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ACT考试模拟练习题2

发布日期：2012-06-26

•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

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•Question 2: Celsius degrees can be transformed to Fahrenheit degrees by using the following formula: °C=(5/9) x (°F-32). What is the number x, if x degrees Celsius is equal to x degrees Fahrenheit?
(a) -40
(b) -60
(c) -44
(d) -32
(e) -20
•Answer: x = (5/9)· (x - 32) results in x = -40.
In conclusion, -40C = -40F.

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•Question 3: A jar contains a nickel, a dime, and six quarters. Tom draws one coin from the jar, and then Mary draws a coin from those remaining. If the probability that Tom draws the nickel and Mary draws the dime is 1/x, what is the value of x?

(a) 50
(b) 56
(c) 1/50
(d) 1.56
(e) 50%
•The probability that Tom draws nickel is (number of nickels)/(number of coins in the jar) = 1/8
After Tom draws a coin, the number of coins in the jar is 8 - 1 = 7
The probability that Mary draws the dime is (number of dimes)/(number of coins in the jar) = 1/7
The probability that Tom draws the nickel AND Mary draws the dime is the product of the 2 probabilities calculated above.
1/8 · 1/7 = 1/56 so x = 56.

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•Question 4: What is m if the following system of equations has an infinity of solutions?
2x + 6y = 3
4x + 3my = 6

(a) 1
(b) 2
(c) 3
(d) 4
(e) 5
•Answer: The system of equations has an infinity of solutions if the 2 lines are one and the same.
3m = 2·6.
3m = 12.
m = 4.

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•Question 5: sin(x)cos(x)(1 + tan2(x)) =
(a) tan(x) + 1
(b) cos(x)
(c) sin(x)
(d) tan(x)
(e) sin(x) + cos(x) •Answer: sin(x)cos(x)(1 + tan2(x)) =sin(x)cos(x)[(1 + sin2(x)/cos2(x)] =
= sin(x)cos(x)[(cos2(x) + sin2(x))/cos2(x)] =

= sin(x)cos(x)[1/cos2(x)] = sin(x)/cos(x) = tan(x)

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•Question 6: What is the radius of the circle defined by the equation (x - 3)2 + (y - 1)2 = 81?
(a) 3
(b) 4
(c) 9
(d) 12
(e) 18
•Answer: In the standard coordinate plane, the equation of a circle is:
(x - a)2 + (y - b)2 = r2.
If we compare the 2 equations, r2 = 81 and r = 9.

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