[2023年05月30日] 無料ACT Mathematics Test ACT-Math公式認定ガイドPDFダウンロード [Q142-Q165]

[2023年05月30日] 無料ACT Mathematics Test ACT-Math公式認定ガイドPDFダウンロード

ACT ACT-Math公式認定ガイドPDF

ACT-Mathセクションは、大学レベルの数学コースの準備ができているかどうかを測定する、ACT試験の重要な部分です。広範なトピックをカバーしており、挑戦的に設計されています。学生は時間を有効に管理し、批判的思考と問題解決能力を使用して、正しい答えを導き出す必要があります。ACT-Mathセクションでの良いスコアは、希望する大学に受け入れられる可能性を高め、奨学金やその他の金融支援プログラムの資格を得ることができます。

ACT ACT-Math（American College Testing：Math Section）認定試験は、数学における学生の知識とスキルを測定するために設計された標準化テストです。このテストは、アメリカの大学に進学する予定の高校生によって受けられることが一般的です。ACT ACT-Math試験は、アメリカの多くの大学で入学プロセスにおいて重要な要素として認められています。

ACT-Mathセクションは、大学や短大による学生の数学の知識や推論力を評価するためのACTテストの重要なコンポーネントです。学生たちは、さまざまな問題のカテゴリーに精通し、徹底的に準備して高得点を狙う必要があります。十分な準備と練習により、学生たちはACT-Mathセクションで卓越した成績を収め、望む大学や短大への入学のチャンスを高めることができます。

質問 # 142
If p < 0, q > 0, and r > p, then which of the following must be true?

A. r + q > q
B. rp < rq
C. p + r > 0
D. pr < rq
E. p + r < r + q

正解：E

質問 # 143
What is the slope of the line -3y = 12x - 3?

A. 0
B. 1
C. 2
D. 3
E. 4

正解：A

質問 # 144
A circle has a circumference of 16π feet.
What is the radius of the circle, in feet?

A.
B. 0
C. 1
D. 2
E. 3

正解：B

質問 # 145
The average of five consecutive odd integers is -21.
What is the least of these integers?

A. 0
B. 1
C. 2
D. 3
E. 4

正解：B

質問 # 146
The 3rd and 4th terms of an arithmetic sequence are13 and 18, respectively.
What is the 50th term of the sequence?

A. 0
B. 1
C. 2
D. 3
E. 4

正解：A

質問 # 147
Ray

bisects

, the measure of

is 11x °, and the measure of

is
(4x + 18)°. What is the measure of

?

A. 12°
B. 66°
C. 42°
D.
E.

正解：B

質問 # 148
Rob has six songs on his portable music player.
How many different four-song orderings can Rob create?

A. 0
B. 1
C. 2
D. 3
E. 4

正解：D

質問 # 149
In the diagram above, line AB is parallel to line CD,

measures 140º and

measures 55º.

What is the measure of

?

A. 135º
B. 55º
C. 85º
D. 40º
E. 95º

正解：C

質問 # 150
The sum of 2 positive numbers is 151. The lesser number is 19 more than the square root of the greater number.
What is the value of the greater number minus the lesser number?

A. 0
B. 1
C. 2
D. 3
E. 4

正解：E

質問 # 151
The population ( x ) of town ( y ) since 2000 can be estimated by the equation x = 1.0635 z + 3,250, where z is the number of years since 2000 and 0 ≤ z ≤ 20.
In the context of this equation, what does the number 1.0635 most likely represent?

A. The factor by which the population of town (y) has decreased annually.
B. The estimated population of town (y) in 2017.
C. The factor by which the population of town (y) has grown annually.
D. The estimated population of town (y) in 2000.

正解：C

質問 # 152
FILL BLANK
What is the distance from the point where the line given by the equation 3y = 4x + 24 crosses the x-axis to the point where the line crosses the y-axis?

正解：

解説：
10

質問 # 153
In the diagram above, lines EF and GH are parallel, and line AB is perpendicular to lines EF and GH.

What is the length of line AB?

A.
B.
C. 0
D.
E.

正解：E

質問 # 154
In the diagram above, triangle ABC is a right triangle and the diameter of circle O is 2/3 the length of AB.

Which of the following is equal to the shaded area?

A. 20π square units
B. 48 - 4π square units
C. 24 - 16π square units
D. 24 - 4π square units
E. 48 - 16π square units

正解：D

質問 # 155
Drag and drop

A. 0
B. 1
C. 2
D. 3

正解：C

質問 # 156
If graphed, which of the following pairs of equations would be parallel to each other?

A. y = 3x + 3, y = -1/3x - 3
B. y = 5x + 5, y = 1/5x + 5
C. y = 4x + 1, y = 1/5x + 5
D. y = 6x + 6, y = 6x - 4
E. y = 2x + 4, y = x + 4

正解：D

質問 # 157
For what positive real value of k , if any, is the determinant of the matrix

equal to k ? (Note: The determinant of matrix

equalsad - bc .)

A.
B. 0
C. 1
D. There is no such value of k.
E. 2

正解：C

質問 # 158
How does the area of a rectangle change if both the base and the height of the original rectangle are tripled?

A. The area is six times larger.
B. The area cannot be determined.
C. The area is tripled.
D. The area remains the same.
E. The area is nine times larger.

正解：E

質問 # 159
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. 25 cm2
E. 78 cm2

正解：A

質問 # 160
In the diagram above, ABC and DEC are right triangles, the length of side BC is 15 units, and the measure of

is 60º.

If

is congruent to

, what is the length of side DC?

A. √15 units
B. 15/2 × √3 units
C. 15√3 units
D. 15/2 units
E. 9 units

正解：D

質問 # 161
In the diagram above, line AB is parallel to line CD, both lines are tangents to circle O and the diameter of circle O is equal in measure to the length of line OH.

If the diameter of circle O is 24 in, what is the measure of

?

A. 60º
B. 75º
C. 45º
D. Cannot be determined.
E. 30º

正解：E

質問 # 162
If x × y = 156, x + y = 43, and x < y, what is the value of x - y?

A. 0
B. 1
C. 2
D. 3

正解：D

質問 # 163
In a restaurant, the ratio of four-person booths to two-person booths is 3:5.
If 154 people can be seated in the restaurant, how many two-person booths are in the restaurant?

A. 0
B. 1
C. 2
D. 3
E. 4

正解：B

質問 # 164
A car departs Little Rock, Ark., traveling to a baseball game located nine miles east and 12 miles north of the departure point. About how many miles is the game from the departure point?