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ACT Math Practice Test 17

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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Câu 1: 1 điểm

A rectangular kitchen is 8 feet longer than it is wide. Its area is 240 square feet. How long, in feet, is it?

A.  

12

B.  

16

C.  

20

D.  

24

E.  

30

Câu 2: 1 điểm

What is the equation of the circle in the standard (x, y) coordinate plane that has a radius of 4 units and the same center as the circle determined by x2 +y2 −6y+4 = 0?

A.  

x2 + y2 = −4

B.  

(x + 3)2 + y2 = 16

C.  

(x − 3)2 + y2 = 16

D.  

x2 + (y + 3)2 = 16

E.  

x2 + (y − 3)2 = 16

Câu 3: 1 điểm

The perimeter of a square is 36 units. How many units long is the diagonal of the square?

A.  

8

B.  

9√2

C.  

16

D.  

18

E.  

18√3

Câu 4: 1 điểm

If y ≠ z, what are the real values of x that make the following inequality true?
xyxz3y3z\frac{xy − xz}{3y − 3z} < 0

A.  

All negative real numbers

B.  

All positive real numbers

C.  

−1⁄3 only

D.  

1⁄3 only

E.  

3 only

Câu 5: 1 điểm

What is cos 5π12\frac{5\pi }{12} given that 5π12\frac{5\pi }{12} = π4 + π6 and that cos(α + β) = (cos α)(cos β) − (sin α)(sin β)? (Note: You may use the following table of values.)

Hình ảnh

A.  

1⁄4

B.  

1⁄2

C.  

624\frac{\sqrt{6}-\sqrt{2}}{4}

D.  

322\frac{\sqrt{3}-\sqrt{2}}{2}

E.  

624\frac{\sqrt{6}-2}{4}

Câu 6: 1 điểm

What is the solution set of |3a − 3| ≥ 12?

A.  

a ≥ 5 and a ≤ −5

B.  

a ≥ 5 and a ≤ −3

C.  

a ≥ −5 and a ≤ 5

D.  

a ≥ −5 and a ≤ 3

E.  

a ≤ 5 and a ≥ −5

Câu 7: 1 điểm

Which of the following calculations will yield an even integer for any integer a?

A.  

2a2 + 3

B.  

4a3 + 1

C.  

5a2 + 2

D.  

6a4 + 6

E.  

a6 − 3

Câu 8: 1 điểm

For what value of b would the following system of equations have an infinite number of solutions?
3x + 5y = 27
12x + 20y = 3b

A.  

9

B.  

27

C.  

36

D.  

81

E.  

126

Câu 9: 1 điểm

If r and s are constants and x2 + rx + 12 is equivalent to (x + 3)(x + s), what is the value of r?

A.  

3

B.  

4

C.  

7

D.  

12

E.  

Cannot be determined from the given information

Câu 10: 1 điểm

A certain rectangle is 5 times as long as it is wide. Suppose the length and width are both tripled. The perimeter of the second rectangle is how many times as large as the perimeter of the first rectangle?

A.  

3

B.  

5

C.  

6

D.  

12

E.  

15

Câu 11: 1 điểm

A triangle, ΔABD, is reflected across the line y = x 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’?

A.  

(−m, n)

B.  

(m, −n)

C.  

(−m, −n)

D.  

(n, m)

E.  

Cannot be determined from the given information.

Câu 12: 1 điểm

In the right triangle below, YZ = 10 units, and XZ = 4 units. What is sin Z?

Hình ảnh

A.  

410\frac{4}{10}

B.  

10221\frac{10}{2\sqrt{21}}

C.  

22110\frac{2\sqrt{21}}{10}

D.  

104\frac{10}{4}

E.  

4221\frac{4}{2\sqrt{21}}

Câu 13: 1 điểm

A computer repair person charges $50.00 per hour, plus an additional mileage fee. The charge for mileage varies directly with the square root of the number of miles traveled. If one hour plus 25 miles traveled costs $140.00, what is the total amount charged for one hour plus 36 miles traveled?

A.  

$218.00

B.  

$196.92

C.  

$179.60

D.  

$158.00

E.  

$143.60

Câu 14: 1 điểm

For some real number n, the graph of the line y = (n + 1)x + 6 in the standard (x, y) coordinate plane passes through (4,8). What is the value of n?

A.  

−3⁄2

B.  

−1⁄2

C.  

1⁄2

D.  

3⁄2

E.  

2

Câu 15: 1 điểm

Which of the following expresses the number of miles a runner must travel in a 4-lap race where the course is a circle of radius m miles?

A.  

4m

B.  

4πm

C.  

4πm2

D.  

8πm

E.  

16πm

Câu 16: 1 điểm

When graphed in the standard (x, y) coordinate plane,the lines x = −5 and y = x − 5 intersect at what point?

A.  

(−5,−10)

B.  

(−5,−5)

C.  

(−5,0)

D.  

(0,−5)

E.  

(0,0)

Câu 17: 1 điểm

A horse eats 12 bales of hay in 5 days. At this rate, how many bales of hay does the horse eat in 5 + x days?

A.  

12 + 12x5\frac{12x}{5}

B.  

12 + x⁄5

C.  

125+125x\frac{12}{5}+\frac{12}{5x}

D.  

125+x5\frac{12}{5}+\frac{x}{5}

E.  

125\frac{12}{5} + x

Câu 18: 1 điểm

The picture shown below has a uniform frame-width of 58 inches. What is the approximate area, in square inches, of the view able portion of the picture?

Hình ảnh

A.  

426.25

B.  

481.56

C.  

510.40

D.  

510.75

E.  

540.00

Câu 19: 1 điểm

If 38x = 813x−2, what is the value of x?

A.  

−2

B.  

0

C.  

2

D.  

3

E.  

4

Câu 20: 1 điểm

What is the slope of a line that is parallel to the line determined by the equation 5x − 4y = 8?

A.  

−4

B.  

−5⁄4

C.  

5⁄4

D.  

2

E.  

4

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