ACT · Practice test 3

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

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Question Math · 1

Multiple choice
Question Math · 1 — 1. In the section of Middleton shown on the given map, the avenues and boulevards form a uniform square grid. At the annual Middleton Scavenger Hunt, the winners receive wonderful prizes. Clue 1 states that Clue 2 will…

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Question Math · 7

Multiple choice
Question Math · 7 — 7. An absolute value function is shown in the standard ( x,y ) coordinate plane. Which of the following lists all the x -intercepts of the graph? y x 2 3 1 1 −1 4 5 6 7 8 9 −4 −4 −5 −2 −3 −3 −2 −1 O A. ( 0,−3 ) only B.…

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Question Math · 10

Multiple choice
Question Math · 10 — 10. If ⎪4x − 3⎪ = 7 , which of the following is a possible value for x ? F. −3 G. −1 H. 1 J. 3

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Question Math · 12

Multiple choice
Question Math · 12 — 12. Which of the following is equivalent to the given expression? 3x y 2 − 4 x 2 y + 12 x 2 y − 7x y 2 F. −8 x 2 y + 4x y 2 G. − x 2 y + 5x y 2 H. x 2 y − 5x y 2 J. 8 x 2 y − 4x y 2

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Question Math · 14

Multiple choice
Question Math · 14 — 14. The 1 st through 5 th terms, in order, of an infinite arithmetic sequence are −3 , −7 , −11 , −15 , and −19 . What is the 21 st term of the sequence? F. −63 G. −77 H. −79 J. −83

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Question Math · 16

Multiple choice
Question Math · 16 — 16. If (x + k) 2 = x 2 + 94x + k 2 , then k = ? F. 47 G. 94 H. 188 J. 376

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Question Math · 17

Multiple choice
Question Math · 17 — 17. Given that f (x) = −10 + x and g (x) = 2 , it must be true that f _ g (x) = ? A. −10 + x _ 2 B. −10 + 2x C. −5 + x _ 2 D. −5 + 2x

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Question Math · 20

Multiple choice
Question Math · 20 — 20. The inequality 7 (x + 4) > 8 (x − 2) is equivalent to which of the following inequalities? F. x < 2 G. x < 6 H. x < 12 J. x < 44

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Question Math · 21

Multiple choice
Question Math · 21 — 21. In the figure shown, ⟶ PR bisects ∠QPS , m∠QPS = 64° , and m∠RPS = (2x + 10) ° . What is the value of x ? Q P R S A. 11 B. 21 C. 27 D. 53

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Question Math · 22

Multiple choice
Question Math · 22 — 2 22. Given that sin θ = 1_ 3 and cos θ = 2 √ _ 2 _ 3 , what is tan θ ? F. 1 _ 2 √ _ 2 G. 3 _ 2 √ _ 2 H. 2 √ _ 2 _ 3 J. 2 √ _ 2

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Question Math · 23

Multiple choice
Question Math · 23 — 23. The graph of 4 (x + 1) 2 − 5 (y + 9) 2 = 100 is a hyperbola in the standard (x,y) coordinate plane. What is the point of intersection of the hyperbola’s asymptotes? A. (−4,5) B. (−1,−9) C. (1,9) D. (4,−5)

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Question Math · 24

Multiple choice
Question Math · 24 — 24. ( √ _ 3 + √ _ 7 ) 2 = ? F. 10 G. 10 + √ _ 42 H. 10 + 2 √ _ 21 J. 2 √ _ 3 + 2 √ _ 7

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Question Math · 27

Multiple choice
Question Math · 27 — 27. Rectangle R has vertices (−4,3) , (2,3) , (2,−2) , and (−4,−2) in the standard (x,y) coordinate plane. Reflecting R across the x -axis will result in rectangle R′ . Reflecting R′​ across the y -axis will result in…

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Question Math · 28

Multiple choice
Question Math · 28 — 28. Let f ( x ) = −x + 5 and g(x) = 4 x 2 + 8x − 4 . One of the following points is a point of intersection of the graphs of y = f ( x ) and y = g ( x ) in the standard ( x,y ) coordinate plane. Which one? F. (−3, 3 _ 4…

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Question Math · 30

Multiple choice
Question Math · 30 — 30. Points K and W are on the given circle with center C such that WK = 5 √ _ 2 inches and the measure of ∠WCK is 90° . What is the area, to the nearest 0.1 inch, of the circle? C W K F. 31.4 G. 39.3 H. 78.5 J. 157.1

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Question Math · 31

Multiple choice
Question Math · 31 — 31. A formula was evaluated with the nonzero real numbers a , b , m , and d . The resulting equation a = bmd is not true, but it becomes a true equation when m is increased by n . Which of the following equations gives…

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Question Math · 32

Multiple choice
Question Math · 32 — 32. As given, a right pyramid has a square base, PQRS , and a vertex, T . Points M and N are the midpoints of ‾ PQ and ‾ RS . The height of the pyramid is 12 cm, and each side length of the base is 5 cm. Among the…

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Question Math · 34

Multiple choice
Question Math · 34 — 34. The function p is defined by p ( x ) = −4 x 2 . The function r is defined by r ( x ) = p ( x + 6 ) . The graph of y = r ( x ) in the standard ( x,y ) coordinate plane is the graph of y = p ( x ) : F. shifted in the…

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Question Math · 35

Multiple choice
Question Math · 35 — 35. The equation a [ 5 b 1 bc ] = [ 10 2 c d ] is true for the fixed real numbers a , b , c , and d . What is the value of d ? A. 1 B. 2 C. 4 D. 8

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Question Math · 37

Multiple choice
Question Math · 37 — 37. Haruka is a long-distance runner who competes both in 10,000 -meter races and in marathons, which are run over a distance of 26.2 miles. Given that 1.0 mile is approximately 1.6 kilometers, which of the following…

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Question Math · 38

Multiple choice
Question Math · 38 — 38. What is the value of cos (Arcsin ( 8 _ 17 ) ) ? F. 8 _ 17 G. 15 _ 17 H. 8 _ 15 J. 17 _ 8

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Question Math · 39

Multiple choice
Question Math · 39 — 39. An object is launched vertically at 44.1 meters per second from a 931 -meter-tall platform. The function s = −4.9 t 2 + 44.1t + 931 gives the object’s height, s meters, at the time t seconds after launch. What is…

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Question Math · 40

Multiple choice
Question Math · 40 — 40. 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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Question Math · 41

Multiple choice
Question Math · 41 — 41. For all x and y such that y = log 10 (2x) , which of the following expressions is equal to x ? A. ( 1 _ 2 ) 10 y B. 10 y −​2 C. 10 √ _ y D. 10 2y

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Question Math · 42

Multiple choice
Question Math · 42 — 42. What is the binomial expansion of (x − 5) 4 ? F. x 4 + 625 G. x 4 − 20 x 2 + 625 H. x 4 − 5 x 3 + 25 x 2 − 125x + 625 J. x 4 − 20 x 3 + 150 x 2 − 500x + 625

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Question Math · 43

Multiple choice
Question Math · 43 — 43. Triangle A has an area of 16 √ _ 3 square feet. Triangle B is the result of a dilation on Triangle A and has sides that are 1 _ 2 as long as the corresponding sides of Triangle A. What is the area, in square feet,…

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Question Math · 45

Multiple choice
Question Math · 45 — 45. A skater’s speed increased over a 6 -second interval. His initial speed was 4 meters per second, and his speed 6 seconds later was 6 meters per second. Which of the following was the average rate of change of the…

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