ACT sample questions, with worked answers

C: logbook: the weather. The words after "logbook" list what she recorded, and a colon introduces a list after a complete clause. A semicolon needs a complete sentence after it, and the comma is unclear.

D: tell me. The subject is "Those two words" (plural), so the verb is "tell."

C: No, because it adds a detail about the lens that distracts from the description of her nightly routine.. Sentences 2 and 3 describe her routine; the origin of the lens is off topic. It does not repeat sentence 1.

B: there are. The subject comes after the verb: "more than sixty" (tables) is plural, so the verb is "are." "Was" also breaks the present-tense "Now."

1. Find the subject: "more than sixty" tables.
2. It is plural, so the verb is "are."
3. "Now" calls for present tense: "there are."

The trap: Keeping NO CHANGE because "there is" sounds natural in speech. After "there," the verb agrees with what follows.

C: No, because it does not relate to the market's growth described in sentences 3 and 4.. Sentences 3 and 4 trace how the market grew. A general fact about corn interrupts that and adds nothing to the point.

1. What do sentences 3 and 4 do? Show the market growing.
2. Does the new sentence help with that? No.
3. So do not add it, for that reason.

The trap: Saying no for the wrong reason. It does not repeat sentence 2, so the reason must be that it is off topic.

D: 42. a² + b² = c²: 58² − 40² = 3364 − 1600 = 1764, so the other leg is 42. Subtracting the sides without squaring gives 18.

A: 10. Factor: (x − 1)(x − 9) = 0, so x = 1 or x = 9. Their sum is 10. Shortcut: for x² + bx + c = 0 the sum of the solutions is −b and the product is c; answering −10 forgets the minus sign.

D: 3. log₃ 27 asks: 3 to what power is 27? 3³ = 27, so the answer is 3. 27 ÷ 3 = 9 confuses a logarithm with division.

A: 50. Three steps take 5 to 20, so the common difference is 5. The 10th term is 5 + 9 × 5 = 50.

1. From term 1 to term 4 is 3 steps: d = (20 - 5) ÷ 3 = 5.
2. Term n = 5 + (n - 1) × 5.
3. Term 10 = 5 + 45 = 50.

The trap: Using 10 steps instead of 9 (55), or dividing by 4 steps instead of 3.

A: 13. This is a difference of squares: 3² - (2i)² = 9 - 4i² = 9 + 4 = 13.

1. (a - b)(a + b) = a² - b².
2. 3² - (2i)² = 9 - 4i².
3. i² = -1, so 9 + 4 = 13.

The trap: Treating i² as +1, which gives 5.

A: 3/5. The hypotenuse is √(81 + 144) = √225 = 15. Sine is opposite over hypotenuse: 9/15 = 3/5.

1. Hypotenuse: √(9² + 12²) = √225 = 15.
2. Sine = opposite ÷ hypotenuse.
3. 9 ÷ 15 = 3/5.

The trap: Using the other leg as the hypotenuse (9/12 = 3/4, the tangent), or taking the cosine (12/15 = 4/5).

C: a childhood encounter that stayed with the narrator's main character into adulthood.. The passage centers on Clara watching the tuner and the answer she remembered "years later." There is no dispute, history or money problem.

C: She let him in, offered him coffee, and left him alone to work.. The first paragraph says her mother "let him in, offered him coffee he always refused, and left him alone."

A: his visits followed a familiar, repeated pattern.. "Always" shows the offer and refusal happened every visit, like the visit itself every spring.

A: explain why the cause of purring is still debated.. The passage questions the "contentment" explanation, offers two others, and ends with scientists "divided." Its purpose is to show the question is open.

1. Paragraph 1: the obvious explanation does not cover all cases.
2. Paragraph 2: two other ideas, one untested.
3. Ending: scientists remain divided. So, explaining a debate.

The trap: Choosing the healing idea. The passage calls it "speculative" and untested, so it does not prove it.

A: show that purring cannot be explained by contentment alone.. Purring in unpleasant situations is the evidence against "cats purr because they are content." That is why the passage mentions them.

1. Which claim comes just before? Cats purr because they are content.
2. The details are situations that are "hardly pleasant."
3. So they challenge the contentment explanation.

The trap: Reading too much into the details. Nothing says purring causes injuries or that cats feel no pain.

A: 11 mm. Find the 35°C row and read the Strain 1 column: 11 mm. The other values are Strain 2's at the same temperature or Strain 1's in neighboring rows.

D: increased and then decreased. Read down the Strain 2 column: 7, 11, 18, 12, 8. The values rise to 18 at 30°C and then fall.

B: Between 3 mm and 11 mm. 37.5°C lies between 35°C and 40°C, where Strain 1's colony diameter was 11 mm and 3 mm. The data change steadily between those points, so the value would most likely fall between them.

A: between 238 and 287 g. 50°C lies between the 40°C and 60°C rows, and the amount rises steadily with temperature, so it falls between 238 and 287 g.

1. Find the rows on either side of 50°C: 40°C and 60°C.
2. Their values are 238 and 287 g.
3. The trend is steady, so the answer lies between them.

The trap: Picking the 60°C to 80°C interval by reading the wrong pair of rows.

A: gets larger with each step. The increases are 38 g (20 to 40°C), 49 g (40 to 60°C) and 75 g (60 to 80°C), so each step adds more than the last.

1. Subtract neighbors: 238 - 200 = 38.
2. 287 - 238 = 49; 362 - 287 = 75.
3. The increases grow: 38, 49, 75.

The trap: Answering "stays the same" because the temperature steps are equal. Equal steps in x do not mean equal steps in y.

A: greater than 362 g. The amount rises at every step and the increases are getting larger, so at 100°C, beyond the last row, it should be more than the 362 g measured at 80°C.

1. 100°C is past the last row (80°C), so this is extrapolation.
2. Every step up in temperature raised the amount, and by more each time.
3. So the value at 100°C should exceed 362 g.

The trap: Choosing an interval from inside the table. Beyond the last row, a rising trend points past the last value.