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ACT考试模拟练习题2

Question #1: You have large, medium, and small books in the ratio of 7:6:3 and you have a total of 32 books. How many small books do you have?

(a) 3
(b) 4
(c) 5
(d) 6
(e) 7

Solution: If the number of large books is x, the number of medium books is y and the number of small books is z,
x/y = 7/6
x/z = 7/3
x + y + z = 32(6/7)x + (3/7)x + x = 32
x = 14 and
z = 6
Question #2: In the standard coordinate plane (x, y), what are the coordinates x1 and y1 of A, if A is the point in the first quadrant of the plane that is determined by the intersection of the y = 2x line and the x2 + y2 = 1 circle?

(a) x1 = 1/√5 and y1 = 2/√5
(b) x1 = 1/√3 and y1 = 2/√3
(c) x1 = 1/ and y1 = 1
(d) x1 = √5 and y1 = 2√5
(e) x1 = 2 and y1 = 2

Answer:

We solve the system of equations:
x2 + y2 = 1.
x2 + (2x)2 = 1.
5·x2 = 1.
Since x and y are positive,
x1 = 1/√5 and y1 = 2/√5
Question #3: What is the length of side b in the triangle below?
Figure not drawn to scale
act
    test, geometry?

(a) 2
(b) 3
(c) 4
(d) 5
(e) 6

Answer: sin(30o) = b/c.
1/2 = b/c.
b = 3.