ACT-Math無料問題集「ACT American College Testing: Math Section」

質問 1

The expression 4x 2 - 2x + 3 is equal to 3 when x = 0 and when x =

（A）1/2

（B）1/4

（C）-1/2

（D）-1/4

（E）1/8

正解：A 解答を投票する

質問 2

What is the value of the expression below?

（A）-18

（B）-2

（C）2

（D）18

（E）0

正解：C 解答を投票する

質問 3

The Smith family is planning to build a 3-room cabin which consists of 2 bedrooms (BR) and 1 living room (LR). Shown below are the rectangular floor plan (left figure) and a side view of the cabin (right figure). In the side view, the roof forms an isosceles triangle (ABC), the walls are perpendicular to the level floor (

),

, F is the midpoint of

, and

.

During the week the Smiths plan to roof the cabin, there is 20% chance of rain each day.
Mr, Smith plans to build a 3-foot-wide walkway around the outside of the cabin, as shown in the floor plan.
What will be the area, in square feet, of the top surface of the walkway?

（A）360

（B）720

（C）171

（D）396

（E）324

正解：A 解答を投票する

質問 4

Which of the following represents four times the sum of x and 8?

（A）4 × (x + 8)

（B）x + 8

（C）4x

（D）4x + 8

正解：A 解答を投票する

質問 5

In triangle DEF, the length of

is
√30inches, and the length of

is 3inches. If it can
be determined, what is the length, in inches, of

?

（A）3

（B）

（C）

（D）Cannot be determined from the given information.

（E）

正解：D 解答を投票する

質問 6

The list of numbers 41, 35, 30, X, Y, 15 has a median of 25. The mode of the list of numbers is 15.
To the nearest whole number, what is the mean of the list?

（A）20

（B）26

（C）30

（D）25

（E）27

正解：B 解答を投票する

質問 7

The diagonal of one face of a cube measures 4√2 in.
What is the volume of the cube?

（A）64 in 3

（B）96 in 3

（C）24√2 in 3

（D）128√2 in 3

（E）192 in 3

正解：A 解答を投票する

質問 8

Ray

bisects

, the measure of

is 11x °, and the measure of

is
(4x + 18)°. What is the measure of

?

（A）

（B）42°

（C）12°

（D）

（E）66°

正解：E 解答を投票する

質問 9

An empty crate weighs 8.16 kg and an orange weighs 220 g.
If Jon can lift 11,000 g, how many oranges can he pack in the crate before lifting it onto his truck?

（A）13

（B）12

（C）50

（D）46

（E）37

正解：B 解答を投票する

質問 10

The volume of a glass of water placed in the sun decreases by 20%.
If there are 240 ml of water in the glass now, what was the original volume of water in the glass?

（A）360 ml

（B）260 ml

（C）19 2 ml

（D）300 ml

（E）288 ml

正解：D 解答を投票する

質問 11

Four copy machines make 240 total copies in three minutes.
How long will it take five copy machines to make the same number of copies?

（A）3 minutes, 36 seconds

（B）2 minutes

（C）2 minutes, 24 seconds

（D）2 minutes, 15 seconds

（E）2 minutes, 45 seconds

正解：C 解答を投票する

質問 12

The equation

is undefined when x =:

（A）-9

（B）-2

（C）9

（D）-6

（E）0

正解：A 解答を投票する

質問 13

In the diagram above, the length of a side of square ABCD is four units.

What is the area of the shaded region?

（A）16π

（B）4 - 4π

（C）4

（D）4 - π

（E）16 - 4π

正解：D 解答を投票する

質問 14

In the standard (x, y) coordinate plane, what are the coordinates of the midpoint of a line segment whose endpoints are (-3, 0) and (7, 4)?

（A）(5, 4)

（B）(5, 2)

（C）(5, 5)

（D）(2, 2)

（E）(2, 4)

正解：D 解答を投票する

質問 15

Greg has nine paintings. The Hickory Museum has enough space to display three of them.
From how many different sets of three paintings does Greg have to choose?

（A）168

（B）84

（C）504

（D）56

（E）27

正解：B 解答を投票する

質問 16

Rob has six songs on his portable music player.
How many different four-song orderings can Rob create?

（A）360

（B）120

（C）30

（D）720

（E）60

正解：A 解答を投票する

質問 17

In the diagram above, ABCD is a square with an area of 100 cm 2 and lines BD and AC are the diagonals of ABCD.

If line EF is parallel to line BC and the length of line CF = 3√ 2 cm, which of the following is equal to the shaded area?

（A）39 cm2

（B）64 cm2

（C）89 cm2

（D）78 cm2

（E）25 cm2

正解：A 解答を投票する

質問 18

In the graph above, ABCD is a square.

What are the coordinates of point B?

（A）(-1, -4)

（B）(-1, 4)

（C）(-1, 6)

（D）(-3, 1)

（E）(-3, 4)

正解：B 解答を投票する

質問 19

The ABC Book Club charges a $40 monthly fee, plus $ 2 per book read in that month. The Easy Book Club charges a $35 monthly fee, plus $3 per book read in that month.
For each club, how many books must be read in 1 month for the total charges from each club to be equal?

（A）5

（B）1

（C）4

（D）6

（E）75

正解：A 解答を投票する

質問 20

FILL BLANK

In the diagram above, the radius of the circle is 20 units and the length of arc AB is 15π units.
What is the measure in degrees of

?

正解：

135

ACT-Math 無料問題集「ACT American College Testing: Math Section」

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