美国高考数学训练题Free-ACT-Math-Test-Practice-Questions-with-Answer1.docx

Free ACT Math Test Practice Questions with Answers 
sample 2
Math questions, with answers and detailed solutions, similar to the questions in the ACT math test. The answers are at the bottom of the page.
1. What is the greatest common factor of 45, 135 and 270? 
A) 5 B) 9  C) 15  D) 25  E) 45
2. What is the value of 2x + 1/2 when 5x - 3 = -3x + 5 
A) -1/2  B) -1/4  C) 1  D) 2 and 1/2 (mixed number)  E) Value cannot be calculated
3. The width W of a rectangle is 2 inches less than half its length L. Express the perimeter P of the rectangle in terms of the length L. 
A) 3L - 4  B) 4L - 4  C) 4L  D) 3L - 2  E) 2L - 2
4. The total surface area of all six sides of the rectangular box below is equal to 80 square inches. What is the volume of the rectangular box in inches cubed? 
.A) 40  B) 48  C) 12  D) 30  E) 16
5. The points (-4 , -4), (-1 , -2) and (x , -8) are the vertices of a right triangle with the right angle at (-1 , -2). Find the value of x. 
A) 0  B) 2  C) 3  D) -1  E) -4
6. In the figure below, L1 and L2 are parallel lines. The correct relationship between angles y and x is 
.A) y = x  B) x + y = 180o  C) x + y = 360o 
D) y = x + 90o  E) y - x = 180180o
7. If (x + y)2 = 144 and x2 - y2 = 24, then what is x if x and y are both positive? 
A) 7  B) 5  C) 12  D) 2  E) 8
8. How many 3 digit numbers can we make using the digits 4, 5, 7 and 9 and where repetition is allowed? 
A) 34  B) 33  C) 44  D) 12  E) 43
9. A boat travels 10 miles East and then 24 miles South to an island. How many miles are there from the point of departure of the boat to the island? 
A) 34  B) 14  C) 26  D) 2√119  E) 44
10. What is the slope of any line perpendicular to the line -5x + 3y = 9? 
A) -3/5  B) 5/3  C) 3/5  D) -5/3  E) -1/5
11. Which of the following is a factor of the polynomial -2x2 + 7x - 6? 
A) -2x - 3  B) 2x + 2  C) x - 6  D) 2x - 2  E) -2x + 3
12. √(-9)(-4) + √(-4) = ? 
A) 6 + 2i  B) 6 - 2i  C) 8  D) 4  E) 2 + 6i
13. Find the linear function f such that f(2) = 5 and f(3) = -5. 
A) f(x) = 2x + 1  B) f(x) = -10x - 5  C) f(x) = 3x - 1 
D) f(x) = -10x + 25  E) f(x) = -10x - 25
14. A circular garden has an area of 100π feet squared. What is the circumference of the garden in feet? 
A) 20  B) 10π  C) 20π  D) 400π  E) 2500π
15. If 5/x = 10 and 2/y = 6 then x/y = ? 
A) 5/3  B) 3/2  C) 3/5  D) 2/3  E) 5/2
16. If 2m-3 / 42m = 8, then 2m - 1 = ? 
A) 0  B) 1  C) 2  D) -5  E) -9
17. In the figure below, ABC is a right triangle. Points B, C and D are collinear; points D, E and F are also collinear and so are points B, A and F. The length of segments DC and DE are equal. What is the size, in degrees, of angle AFE? 
.A) 50o  B) 40o  C) 30o  D) 45o  E) 55o
18. Which of the following is an equation of a line perpendicular to the line with equation 3x - 6y = 9? 
A) y = 2  B) 3x + 6y = 9  C) x - 2y = 3  D) 2x + 2y = 3  E) 2x + y = 7
19. If a and b are any real numbers, then which of the following expressions is always positive? 
A) |a|  B) |a + b|  C) |a - b| + 1/2  D) a2 + b2  E) (a + b)2

20. The geometric figure below consists of a right triangle and 2 semicircles. The diameters of the semicircles are the sides of the triangle. What is the area of the shaded region in square centimeters if the length of the hypotenuse of the triangle is 8 centimeters? 
A) 64  B) 8π  C) 64π  D) 10π  E) 16
21. The mean of the numbers a, b, c, d and e is 23. The mean of the numbers a, b, c, d, e and f is 22. What is the value of f? 
A) 23  B) 18  C) 22  D) 22.5  E) 20
22. Which of the following equations corresponds to the graph shown below? 
.A) y = (x - 3)2 - 1  B) y = -(x - 3)2 + 1 
C) y = (x - 3)2 + 1  D) y = x – 3 E) y = -(x - 3)2 - 1
23. Functions f and g are defined by f(x) = x2 + x and g(x) = √(x + 6). What is the value of g(f(2))? 
A) 3  B) -3  C) 7  D) 6  E) -6
24. The sum of three consecutive integers is equal to 192. What is the product of these numbers? 
A) 216000  B) 7077888  C) 576  D) 110592  E) 262080
25. What are the x-coordinates of the points intersection of the line with equation y = x + 1 and the circle with equation x2 + y2 = 5 
A) -2 , 0  B) 1 , 2  C) -2 , 1  D) -2 , -1  E) 1 , 3
26. (1/2)sin(2x)(1 + cot2(x)) = 
A) tan(x)  B) sin(x)  C) cos(x) D) cot(x)  E) sec(x)
27. Find the area of the rectangle ABCD shown in the figure below. 
A) 2500 / √2  B) 2500  C) 2500 / √3  D) 1250  E) 5000
28. Solve for x: logx(1024) = -5 
A) 1/4  B) 4  C) 1/2  D) 1/8  E) 2

29. Simplify: 6 3√32 + 2 3√108 
A) 32  B) 18 3√2  C) 36 3√2  D) 18 3√4  E) 36 3√4
30. Evaluate: 1 / (-5)2 
A) - 1 / 25  B) 1 / 25  C) 25  -25  E) 1 / 10
Answers to the Above Questions
1. E
2. D
3. A
4. B
5. C 
6. B
7. A
8. E
9. C
10. A 
11.
12. 22、绿色植物的一些细胞能进行光合作用，制造养料，它们好像是一个个微小的工厂。E
13. A
14. D
15. C
16. B 
17.
18. 答：当月球运行到地球和太阳的中间，如果月球挡住了太阳射向地球的光，便发生日食。D
19. A
20.
21. 18、北斗七星构成勺形，属于大熊座，北极星属于小熊座。E
22. C
23. B 
24. B
25. E
26.
27. 8、晶体的形状多种多样，但都很有规则。有的是立方体，有的像金字塔，有的像一簇簇的针……有的晶体较大，肉眼可见，有的较小，要在放大镜或显微镜下才能看见。A
28.
29. 1、我们每天都要消耗食物和各种各样的生活用品，与此同时，也产生了许多垃圾。E
30.
31. 6、月球是一个不发光、不透明的球体，我们看到的月光是它反射太阳的光。C 
32. D
33.
34. 第一单元 微小世界C
35.
36. 18、建立自然保护区是保护生物多样性的有效方法，我国的九寨沟、长白山、四川卧龙等地都建立了自然保护区，自然保护区为物种的生存、繁衍提供了良好的场所。A
37.
38. 一、填空：D
39. B 

4、科学家研究表明昆虫头上的触角就是它们的“鼻子”，能分辨出各种气味，比人的鼻子灵敏得多。