ACT Math Practice Test 23
Đề thi nằm trong bộ sưu tập: Tuyển Tập Bộ Đề Thi Đại Học Hoa Kỳ (ACT) - Có Đáp Án Chi Tiết
Số câu hỏi: 20 câuSố mã đề: 1 đềThời gian: 1 giờ
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A formula for the volume, V, of a right circular cylinder is V = πr2h, where r is the radius and h is the height. If a tanker truck has a tank as shown below with a diameter of 3 meters and a length of 10 meters and is filled with water, then the weight, in pounds, of the water cargo is: (Note: 1 cubic meter of water weighs approximately 2,205 pounds.)
less than 75,000.
between 125,000 and 175,000.
between 175,000 and 225,000.
between 225,000 and 275,000.
more than 275,000.
In the standard (x,y) coordinate plane, what is the distance between the points (4,−7) and (−1,5)?
5
12
13
20
26
Rebecca is trying to schedule volunteers to help at a school carnival. There are 5 one-hour shifts to be filled by 5 different volunteers. If each shift must have one and only one volunteer, how many different arrangements can the schedule have?
5
20
25
50
120
When entering information about the budget of her charity ball, Laura records an expense of $20.00. However, Laura accidentally enters the $20.00 as income instead of an expense. The balance of the charity ball budget now shows:
$40 less than it should.
$20 less than it should.
the correct amount.
$20 more than it should.
$40 more than it should.
If |x| = x + 12, then x = ?
−12
−6
0
6
12
What fraction lies exactly halfway between 1⁄3 and 1⁄2?
3⁄8
1⁄6
2⁄5
The graph of y = ax2 + bx + c in the standard (x,y) coordinate plane is shown below. When y = 0, which of the following best describes the solution set for x?
2 imaginary solutions
1 double imaginary solution
1 real and 1 imaginary solution
1 double imaginary solution
2 real solutions
The line graphed below shows the predicted gasoline use for a certain truck. Which of the following is the closest estimate of this truck’s predicted rate of gasoline use, in miles per gallon?
25
20
16
10
8
The formula for the area of a trapezoid is A = 1⁄2h (b1 + b2), where b1 and b2 are the lengths of the two parallel sides and h is the height. Which of the following is an expression for b1?
2(Ah − b2)
1⁄2Ah + b2
For positive real numbers x, y, and z, which of the following expressions is equivalent to x1⁄2y3⁄4z5⁄8?
What is the slope of a line that is perpendicular to the line determined by the equation 5x + 8y = 17?
−3
−5⁄8
If the volume of a cube is 64, what is the shortest distance from the center of the cube to the base of the cube?
2
4
2√4
16
For which of the following values of c will there be 2 distinct real solutions to the equation 5x2+16x+ c = 0?
3
12
14
15
20
If a is inversely proportional to b and a = 36 when b = 12, what is the value of a when b = 48?
0
1⁄3
1⁄4
4
9
For values of x where sin x , cos x, and tan x are all defined, =?
tan2x
1
sin2 x
sec x
Which of the following is (are) equivalent to the mathematical operation a(b − c) for all real numbers a, b, and c?
I. ca − ba
II. ab − ac
III. (b − c)a
II only
I and II only
I and III only
II and III only
I, II and III
If x2 − 45b2 = 4xb, what are the 2 solutions for x in terms of b?
15b or −3b
5b or −9b
15b or 3b
45b or −4b
9b or −5b
It is estimated that, from the beginning of 1993 to the end of 1997, the average number of CDs bought by teenagers increased from 7 per year to 15 per year. During the same time period, the average number of video games purchased by teenagers increased from 6 per year to 18 per year. Assuming that in each case the rates or purchase are the same, in what year did teenagers buy the same average number of CDs and video games?
1993
1994
1995
1996
1997
The figure below is a regular hexagon. What is the measure of one of the interior angles of the hexagon?
108°
120°
135°
150°
720°
In the figure below, line AB is parallel to the base of the triangle and creates a smaller triangle inside of the original triangle. If the lengths of segments are as shown and the smaller triangle has an area of 8 cm2, what is the area, in centimeters, of the original triangle?
16
24
32
64
128