ACT Math Practice Test 8
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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After polling a class of 24 students by a show of hands, you find that 9 students play soccer and 21 students play basketball. Given that information, what is the number of students in the class who must play both soccer and basketball?
zero
1
3
6
9
Which of the following describes the total number of dots in the first n rows of the triangular arrangement below?
30
2n
n2
n(n + 1)
2n + 2(n − 1)
Using the complex number i, where i2 = −1, =?
1 + i
i − 1
1 − i
2(1 + i)
2(1 − i)
A circle in the standard (x, y) coordinate plane is tangent to the x-axis at 4 and tangent to the y-axis at 4. Which of the following is an equation of the circle?
x2 + y2 = 4
x2 + y2 = 16
(x − 4)2 + (y − 4)2 = 4
(x − 4)2 + (y − 4)2 = 16
(x + 4)2 + (y + 4)2 = 16
The ratio of the radii of two circles is 9:16. What is the ratio of their circumferences?
3:4
9:16
18:32
3:4π
9π:16
What is the distance in the standard (x, y) coordinate plane between the points (2,3) and (5,5)?
3
5
Let x ◙ y = (x − 2y)2 for all integers x and y. Which of the following is the value of 5 ◙ (−3)?
121
64
41
1
−31
If 125% of a number is 425, what is 65% of the number?
221
276
284
308
340
Of the 517 graduating seniors at Brighton High School, approximately 4⁄5 will be attending college, and approximately 1⁄2 of those going to college will be attending a state college. Which of the following is the closest estimate of the number of graduating seniors who will be attending a state college?
170
200
260
300
320
In the figure shown below, each pair of intersecting line segments meets at a right angle, and all the lengths are given in inches. What is the perimeter, in inches, of the figure?
30
36
42
52
62
What is cos given that = π⁄3 − π⁄4 and that cos(α − β) = (cos α)(cos β) + (sin α)(sin β)?
1⁄4
1⁄2
If x = 3r − 4 and y = 3r + 2, which of the following expresses y in terms of x?
y = x + 2
y = x + 6
y = 9r + 14
y = 6r − 2
y = 3x + 14
A triangle, ΔABD, is reflected across the y-axis to have the image ΔA’B’D’ in the standard (x, y) coordinate plane: thus A reflects to A’ . The coordinates of point A are (m, n). What are the coordinates of point A’ ?
(−m, n)
(m, −n)
(−m, −n)
(−m, −n)
Cannot be determined from the given information.
Which of the following is the graph, in the standard (x, y) coordinate plane, of y = ?
If f (x) = 2x2 + 3, then f (x + h) = ?
2x2 + h2
2x2 + h + 3
2x2 + 2h2 + 3
x2 + 2xh + h2 + 3
2x2 + 4xh + 2h2 + 3
Which of the following systems of inequalities is represented by the shaded region of the graph below?
y ≤ x + 1 or y ≥ x − 3
y ≤ x + 1 and y ≥ x − 3
y ≤ x + 1 or y ≥ (−3⁄2)x − 3
y ≤ x + 1 and y ≤ (−3⁄2)x − 3
y ≤ x + 1 and y ≥ (−3⁄2)x − 3
If sin θ = 4⁄5 and π⁄2 < θ < π, then tan θ = ?
- 5⁄4
- 4⁄3
- 3⁄5
4⁄3
3⁄4
John wants to draw a circle graph showing his friends’ favorite ice cream flavors. When he polled his friends asking each their favorite flavor of ice cream, 35% of his friends said chocolate, 20% of his friends said vanilla, 15% of his friends said strawberry, 25% of his friends said mint chocolate chip, and 5% of his friends said flavors other than those previously listed. What will be the degree measure of the vanilla sector of the circle graph?
126°
108°
90°
72°
36°
Pentagons have 5 diagonals, as illustrated below. How many diagonals does the heptagon (7 sides) below have?
7
12
14
21
28
Which of the following is the set of all real numbers x such that x + 2 > x + 5 ?
The set containing only zero
The set containing all nonnegative real numbers
The set containing all negative real numbers
The set containing all real numbers
The empty set