# ACT部分數學真題回顧與答案解析

ACT考試中，ACT真題是最好的練習題目。下面是3道ACT數學真題，大家可以作為參考。

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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