ACT · Practice test 4

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

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Question Math · 1

Multiple choice
Question Math · 1 — 1. Circles A and B are externally tangent to each other, and 3 sides of rectangle RSTU are tangent to each circle, as shown. The radii of circles A and B are both 5 centimeters. What is the length, in centimeters, of ‾…

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Question Math · 4

Multiple choice
Question Math · 4 — 4. The yearly profits, in dollars, of a small business are modeled by P ( t ) = t 3 + 3 t 2 − 4 , where P is the yearly profit and t is the number of years since the business started. What are the profits of this small…

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Question Math · 5

Multiple choice
Question Math · 5 — 5. Which of the following equations has the solution set {4,−7} ? A. (x − 4) (x + 7) = 0 B. (x − 3) (x − 11) = 0 C. (x − 3) (x + 11) = 0 D. (x + 4) (x − 7) = 0

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Question Math · 9

Multiple choice
Question Math · 9 — 9. Given the rectangular prism shown, which of the following statements is true? B A E D C G F H A. A , B , F , and H lie in the same plane. B. B , C , and D lie on the same line. C. Plane ABCD is parallel to plane AEHD…

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Question Math · 10

Multiple choice
Question Math · 10 — 10. Consider the function g (x) = −2 x 2 and its graph in the standard (x,y) coordinate plane. Which of the following transformations on the graph of y = g (x) will result in the graph of y = g (x) + 7 ? F. A shift of 7…

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Question Math · 12

Multiple choice
Question Math · 12 — 12. Triangles nXYZ and nABC are shown with side lengths given in inches. Given nXYZ ~ nABC , what is the value of x ? F. −4 G. 4_ 7 H. 8 J. 12

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Question Math · 13

Multiple choice
Question Math · 13 — 13. For the first 10 weeks of his new job, Bill’s take-home pay was $200 a week. Each week he put $30 in a savings plan. His take-home pay increased to $240 beginning with the 11 th week, and he increased his weekly…

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Question Math · 14

Multiple choice
Question Math · 14 — 14. If (x + k) 2 = x 2 + 70x + k 2 , then k = ? F. 35 G. 70 H. 140 J. 280

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Question Math · 15

Multiple choice
Question Math · 15 — 15. For what value of x is the given function undefined? f (x) = 5 _ 2 (x − 7) A. 7 B. 5 C. 0 D. −7

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Question Math · 16

Multiple choice
Question Math · 16 — 16. 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 · 17

Multiple choice
Question Math · 17 — 17. When x = 2 , 2 _ 2 + 2 _ x + 2 = ? A. 1 _ 2 B. 4 _ 5 C. 2 D. 5 _ 2

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Question Math · 18

Multiple choice
Question Math · 18 — 18. For all real values of x , which of the following expressions is equal to 9 x 2 + 9x − 4 ? F. 9 ( x 2 + x − 4) G. (9x + 4) (x − 1) H. (3x − 4) (3x + 1) J. (3x + 4) (3x − 1)

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Question Math · 20

Multiple choice
Question Math · 20 — 20. For all x , 12 x 2 + 4 _ 4 = ? F. 3 x 2 G. 3 x 2 + 1 H. 3 x 2 + 4 J. 12 x 2

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Question Math · 21

Multiple choice
Question Math · 21 — 21. In the given figure, ∠RVS is congruent to ∠UVT and ‾ SV is congruent to ‾ VT . One of the following angle congruences completes what is needed to prove as directly as possible that nRSV is congruent to nUTV by…

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Question Math · 23

Multiple choice
Question Math · 23 — 23. The first 4 terms of a geometric sequence are given. 3i , −6 , −12i , 24 , … What is the 5 th term of this sequence? A. −48 B. −48i C. 48 D. 48i

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Question Math · 24

Multiple choice
Question Math · 24 — 24. The graph of the function y = 6 cos x is given in the standard (x,y) coordinate plane. What are the amplitude and period of the function? F. The amplitude is 6 , and the period is π . G. The amplitude is 6 , and the…

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Question Math · 28

Multiple choice
Question Math · 28 — 28. If 3x − y _ x + y = 5 _ 8 , then x _ y = ? F. 2 _ 19 G. 13 _ 19 H. 5 _ 8 J. 13 _ 7

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Question Math · 29

Multiple choice
Question Math · 29 — 29. Which of the following statements about rational and irrational numbers is true? A. The sum of any rational number and any irrational number is a rational number. B. The sum of any rational number and any irrational…

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Question Math · 30

Multiple choice
Question Math · 30 — 30. How many solutions does the given equation have? 1 _ √ _ x + 1 = 0 F. 0 G. 1 H. 2 J. 3

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Question Math · 31

Multiple choice
Question Math · 31 — 31. One side of a triangle in the standard ( x,y ) coordinate plane is parallel to the x -axis, and another side is parallel to the y -axis. Two of the vertices of the triangle are ( 3,4 ) and ( −1,−2 ) . What is the…

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Question Math · 32

Multiple choice
Question Math · 32 — 32. Which of the following is 1 of the solutions of the quadratic equation 2 x 2 + 3x + 8 = 0 ? F. 3 _ 4 + i √ _ 55 _ 4 G. − 3 _ 4 + i √ _ 55 _ 4 H. 3 _ 4 − √ _ 55 _ 4 J. − 3 _ 4 − √ _ 55 _ 4

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Question Math · 35

Multiple choice
Question Math · 35 — 35. For a measure of time, t , which of the following functions is that of an exponential growth function? A. y = √ _ t B. y = 3 t 10 C. y = 1. 05 t D. y = t t

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Question Math · 37

Multiple choice
Question Math · 37 — 37. For the 3 triangles in the figure, nABC is congruent to nDEF ( nABC ≅ nDEF ), and nDEF is similar to nGHI ( nDEF ~ nGHI ). Which of the following distances is necessarily equal to (DE) (GI) _ (GH) ? A C D E F B I H…

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Question Math · 38

Multiple choice
Question Math · 38 — 38. Point P (a,b) is reflected across the x -axis and then the reflection is translated 2 units in the positive y -direction in the standard (x,y) coordinate plane. What are the coordinates of the resulting point? F.…

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Question Math · 39

Multiple choice
Question Math · 39 — 39. The hyperbolas x 2 _ 9 − y 2 _ 4 = 1 and y 2 _ 36 − x 2 _ 25 = 1 are graphed in the standard (x,y) coordinate plane. Which of the following equations is an ellipse that intersects all 4 vertices of the hyperbolas? y…

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Question Math · 40

Multiple choice
Question Math · 40 — 40. The side lengths of a specific right triangle are 6 cm, 8 cm, and 10 cm. Which of the following equations, when solved for x , gives the measure of the smallest angle of the triangle? (Note: For a triangle with…

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Question Math · 41

Multiple choice
Question Math · 41 — 41. Mandy and her husband, Collier, work for the Krenke Furniture Outlet. The pay for each consists of $11 per hour worked, plus a commission of 8% of their individual sales total. For 1 certain week, Mandy worked 3…

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Question Math · 42

Multiple choice
Question Math · 42 — 42. A polynomial function, f , has zeros of −2 , 3 , and i . The polynomial function f has no other real zeros. One of the following is the graph of y = f (x) in the standard (x,y) coordinate plane. Which one? F. G. x y…

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Question Math · 43

Multiple choice
Question Math · 43 — 43. The sum of the infinite geometric series −16 + 8 + −4 + … is closest to which of the following? A. −16 B. −12 C. −11 D. −8

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Question Math · 44

Multiple choice
Question Math · 44 — 44. A rectangle has a length of 24 feet and a width of 36 feet. What is the area, in square inches, of the rectangle? F. 6 G. 864 H. 10,368 J. 124,416

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