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1. Pierre competes in a triathlon, along a course as shown in the figure below. He begins swimming at starting point S and swims straight across the lake, gets on his bicycle at station A , bikes to station B , and then runs to finishing line F . The judges use a stopwatch to record his elapsed times of t A , t B , and t F , respectively. If the distance, in miles, between points S and A along the racecourse is denoted by SA , then what is Pierre's average speed for this race, in miles per hour?
(F) SA ⁄ t A (G) SB ⁄ t B (H) SF ⁄ t F (J) SA ⁄ t F (K) SF ⁄ t A
You can determine Pierre's average speed, in miles per hour, by dividing his total mileage by his total time. The total number of miles he covers is the distance from starting point S to finish line F , which is SF . You can eliminate choices (F), (G), and (J) because they don't include the entire length of the racecourse. The total elapsed time from point S to point F is t F . You can eliminate choices (F), (G), and (K) because they don't use the elapsed time clocked at the end of the race.
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2. In the grid shown below, each small square has a side length of 1 unit. In the shaded region, each vertex lies on a vertex of a small square. What is the area, in square units, of the shaded region?
(A) 35 (B) 25 (C) 24 (D) 19 (E) 13
Estimate by calculating the area of a 6 x 6 square surrounding the shaded figure, then counting and subtracting the unshaded squares within that 36 unit area: roughly 18 squares. Subtract 36 - 18 = 18. Answer choice (D) is closest.
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3. (2 – 4t + 5t 2 ) – (3t 2 + 2t – 7) is equivalent to:
(A) 2t 2 – 6t + 9 (B) 2t 2 – 2t + 9 (C) 2t 4 – 2t 2 – 5 (D) 8t 2 – 6t – 5 (E) 8t 4 – 6t 2 – 5
Distribute the minus sign throughout the parentheses before combining like terms: (2 – 4t + 5t 2 ) – 3(t 2 + 2t – 7) = 2 – 4t + 5t 2 – 3t 2 – 2t + 7 = 2t 2 – 6t + 9. The other choices all confuse signs in calculating. Choices (C) and (E) also add the exponents of the terms.
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After reading the passage, choose the best answer to each question. You may refer to the passage as often as necessary. Check out these ACT reading strategies.
This passage is adapted from the novel A Passage to India by Aditi C. Thakur (©2003 by Aditi Thakur).
I'm shivering in the air conditioning. I've never gotten used to the swirl of chilled air in the apartment. I'd like to open the window, to welcome in the hot bright yellow sun, but the superintendent has painted all the building's windows (5) shut for some unexplained reason.
Ramesh won't be home from the university for several hours, I know. The project he's working on is keeping him at the lab until later in the evenings these days. Still shivering, I mull the choices for our evening meal, scanning the vegetables, (10) herbs, and spices I collected at the specialty food market this morning. Even after five years in the United States, I find I still seek the patterns of our life in India, including my daily morning visits to the market for the day's food shopping.
(15) As I pore over the curled turmeric roots and the bright orange and red mangoes—both of which appeared in the market's bins today for the first time—I remember the first time I went to an American-style supermarket. Intimidated by the unfamiliar streets and landmarks of our new city, Ramesh (20) and I had spent the first month of our American life eating all our meals at restaurants within walking distance of the flat. Ramesh had concocted his lunch from items purchased at the university's "convenience store"; he joked that convenience was really the only desirable thing the shop offered. Once we (25) had exhausted the menus at each of the nearby restaurants, I promised that I would brave the supermarket so we could both have a taste of the home we'd been aching for.
Naturally—or rather, unnaturally—the store was cold, and I was glad I had decided to bring along my dupatta to (30) shield my otherwise bare shoulders.
At first, the enormous quantity of goods and the wildly varied colors everywhere I looked were impressive. But then I noticed that the produce section—it seemed surprisingly tucked away on the end farthest from the doors, as if the store (35) were somehow ashamed of it—lacked items we considered favorites or even staples: no dried lentils or chickpeas, no cherimoyas or pomegranates. I wandered up and down the aisles, wondering at the slabs of meat sealed within cocoons of plastic, and at the seemingly infinite rows of boxes, (40) each of which somehow housed "dinner for the whole family." Unable after a time to focus on the boxes' labels, I turned to a gangly, uniformed teenager who was pretending to straighten the ginger ale bottles on the bottom shelf.
"Excuse me, please, I am wondering whether you could (45) help me find. " I began.
He glanced up at me, noting my sari with an eye that felt at once piercing and uncritical. "Aisle 7, on the right," he squeaked, with a wide, unexpectedly amiable grin.
My irritation at having been so easily categorized faded (50) somewhat at discovering two shelves’ worth of jars of chutneys and mixes, including one imported tandoor paste that had been one of our favorites back in India. But as I unsteadily but successfully navigated the checkout lines and paid for my few, familiar products, I observed that the supermarket's (55) fluorescent ceiling bulbs effectively bleached out the shelves' contents. The bottles and boxes no longer seemed exotic or glamorous. It seemed to me that no matter how insistently the labels tried to draw attention to the wonders within their containers, the vividness of their colors would inevitably (60) appear flat and lifeless under the homogenizing light.
I still go to the supermarket sometimes, but recently a colleague of Ramesh's recommended that we go to the outskirts of the city to shop at a new Indian market, where I went this morning. The old woman who manages the places (65) moves quickly from stall to stall, urging customers to sample pieces of fruit or explaining how adding one more ingredient will perfect the planned dish. She reminds me, almost painfully, of my grandmother, who was similarly convinced that she could make others' lives better though shared food or (70) wisdom—my grandmother, to whose image I've often come back whenever I've needed consolation or company.
I trace my finger along the beige granite countertop, as if conjuring up the rough wooden surface in my grandmother's kitchen. As a child, I'd believed the dark wood had retained (75) every nick from every vegetable chopped, and every stain from every fruit that had yielded its sticky sweetness to my grandmother's swift, sure knife. I think of the fourteen distinct spices, each with its own grainy texture and subtle but memorable color, that she pounded into dust with her mortar (80) and pestle. Then I recall the grayish, unfriendly curry powder I'd seen in the American supermarket, so unlike the familiar result of my grandmother's efforts. I sigh.
I don't really need to begin to prepare our dinner yet. I've learned to combine the specialty market's fresh produce with (85) the supermarket's "quick prep" sauces and pastes, so making dinner isn't the all-day task it often was for my grandmother and even my mother. Even so, I decide to ward off the cold by shrugging on a sweatshirt embossed with the university's logo, and I set myself to work.
1. It can most reasonably be inferred from the passage that the narrator regards her grandmother as:
(A) comforting.
(B) frightening.
(C) foolish.
(D) out of touch.
Although the narrator recalls the memory of her grandmother almost painfully (lines 67—68), she goes on to note that her grandmother's image was one to which the narrator has often come back whenever I've needed consolation or company (lines 70—71). This description doesn't match the words featured in choices (B), (C), or (D), so choice (A) is the best selection here.
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2. The narrator refers to the supermarket's "fluorescent ceiling bulbs" (line 55) in order to:
(A) draw a contrast between the supermarket and the outdoor markets she remembers from India.
(B) explain how her perception of the store's offerings had changed.
(C) suggest one reason that the supermarket terrified her.
(D) describe why she was able to see the fruits and vegetables more clearly.
First, find the reference to fluorescent lighting; the narrator says that it bleached out the packages' colors, making them flat and lifeless (line 60). Choice (D) is nearly an opposite answer, whereas choice (A) refers to a contrast the narrator doesn't draw in the passage. Choice (C) points to an earlier part in the passage; by the time the narrator describes the lighting, she is no longer intimidated by the store (and terrified is certainly too strong in any case). Choice (B) correctly references the passage's description of the fluorescent lights: I observed that the supermarket's fluorescent ceiling bulbs effectively bleached out the shelves’ contents. The bottles and boxes no longer seemed exotic or glamorous (lines 53—56).
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3. As it is used in line 80 the word unfriendly most nearly suggests that:
(A) the narrator thinks that the clerk doesn't want her to buy the curry powder.
(B) the narrator considers this curry powder to be different from the curry powder with which she is familiar.
(C) the narrator doesn't like the ingredients in the curry powder.
(D) the curry powder has been imported from another country.
Unfriendly is a strange word to apply to an inanimate object such as a jar of curry powder, so examine the context to try to make sense of that term here. The narrator has just been thinking about the difference spices— each with its own. subtle but memorable color —that her grandmother used to make homemade curry powder (lines 78-79). In the next lines, the narrator sets up a contrast between the unfamiliar curry powder in the supermarket and the familiar result of her grandmother's efforts . Consequently, choice (B) is the best option. Choices (C) and (D) don't work because the narrator doesn't mention either the curry powder’s ingredients or its country of origin. And you can eliminate choice (A) because the clerk in fact tells the narrator where to find the product.
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Questions 1—6 are based on the following passage.
In the passage that follows, certain words and phrases are underlined and numbered. In the questions, you will find alternatives for the underlined parts. In most cases, you are to choose the one that best expresses the idea, makes the statement appropriate for standard written English, or is worded most consistently with the style and tone of the passage as a whole. If you think the original version is best, choose "No Change." In some cases you will find a question about the underlined part. You are to choose the best answer to the question. Stumped? Check out these tips for tackling the ACT English test.
André Bazin's Nouevelle Vague
André Bazin died on November 11, 1958 after over 15 years of pioneering work in film criticism. His magazine, Cahiers du Cinéma (Cinema Notebooks), had been issued regularly since its founding in 1951, and it had become the premier journal in French for the serious discussion of films. Bazin, working and living in Paris, had become one of the (1) cities premier intellectuals. Despite all of the achievements of Bazin's lifetime, the true fruit of his labor did not begin to become truly apparently until the year following Bazin's death. It was (2) in 1959 in Paris that the nouvelle vague (new wave) in French cinema (3) exploded onto the international film scene.
Bazin published his first piece of film criticism in 1943 and pioneered a new way of writing about (4) film, he championed the idea that cinema was the "seventh art," every bit as deserving as the more respected arts (5) of: architecture, poetry, dance, music, painting, and sculpture. Many before Bazin's time thought of the cinema as a simple extension of another art form: theater. In fact, in many early writings about film, it is not uncommon to hear the authors speak of film. (6) Bazin, though, sought to show that the cinema had every bit as much creative vitality and craftsmanship as any of the other six arts. From this fundamental belief came what was possibly Bazin's greatest contribution to film criticism: auteur theory.
1.
(A) NO CHANGE
(B) citys
(C) cities'
(D) city's
Bazin is described in this sentence as being the premier intellectual who belongs to or is part of a city. Since you need to show this possessive relationship, you can eliminate choices (A) and (B). To decide between choices (C) and (D), you need to figure out whether you're dealing with a singular city or plural cities . In this situation, the city is Paris and none other, so the best answer is (D).
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2.
(F) NO CHANGE
(G) in 1959 in Paris,
(H) in 1959, in Paris
(J) in, 1959 in Paris,
Don't insert a comma into this sentence if you don't need to. There is nothing in the sentence that has to be set off as unnecessary or interruptive, so no commas are necessary. Note how choices (G), (H), and (J) all break the flow of the sentence.
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3. Which of the following alternatives to the underlined portion is LEAST acceptable?
(A) emerged
(B) released
(C) erupted
(D) burst
All the words in the answer choices can be synonyms for the word exploded , but in this case, the word released does not make sense. The films were released , but it doesn't make sense to say that the films released , making choice (B) the LEAST acceptable alternative.
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4.
(F) NO CHANGE
(G) film. He
(H) film he
(J) film. Although he
Note the context on either side of the punctuation. Before the comma, you have Bazin published his first piece of film criticism in 1943 and pioneered a new way of writing about film and after the comma you have he championed the idea that cinema was the seventh art. . Since both of these are complete ideas, choices (F) and (H) cannot work because neither separates those complete ideas appropriately. Choice (J) introduces a period but, with the word although , turns the part after the period into a sentence fragment. Only choice (G) has the appropriate punctuation.
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5.
(A) NO CHANGE
(B) of, architecture,
(C) of architecture,
(D) of, architecture
Architecture is the first word in a series here, and every word in a series must be succeeded by a comma, so you can eliminate choice (D). If you are to use a colon to introduce a list, the words directly before it must form a complete sentence, which every bit as deserving as the more respected arts of does not—eliminate choice (A). Choice (B) introduces an unnecessary pause before the word architecture . Only choice (C) preserves the flow of the sentence and properly situates the word architecture in a list.
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6. The writer is considering adding the following phrase to the end of the preceding sentence (deleting the period after the word film ):
as a second class substitute for the "legitimate theatre."
Should the writer make this addition there?
(F) Yes, because it clarifies the sentence to show more specifically how critics talked about film.
(G) Yes, because it helps the reader to understand more clearly the subjects of Bazin's writing.
(H) No, because it fails to maintain this paragraph's focus on the Cahiers du Cinéma .
(J) No, because it speaks disparagingly about the practice of filmmaking.
Without the proposed addition, the sentence does not have any clear connection to its context. To include the proposed addition is to tie the sentence to the previous sentence's mention of the word theatre . Because you'll want to include the sentence, you can conclusively eliminate choices (H) and (J). You can also eliminate choice (G) because this sentence is not discussing Bazin's own writing; rather, it is discussing the work of authors of many early writings about film . Only choice (F) advises that the writer add the clause and indicates that the writer do so because this will make this sentence more clear and precise.
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After reading the passage, choose the best answer to each question. Check out these ACT science test-taking tips.
As the pressure on a gas is increased the volume of that gas is expected to decrease by an inversely proportional amount. For example, if pressure is doubled the volume is halved. Under certain conditions, the volume of the gas will change by an amount that deviates from an inverse proportion. Various 10.000 L samples of gas were subjected to increases in pressure. Table 1 shows the resulting volume changes at 300°C, while Tables 2 and 3 show the volume changes at 25°C; and -200°C, respectively. All pressures are measured in atmospheres (atm).
| 300°C | Initial pressure (atm) | Final pressure (atm) | Volume change (L) |
|---|---|---|---|
| Oxygen | 1 | 2 | -5.00 |
| Oxygen | 2 | 4 | -5.00 |
| Oxygen | 3 | 6 | -5.00 |
| Argon | 2 | 4 | -5.00 |
| Argon | 4 | 5 | -2.00 |
| Carbon Dioxide | 1 | 5 | -8.00 |
| Carbon Dioxide | 3 | 6 | -5.00 |
| Carbon Dioxide | 4 | 10 | -6.00 |
| 25°C | Initial pressure (atm) | Final pressure (atm) | Volume change (L) |
|---|---|---|---|
| Methane | 1 | 2 | -5.00 |
| Methane | 2 | 4 | -5.00 |
| Helium | 1 | 2 | -5.00 |
| Helium | 1 | 5 | -8.00 |
| Helium | 2 | 5 | -6.00 |
| Nitrogen | 1 | 5 | -8.00 |
| Nitrogen | 2 | 4 | -5.00 |
| Nitrogen | 4 | 5 | -2.00 |
| -200°C | Initial pressure (atm) | Final pressure (atm) | Volume change (L) |
|---|---|---|---|
| Neon | 1 | 2 | -5.02 |
| Neon | 2 | 4 | -5.03 |
| Neon | 4 | 8 | -5.06 |
| Helium | 1 | 2 | -4.98 |
| Helium | 2 | 4 | -4.97 |
| Hydrogen | 1 | 2 | -5.01 |
| Hydrogen | 1 | 5 | -8.02 |
| Hydrogen | 1 | 10 | -9.03 |
1. Which of the following gases showing in Tables 1–3 was compressed by the same amount each time the pressure was changed, regardless of its initial pressure?
(A) Helium
(B) Carbon Dioxide
(C) Neon
(D) Oxygen
For every trial involving oxygen in Table 1, the volume decreased by exactly 5.00 L. All the other choices had volume changes that varied.
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2. Which of the following is the best explanation for the change in volume seen in any one of the samples of carbon dioxide in Table 1? As pressure on one sample of carbon dioxide was increased, the volume of that sample:
(F) increased as the molecules of carbon dioxide were forced closer together.
(G) increased as the molecules of carbon dioxide were forced farther apart.
(H) decreased as the molecules of carbon dioxide were forced closer together.
(J) decreased as the molecules of carbon dioxide were forced farther apart.
In Table I, each trial involving carbon dioxide showed a negative volume change, or decrease in volume. Therefore, choices (F) and (G) are eliminated. The molecules will occupy less volume only if they are pushed closer together, eliminating choice (J).
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3. A scientist concludes that whenever the pressure on helium is increased, its volume will decrease. Based on Tables 2 and 3, is this a valid conclusion?
(A) Yes; in every trial that the pressure of helium was increased, the change in volume was negative.
(B) No; in every trial that the pressure of helium was increased, the change in volume was positive.
(C) Yes; when the pressure on helium was increased from 1 to 2 atm, its change in volume was positive at 25°C and negative at -200°C.
(D) No; when the pressure on helium was increased from 1 to 2 atm, its changes in volume was negative at 25°C and positive at -200°C.
No trials on any of the tables have positive changes in volume, so you can eliminate choice (B). Choices (C) and (D) can be eliminated because while the pressure changes at different temperatures produced differing results for volume, the volume was always decreasing.
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