collect whatever fine particles settle out of the air. Because a moss cannot filter what lands on it, the metals in its tissue closely track the metals drifting through the surrounding neighborhood.

   Air-quality monitors do this job more precisely, but a single station can cost as much as a small house, and most cities run only a handful. Moss, by contrast, is everywhere and costs nothing. In one recent survey, volunteers gathered samples from more than two hundred sites across a mid-sized city in a single weekend. The results revealed a cluster of high cadmium readings around a glassworks that none of the city's four official stations had detected.

   The researchers are careful not to oversell the method. Moss samples cannot show exactly when pollution arrived, and readings vary from one species to another. The value of the survey lies in pointing officials toward the places where an expensive monitor would do the most good.

   The main purpose of the last paragraph is to:

   1. A. argue that moss surveys should replace a city's official air-quality stations.
   2. B. describe the steps volunteers follow when collecting moss samples.
   3. C. explain why cadmium is especially harmful to mosses.
   4. D. acknowledge limits of moss sampling while stating the role it can still serve.
   Show answer and explanation

   Answer: D

   The last paragraph opens by saying the researchers do not want to 'oversell the method', names two weaknesses (no timing information, variation between species), and then states what the method is good for: guiding where to place costly monitors. That is a balance of limits and remaining value, choice D.

   Choice A contradicts the paragraph, which treats moss as a guide for placing monitors, not a substitute for them. Choice B describes nothing in the paragraph; collection is mentioned only briefly in paragraph 2. Choice C is unsupported: the passage says mosses collect metals, not that cadmium harms them.

6. Question 6ReadingOne correct answer

   Tomas had rehearsed the speech on the bus, in the elevator and twice more in the hallway outside his grandmother's apartment. He would tell her calmly that he had left the engineering program after one semester and enrolled in the culinary course across town. He would mention the scholarship first. He would not apologize.

   She opened the door before he knocked, flour on her sleeves, and pulled him into the kitchen, where a tray of empanadas was cooling beside the window. "Crimp the rest," she said, sliding a bowl of filling toward him. "Your fingers were always better at it than mine."

   He worked in silence for a while, pressing the edges with a fork the way she had shown him when he was seven. When he finally looked up, she was watching his hands, not his face, and smiling in a way that made the rehearsed sentences feel unnecessary.

   Which statement best describes how Tomas's feelings change over the course of the passage?

   1. A. He begins excited about his scholarship and ends disappointed that his grandmother ignores his news.
   2. B. He begins confident about his decision and ends worried that his grandmother will disapprove of it.
   3. C. He begins anxious about sharing his decision and ends sensing that his grandmother may already accept it.
   4. D. He begins annoyed at being put to work and ends grateful for the distraction from his speech.
   Show answer and explanation

   Answer: C

   Rehearsing the speech again and again, and planning exactly what to say first and what not to say, shows that Tomas is nervous about the conversation. At the end, his grandmother's smile while watching his skilled hands makes the prepared words 'feel unnecessary', which suggests he now senses she understands and approves of his turn toward cooking. Choice C captures that shift.

   Choice A is wrong because nothing shows disappointment; the ending is warm. Choice B reverses the change: the worry comes first and eases at the end. Choice D is unsupported, since Tomas never shows annoyance at crimping the empanadas.

7. Question 7ScienceOne correct answer

   A student studied how temperature affects the activity of baker's yeast. She added 10 g of dry yeast and 5 g of sugar to each of 5 flasks containing 200 mL of water. Each flask was kept in a water bath at a different temperature, and the volume of carbon dioxide (CO2) gas collected from each flask over 20 minutes was measured.

   Results (temperature: CO2 collected): 15°C: 6 mL; 25°C: 19 mL; 35°C: 34 mL; 45°C: 22 mL; 55°C: 3 mL.

   Based on the results, if the student had also tested a flask kept at 20°C, the volume of CO2 collected in 20 minutes would most likely have been:

   1. A. less than 6 mL.
   2. B. between 6 mL and 19 mL.
   3. C. between 19 mL and 34 mL.
   4. D. greater than 34 mL.
   Show answer and explanation

   Answer: B

   From 15°C to 35°C the CO2 volume rises steadily (6 mL, then 19 mL, then 34 mL). A temperature of 20°C lies between 15°C and 25°C on this rising part of the data, so the volume should lie between the values measured at those two temperatures: between 6 mL and 19 mL.

   Choice A would require activity to drop below the 15°C value, which contradicts the rising trend. Choices C and D describe volumes seen only at or near 35°C, the warmest part of the rising trend, not at 20°C.

8. Question 8ScienceOne correct answer

   Ecologists sampled the bottom of a pond at 4 sites. At each site they measured the dissolved oxygen (DO) in the water and counted the mayfly larvae per square meter of pond bottom.

   Site W: DO 9.1 mg/L, 48 larvae per square meter. Site X: DO 7.4 mg/L, 31 larvae per square meter. Site Y: DO 5.2 mg/L, 12 larvae per square meter. Site Z: DO 3.0 mg/L, 2 larvae per square meter.

   A student hypothesized that the number of mayfly larvae per square meter increases as dissolved oxygen decreases.

   Do the data support the student's hypothesis?

   1. A. Yes; the site with the lowest DO had the most larvae per square meter.
   2. B. Yes; the number of larvae per square meter rose steadily as DO fell.
   3. C. No; the site with the highest DO had the most larvae per square meter, and the site with the lowest DO had the fewest.
   4. D. No; the number of larvae per square meter was about the same at all four sites.
   Show answer and explanation

   Answer: C

   Ordering the sites from highest to lowest DO (W, X, Y, Z) gives larval counts of 48, 31, 12 and 2. As DO decreases, the number of larvae decreases, which is the opposite of the hypothesis. So the answer is No, for the reason given in choice C.

   Choices A and B misread the data: the lowest-DO site (Z) had the fewest larvae, not the most. Choice D is wrong because the counts range widely, from 2 to 48 per square meter.