本文为大家介绍的是8道ACT数学练习题及解析的内容，大家可以参考一下，结合之前的练习题一起练习，相信会有所收获。
ACT数学练习题及解析,ACT数学
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Question 1: A rectangle is four times as long as it is wide. If the total area of the rectangle is 16 square inches, what is the length of the rectangle?
(a) 2 inches
(b) 4 inches
(c) 6 inches
(d) 8 inches
(e) 16 inches
Solution: If x is the width of the rectangle, the length is 4x.
The area of the rectangle is x·4x = 4x2.
4x2 = 16 and x = 2 inches.
The length of the rectangle is 4x = 8 inches.
Question 2: What is f(f(2)) if f(x) = x2 + 2?
(a) 12
(b) 26
(c) 38
(d) 42
(e) 48
Answer:
f(2) = 22 + 2 = 6.
f(f(2)) = f(6) = 62 + 2 = 38.
Question3:Which of the following is a factored form of the expression 6x2 + x - 2?
(a) (3x + 2)(2x - 1)
(b) (2x + 2)(3x - 1)
(c) (3x + 2)(2x + 1)
(d) (3x - 2)(2x - 1)
(e) (2x + 2)(3x - 2)
Answer: 6x2 + x - 2 = 6x2 + 4x - 3x - 2 = 2x(3x + 2) - (3x + 2) = (3x + 2)(2x - 1).
Question4: If x2 - nx - 32 = 0 when x = 4, what is the value of n?
(a) -4
(b) 4
(c) 6
(d) -2
(e) 10
Answer: We substitute x = 4 in x2 - nx - 32 = 0.
42 - n·4 - 32 = 0.
16 - 4n - 32 = 0.
n = -4.
Question 5: If f(x) = |x| and g(x) = x2, how many solutions has f(x) = g(x)?
(a) 1
(b) 2
(c) 3
(d) 4
(e) 5
Answer: The simplest way to solve this problem is to draw the 2 functions in the x, y plane.
We find that the 2 functions intersect each other in 3 locations, at
x = -1, 0 and 1.
Question6: Given the list of integers: -2, 2, 0, 6, 8, 0, -5, 9, 10, 4, which of the following statements is true?
(a) mode < median < average
(b) median < mode < average
(c) median < average < mode
(d) mode = median < average
(e) average < median < mode
Answer: We need to rearrange the list of integers in ascending order: -5, -2, 0, 0, 2, 4, 6, 8, 9, 10. The average will be the sum of all integers divided by the number of integers, 32/10 = 3.2.
The median will be the mean of the two middle numbers, 2 and 4, so the median is 3.
The mode is 0, as 0 occurs the most in the list.
The correct answer is mode < median < average.
Question7: A vehicle runs from town A to town B at a speed of 20 miles/hour while another vehicle runs from town B to town A at a speed of 60 miles/hour. Both vehicles start their trips at the same time and the distance between towns is 100 miles. How long does it take from the time they start running to the moment they are at the same point on the road?
(a) 1 hour
(b) 1 hour and 15 minutes
(c) 1 hour and 30 minutes
(d) 1 hour and 45 minutes
(e) 2 hours and 15 minutes
Answer: 100 miles = d1 + d2 This is equation #1.
It take the same time for the 2 cars to meet: t = d1/(20 miles/hour) = d2/(60miles/hour). This is equation #2.
We solve the system of 2 equations to find d1 and d2.
From equation #2, 3·d1 = d2.
Then 100 miles = d1 + d2 = 4·d1, so d1 = 25 miles and d2 = 75 miles.
The answer is t = d1/20miles/hour = 25/20 = 5/4 = 1 hour and 15 minutes.
Question8: If x + 4y = 6 and x - 2y = 3, which of the following statements is not true?
(a) y = 1/2
(b) x = 4
(c) y = 2
(d) xy = 2
(e) x + y = 9/2
Answer:
In order to find the values of x and y, we multiply the second equation by 2 and add the 2 equations:
x + 4y = 6
2x - 4y = 3
3x = 12 and x = 4, y = (6 - 3)/4 = 1/2.
y = 2 is the only equality that is false.
以上就是8道ACT数学练习题及解析的内容，希望大家能够用心体会，更多精彩内容小编稍后为您呈现。最后，前程百利小编预祝大家在ACT考试中取得好成绩。
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