ACT · Practice test 2

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

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Question Math · 2

Multiple choice
Question Math · 2 — 2. A function, f , is defined by the equation f ( x ) = x 2 + 5 . What is f ( 3 ) + 1 ? F. 9 G. 11 H. 12 J. 15

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Question Math · 7

Multiple choice
Question Math · 7 — 7. For circle O shown, A , B , C , and D are on circle O ; A and B are as far apart as possible; C is halfway between A and B along circle O ; and D is halfway between C and B along circle O . What percent of the area…

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Question Math · 9

Multiple choice
Question Math · 9 — 9. Given the function f (x) = 4 x 2 − 14x + 12 , which of the following expressions is equivalent to f (x) ? A. (−2x + 4) (2x + 3) B. (2x − 4) (2x − 3) C. (2x − 4) (2x + 3) D. (2x − 3) (2x + 4)

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Question Math · 10

Multiple choice
Question Math · 10 — 10. Which of the following is equivalent to (6x + 3y) − (y − 2x) ? F. 4x + 2y G. 5x + y H. 5x + 5y J. 8x + 2y

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Question Math · 11

Multiple choice
Question Math · 11 — 11. Bryce owns an apartment building. He charges $325 per month for each 1 ‑bedroom apartment and $410 per month for each 2 ‑bedroom apartment. Bryce charged a total of $4,905 in rent for 13 apartments this month. How…

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Question Math · 13

Multiple choice
Question Math · 13 — 13. For what value of n does the quadratic equation x 2 − 4x + n = 0 have solutions of x = 7 and x = −3 ? A. −21 B. −4 C. 4 D. 10

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Question Math · 14

Multiple choice
Question Math · 14 — 14. The lengths of corresponding sides of 2 similar right triangles are in the ratio 4:5 . The hypotenuse of the smaller triangle is 20 inches long. How many inches long is the hypotenuse of the larger triangle? F. 9 G.…

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Question Math · 15

Multiple choice
Question Math · 15 — 15. What is the amplitude of the graph of function f (x) = 1 _ 2 cos (3x + π) , shown in the standard (x,y) coordinate plane? y x O 1 −1 A. 1 _ 3 B. 1 _ 2 C. 2 D. 3

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Question Math · 16

Multiple choice
Question Math · 16 — 16. A circle in the standard (x,y) coordinate plane has its center at (3,−4) and passes through (0,0) . Which of the following is an equation for that circle? F. x 2 + y 2 = 5 G. (x − 3) 2 + (y + 4) 2 = 25 H. (x + 3) 2…

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Question Math · 17

Multiple choice
Question Math · 17 — 17. √ _ 112 + √ _ 63 + √ _ 175 = ? A. 7 √ _ 12 B. 7 √ _ 50 C. 12 √ _ 7 D. 60 √ _ 7

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Question Math · 22

Multiple choice
Question Math · 22 — 22. The 1 st term of a certain sequence is −10 , and the 2 nd term is 1 . Each subsequent term is obtained by adding the 2 immediately preceding terms. What is the 5 th term of this sequence? F. −23 G. −17 H. 19 J. 34

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Question Math · 24

Multiple choice
Question Math · 24 — 24. Some values of the function g are given in the table. One of the following equations defines g . Which one? x −2 0 1 2 3 g (x) 0 −8 −6 0 10 F. g (x) = −2x − 8 G. g (x) = −x − 8 H. g (x) = x 2 + 2 J. g (x) = 2 x 2 − 8

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Question Math · 25

Multiple choice
Question Math · 25 — 25. The vertex angle of an isosceles triangle is 40° . What is the measure of a base angle? A. 40° B. 70° C. 100° D. 140°

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Question Math · 26

Multiple choice
Question Math · 26 — 26. Equilateral triangle nABC is inscribed in circle O , as shown. What is the degree measure of minor arc ⏜ BC ? B A C O F. 60° G. 90° H. 120° J. 180°

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Question Math · 28

Multiple choice
Question Math · 28 — 28. 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 · 29

Multiple choice
Question Math · 29 — 29. Which of the following expressions equals the height, in feet, of the tree shown? 40° 18 feet ? A. 18 tan 40° B. 18 sin 40° C. 18 cos 40° D. tan 40° _ 18

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Question Math · 32

Multiple choice
Question Math · 32 — 32. Whenever −3 x 3 + 12x _ x 3 − x 2 − 6x is defined, it is equivalent to: F. −2 G. 1 _ x + 3 H. 6 − 3x _ x + 3 J. 6 − 3x _ x − 3

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Question Math · 33

Multiple choice
Question Math · 33 — 33. The roots of a polynomial equation are 0 , 2 , and −5 . Which of the following is a factored form of the equation? A. (x − 2) (x + 5) = 0 B. x (x − 2) (x + 5) = 0 C. x (x + 2) (x − 5) = 0 D. (x − 2) (x + 5) = x

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Question Math · 34

Multiple choice
Question Math · 34 — 34. 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 · 36

Multiple choice
Question Math · 36 — 36. The piecewise functions f and g are given. f (x) = { − x 2 for x < 0 1 − x for x ≥ 0 g (x) = { ⎪x⎪ + 7 for x ≤ −1 x − 3 for x > −1 What is the value of f (g (−1) ) ? F. −16 G. −7 H. −5 J. −1

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Question Math · 37

Multiple choice
Question Math · 37 — 37. Let f be defined by f ( x ) = 4x + 7 . Let g be defined by g ( x ) = −2 x 2 + 11x + 1 . The graphs of y = f ( x ) and y = g ( x ) intersect at one of the following ( x,y ) points. Which one? A. ( −2,−1 ) B. ( 1 1 _…

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Question Math · 39

Multiple choice
Question Math · 39 — 39. Given that i is the imaginary unit, which of the following numbers is equal to (7 + 4i) 2 ? A. 33 B. 65 C. 14 + 8i D. 33 + 56i

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Question Math · 40

Multiple choice
Question Math · 40 — 40. The product of 2 complex numbers, x and y , is a real number that is irrational. Which of the following statements cannot be true? F. Both x and y are rational. G. Both x and y are imaginary. H. The product of x and…

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Question Math · 41

Multiple choice
Question Math · 41 — 41. The real solution of the equation 3 e x = 12 is: A. ln 4 B. 3 ln 12 C. 4 e D. ln 12 _ 3

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Question Math · 42

Multiple choice
Question Math · 42 — 42. The figure shows nABC , a right isosceles triangle, inscribed in a circle with center O and radius 10 cm. What is the length, in centimeters, of arc ⏜ AB shown as the thick curved line? A B C O 10 cm F. 20π G. 15π…

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Question Math · 44

Multiple choice
Question Math · 44 — 44. 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 · 45

Multiple choice
Question Math · 45 — 45. Given that f (x) = 3 √ _ 2x − 1 , which of the following expressions is the inverse function, f −1 (x) ? A. 1 _ 3 √ _ 2x − 1 B. 3 √ _ x + 1 _ 2 C. x 3 + 1 _ 2 D. (2x − 1) 3

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