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ACT American College Testing: Math Section 試験
最終更新日: 2026/10/16 収録内容確認済 ｜ PDF問題集: 全 280 問収録
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Question No : 1
If the height of a cylinder is doubled and the radius of the cylinder is halved, the volume of the cylinder:
正解:
Explanation:
The volume of a cylinder is equal to π r 2 h , where r is the radius of the cylinder and h is the height. The volume of a cylinder with a radius of 1 and a height of 1 is π. If the height is doubled and the radius is halved, then the volume becomes π × (1/2) 2 × 2 × 1 = π × 1/4 ×2 = 1/2π. The volume of the cylinder has become half as large.
Question No : 2
Line AC is a diagonal of square ABCD.
What is the sine of
正解:
Explanation:
A square has four right (90-degree) angles. The diagonals of a square bisect its angles. Diagonal AC bisects C, forming two 45-degree angles, 
and
. The sine of 45º is equal to 
.
Question No : 3
The average of five consecutive odd integers is C21.
What is the least of these integers?
正解:
Explanation:
If the average of five consecutive odd integers is C21, then the third integer must be C21. The two larger integers are C19 and C17 and the two lesser integers are C23 and C25. C25 is the least of the five integers. Remember, the more a number is negative, the less is its value.
Question No : 4
If 
, then when a = 8, b could be equal to:
正解:
Explanation:
Substitute 8 for a : 
. Rewrite 1 as 8/8 and add it to 4 b /8, then cross multiply:
4 b 2 C 8 b C 32 = 64
b 2 C 2 b C 8 = 16
b 2 C 2 b C 24 = 0
( b C 6) × ( b + 4) = 0
b C 6 = 0, b = 6
b + 4 = 0, b + C4
Question No : 5
If graphed, which of the following pairs of equations would be parallel to each other?
正解:
Explanation:
Parallel lines have the same slope. The lines y = 6x + 6 and y = 6x C 6 both have a slope of 6, so they are parallel to each other.
Question No : 6
Which of the following expressions is undefined when x = C2?
正解:
Explanation:
An expression is undefined when a denominator of the expression is equal to zero. When x = C2, x 2 + 6 x + 8 = (C2) 2 + 6 × (C2) + 8 = 4 C 12 + 8 = 0.
Question No : 7
The value of d is increased 50%, then decreased 50%.
Compared to its original value, the value of d is now:
正解:
Explanation:
To increase d by 50%, multiply d by 1.5: d = 1.5d. To find 50% of 1.5d, multiply 1.5d by 0.5: 1.5d × 0.5 = 0.75d. Compared to its original value, d is now 75% of what it was. The value of d is now 25% smaller.
Question No : 8
In the diagram above, the length of a side of square ABCD is four units.
What is the area of the shaded region?
正解:
Explanation:
The area of a square is equal to S2 , where S is the length of a side of the square. The area of ABCD is 4 2 = 16 square units. The area of a circle is equal to π r2 , where r is the radius of the circle.
The diameter of the circle is four units. The radius of the circle is 4/2 = 2 square units. The area of the circle is equal to π × 2 2 = 4π. The shaded area is equal to one-fourth of the difference between the area of the square and the area of the circle: 1/4 × (16 C 4π) = 4 C π.
Question No : 9
Which of the following is an irrational number?
正解:
Explanation:
An irrational number is a number that cannot be expressed as a repeating or terminating decimal.
. √2 cannot be expressed as a repeating or terminating decimal, therefore, 128√2 is an irrational number.
Question No : 10
Based on the diagram above, which of the following is true?
正解:
Explanation:
The measure of an exterior angle of a triangle is equal to the sum of the two interior angles of the triangle to which the exterior angle is NOT supplementary. 
is supplementary to
, so the sum of the interior 
and
is
equal to the measure of
.
Question No : 11
The length of a rectangle is one greater than three times its width. If the perimeter of the rectangle is 26 feet, what is the area of the rectangle?
正解:
Explanation:
The perimeter of a rectangle is equal to 2 l + 2 w , where l is the length of the rectangle and w is the width of the rectangle. If the length is one greater than three times the width, then set the width equal to x and set the length equal to 3 x + 1:
2 × (3 x + 1) + 2 x = 26
6 x + 2 + 2 x = 26
8 x = 24
x = 3
The width of the rectangle is 3 ft and the length of the rectangle is 10 ft. The area of a rectangle is equal to lw ; 10 ft × 3 ft = 30 ft 2 .
Question No : 12
If 
anda = 4 and b = 8, which of the following could be true?
正解:
Explanation:
If a = 4, x could be could be less than a . For example, x could be 3: 
, 
, 
. Although x < a is not true for all values of x , it is true for some values of x .
Question No : 13
The area of an isosceles right triangle is 18 cm2.What is the length of the hypotenuse of the triangle?
正解:
Explanation:
The area of a triangle is equal to 1/2bh where b is the base of the triangle and h is the height of the triangle. The base and height of an isosceles right triangle are equal in length. Therefore, 1/2b 2 = 18, b 2 =36. B=6. The legs of the triangle are 6 cm. The hypotenuse of an isosceles right triangle is equal to the length of one leg multiplied by √2. The hypotenuse of this triangle is equal to 6√2 cm
Question No : 14
If the circumference of the circle in the diagram above is 20π units, what is the area of triangle ABC?
正解:
Explanation:
The circumference of a circle is equal to 2πr, where r is the radius of the circle. If the circumference of the circle = 20π units, then the radius of the circle is equal to ten units. The base of triangle ABC is the diameter of the circle, which is twice the radius. The base of the triangle is 20 units and the height of the triangle is eight units. The area of a triangle is equal to 1/2 bth where b is the base of the triangle and h is the height of the triangle. The area of triangle ABC = 1/2 × 80 × 20 = 1/2 × 160 = 80 square units.
Question No : 15
The pie chart above shows the distribution of video rentals from Al’s Video Vault for a single night.
If 250 videos were rented that night, how many more action movies were rented than horror movies?
正解:
Explanation:
22% of the movies rented were action movies; 250 × 0.2 2 = 55 movies; 12% of the movies rented were horror movies; 250 × 0.1 2 = 30 movies. There were 55 C 30 = 25 more action movies rented than horror movies.