ACT · Practice test 1

171 questions, each with its skill and the official answer.

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Question Math · 5

Multiple choice
Question Math · 5 — 5. Which of the following expressions is equivalent to x 2 − x − 30 ? A. (x + 3) (x − 10) B. (x + 6) (x − 5) C. (x − 6) (x + 5) D. (x − 15) (x − 15)

Source: ACT, Inc. — ACT Practice test 1

Question Math · 9

Multiple choice
Question Math · 9 — 9. If 6y = 5x − 1 , then x = ? A. 6 _ 5 y − 1 B. 6 _ 5 y + 1 C. 6y − 1 _ 5 D. 6y + 1 _ 5

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Question Math · 13

Multiple choice
Question Math · 13 — 13. For an angle with measure α in a right triangle, sin α = 5 _ 13 and tan α = 5 _ 12 . What is the value of cos α ? A. 12 _ 13 B. 12 _ √ _ 194 C. 12 _ √ _ 119 D. 13 _ 12

Source: ACT, Inc. — ACT Practice test 1

Question Math · 15

Multiple choice
Question Math · 15 — 15. Which of the following expressions is equivalent to (y + 7) 3 ? A. y 3 + 21 y 2 + 147y + 343 B. y 3 + 14y + 343 C. y 3 + 14y + 49 D. y 3 + 343

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Question Math · 17

Multiple choice
Question Math · 17 — 17. Which of the following expressions is equivalent to ( x 2 − y 2 ) − (6 x 2 + 4xy − y 2 ) ? A. −5 x 2 − 4xy B. −5 x 2 + 4xy − 2 y 2 C. 7 x 2 + 4xy − 2 y 2 D. 7 x 2 + 4xy + 2 y 2

Source: ACT, Inc. — ACT Practice test 1

Question Math · 18

Multiple choice
Question Math · 18 — 18. Given i = √ _ −1 , what is √ _ 9 + √ _ −16 ? F. 7i G. i √ _ 7 H. 3 − 4i J. 3 + 4i

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Question Math · 19

Multiple choice
Question Math · 19 — 19. The first 5 terms of an arithmetic sequence are 7 , 21 , 35 , 49 , and 63 . Let t n represent the n th term of the sequence. What is the value of t 25 ? A. 175 B. 343 C. 357 D. 371

Source: ACT, Inc. — ACT Practice test 1

Question Math · 20

Multiple choice
Question Math · 20 — 20. At a certain time of day, a flagpole casts a 9.0 -foot-long shadow and a nearby 4.0 -foot-tall fence post casts a 2.4 -foot-long shadow. Given that both the flagpole and the fence post are vertical and on level…

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Question Math · 23

Multiple choice
Question Math · 23 — 23. Let f (t) = 7 e 3t + 1 . Which of the following numbers is closest to the value of f (5) ? A. −2 × 10 −1 B. 3 × 10 2 C. 2 × 10 7 D. 6 × 10 7

Source: ACT, Inc. — ACT Practice test 1

Question Math · 24

Multiple choice
Question Math · 24 — 24. Which of the following expresses 40° in radians? F. 2 _ 9π G. 2π _ 9 H. 9π _ 2 J. 7,200 _ π

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Question Math · 25

Multiple choice
Question Math · 25 — 25. Let the function f be defined as f (x) = −9 x 2 . In the standard (x,y) coordinate plane, the graph of y = f (x) undergoes a transformation such that the result is the graph of y = f (x) − 4 . Under this…

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Question Math · 26

Multiple choice
Question Math · 26 — 26. For all positive values of a , b , c , and d , when 1 _ 2 a b 2 + c = d , which of the following expressions is equal to b ? F. √ _ a (d − c) _ 2 G. √ _ 2 (d − c) _ a H. √ _ 2d − c _ a J. √ _ d − c _ 2a

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Question Math · 28

Multiple choice
Question Math · 28 — 28. A regular hexagon is inscribed in a circle with diameter 18 inches, as shown. What is the perimeter, in inches, of the hexagon? 18 in F. 54 G. 108 H. 27 √ _ 3 J. 54 √ _ 3

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Question Math · 29

Multiple choice
Question Math · 29 — 29. Tanya earns $34,000 in her 1 st year at a job. She is given a raise of the same dollar amount each year, resulting in her earning $38,080 in the 4 th year at the job. What is the total of Tanya’s earnings during her…

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Question Math · 30

Multiple choice
Question Math · 30 — 30. In the standard (x,y) coordinate plane, how many points are both 5 coordinate units from the origin and also 2 coordinate units from the line y = 0 ? F. 0 G. 1 H. 2 J. 4

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Question Math · 31

Multiple choice
Question Math · 31 — 31. In nABC , if the measure of ∠A is less than the measure of ∠B , and the measure of ∠B is less than the measure of ∠C , what is the correct ordering of the side lengths, from least to greatest? A. AB < BC < AC B. AB…

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Question Math · 37

Multiple choice
Question Math · 37 — 37. The polynomial function defined by p ( x ) = x 3 + x 2 − 8x − 12 has ( x − 3 ) as one of its linear factors. What are all and only the zeros of p ? A. −3 and −2 B. −3 and 2 C. −2 and 3 D. 2 and 3

Source: ACT, Inc. — ACT Practice test 1

Question Math · 40

Multiple choice
Question Math · 40 — 40. Given the equation 4 √ _ x = y , where y is a real number, what must be true of x ? x is: F. an even real number. G. a rational number. H. an integer. J. a nonnegative real number.

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Question Math · 44

Multiple choice
Question Math · 44 — 44. The table gives values of f (x) , g (x) , and h (x) for all positive integers x ≤ 5 . Given h ( f (g (a) ) ) = 1 where a is a positive integer less than or equal to 5 , what is the value of a ? x f (x) g (x) h (x) 1…

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