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act数学练习题含答案解析(五)

2023-08-24 15:56:00来源:网络整理

  为了帮助大家备考ACT,新东方在线ACT频道整理了act数学练习题含答案解析(五),希望对大家有所帮助,更多精彩尽请关注新东方在线act频道! 

  Question 1:What is sec(a)sin(a) + csc(a)cos(a) , if a =45o?

  (a) √2

  (b) 2

  (c) 1

  (d) 1/√2

  (e) 1/2

  Answer: sec(a)sin(a) + csc(a)cos(a) = [1/cos(a)]sin(a) + [1/sin(a)]cos(a) = sin(a)/cos(a) + cos(a)/sin(a) = (√2/2)/(√2/2) + (√2/2)/(√2/2) = 1 + 1 = 2.

  Question 2:In the standard (x,y) coordinate plane, 3 corners of a square are (4,–3), (–4,3), and (–4,-3). What are the coordinates of the square’s fourth corner?

  (a) (1/4, -1/3)

  (b) (4, 3)

  (c) (3, 4)

  (d) (3, -4)

  (e) (3, -4)

  Answer:The easiest way to solve this problem is to sketch the 3 corners of the square. We notice that the fourth corner of the square is (4, 3).

  Question 3:Prizes totaling $60,000 were awarded unequally between 3 contestants. Which of the following choices could be the highest prize?

  (a) $5,000

  (b) $10,000

  (c) $15,000

  (d) $25,000

  (e) $65,000

  Answer:The highest prize should be higher than one third of $60,000 and lower than $60,000. The only answer that satisfies this condition is $25,000.

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