COURSE 3 Adv
SAMPLE ACT MATHEMATICS TEST QUESTIONS
DIRECTIONS: Solve each problem, show all work on a separate sheet of paper and then choose the correct answer for each problem on this sheet. No points will be given for problems without the work attached!!!!
|1] If one leg of a right triangle is 8 inches long, and the other leg is 12 |2] If 7y = 2 x - 5, then x = ? |
|inches long, how many inches long is the triangle's hypotenuse? | |
| |A. 5y + 5 B. [pic]y - 5 C. [pic]y + 5 D. [pic] E. [pic] |
|F. [pic] G. [pic] H. [pic] J. [pic] K. 4 | |
|3] Which of the following statements completely |4] If a and b are any real numbers such that 0 < a < 1 < b, |
|describes the solution set for 3(x - 4) = 3 x - 12 ? |which of the following must be true of the value of ab ? |
| |F. 0 < ab < a G. 0 < ab < 1 H. a < ab < 1 |
|F. x = 3 only G. x = 0 only H. x = -12 only |J. a < ab < b K. b < ab |
|J. There are no solutions for x. | |
|K. All real numbers are solutions for x. | |
|5] Square ABCD below has a perimeter of 28 inches. |6] What is the perimeter of given scalene triangle? |
|How many inches long is diagonal [pic]? | |
| |(3y – 2) m y m |
|F. 7 G. [pic] H. [pic] |(3y³) m |
| | |
|J. 14 K. [pic] |(4y) m |
| | |
| |A) 7y³ B) 8y³– 2 C) 8y – 2 D) 7y– 2 E) 11y³– 2 |
|7] What is the sum of the 2 solutions to the equation x = 6 – x2 ? |8] What is the area of an inscribed square in a circle if the radius of the |
| |circle is 2? |
|F. 6 G. 2 H. 1 J. –1 K. –6 | A. 4 B. 6 C. 8 D.10 E.12 |
|9] What is the volume of a cylinder with radius of 5 and height of 10? Round |10] What is the length of the diagnoal of a rectangle if the length is 4 and |
|your answer to nearest hundreth. Use 3.14 for Pi. |width is 3? |
| A.785 B. 785.00 C. 973 D.785.07 E. 984 | A. 5 B. 4 C. 3 D. 2 E. |
|11] What is the distance between two coordinate points (3,4) and (-3,7)? Round |12] What is the least value of x that satisfies the equation |
|your answer to nearest hundreth. |x2 – 7x + 6 = 6 ? |
| A. 6.00 B. 7.98 C. 6.71 D. 8.00 E. 6.98 | |
| |A) –7 B) –6 C) –4 D) 0 E) 1 |
|13] Evaluate: 2xº + 3yº + 4z¹ if x= 6, y= 13, z= 4 |14] If x – y = 6 and 3x – 10 = 2y, what is the value of y? |
| | |
|A) 16 B) 13 C) 67 D) 24 E) 4 |A) - 8 B) - 4 C) 4 D) 8 E) 0 |
|15] Which of the following is equivalent to (x)(x)(x)(x) – (4)(4)(y), for all |16] | 3 – 7 | – | 4 – 1 | = ? |
|terms ? | |
| |A) 1 B) 5 C) 7 D) 15 E) –7 |
|A) 4x – 4y B) x4 – 16y² C) x + 4 + y D) 4 x – 4 y E) x4 – 16y | |
|17] You are carpeting a closet. How many square feet of carpet will you need? |18] If m(ABC= 60(, what is the measure of (DCB? |
| | |
|A) 11 232 ft² B) 2024 ft² |A) 22( B) 44( C) 71( |
|C) 2016 ft² D) 175 ft² | |
| |D) 82 ( E) 142( |
|E) 140 ft² | |
|19. |Which of the following is equivalent to (x)(x)(x)(x), for all x ? |20. |Which of the following is divisible by 3 (with no remainder)? |
| |A. 4x B. x4 C. x + 4 D. 4 x E. 2x2 | |A. 2,725 B. 4,210 C. 4,482 |
| | | |D. 6,203 E. 8,105 |
|21. |A rectangle is twice as long as it is wide. If the width of the |22. |A particle travels 1 [pic]10 8 centimeters per second in a straight line for 4 |
| |rectangle is 3 inches, what is the rectangle's area, in square inches?| |[pic]10 -6 seconds. How many centimeters has it traveled? |
| | | |F. 2.5 [pic]10 2 G. 2.5 [pic]10 13 H. 4 [pic]10 2 |
| |F. 6 G. 9 H. 12 J. 15 K. 18 | |J. 4 [pic]10 -14 K. 4 [pic]10 -48 |
|23. |A vendor has 14 helium balloons for sale: 9 are yellow, 3 are red, and|24. |The triangle below is isosceles and is drawn to scale. What is the measure of |
| |2 are green. A balloon is selected at random and sold. If the balloon | |[pic]N ? |
| |sold is yellow, what is the probability that the next balloon, | |[pic] |
| |selected at random, is also yellow? | |A. 22o B. 68o C. 78o D. 79o E. 89o |
| |A. [pic] B. [pic] C. [pic] D. [pic] E. [pic] | | |
|25. |3 [pic]10 - 4 = ? |26. | If 7y = 2 x - 5, then x = ? |
| |F. -30,000 G. -120 H. 0.00003 | |A. 5y + 5 B. [pic]y - 5 C. [pic]y + 5 D. [pic] E. [pic] |
| |J. 0.0003 K. 0.12 | | |
|27. |For all x > 0, [pic]simplifies to: |28. |In the figure below, [pic]and [pic]is 10 units long. What is the area, in |
| |A. x + 3 B. x + 4 C. 2(x + 3) | |square inches, of [pic]ABC ? |
| |D. 2(x + 4) E. 2(x + 3)(x + 4) | |[pic] |
| | | |F. 12.5 G. 25 H. [pic] J. 50 |
| | | |K. Cannot be determined from the given information |
|29. |If one leg of a right triangle is 8 inches long, and the other leg is |30. |Which of the following statements completely describes the solution set for 3(x|
| |12 inches long, how many inches long is the triangle's hypotenuse? | |- 4) = 3 x - 12 ? |
| |F. [pic] G. [pic] H. [pic] J. [pic] K. 4 | |F. x = 3 only G. x = 0 only H. x = -12 only J. There are no solutions |
| | | |for x. |
| | | |K. All real numbers are solutions for x. |
|31. |In the standard (x,y) coordinate plane, the graph of |32. |When graphed in the (x,y) coordinate plane, at what point do the lines x + y = |
| |(x - 2)2 + (y + 4)2 = 9 is a circle. | |5 and y = 7 intersect? |
| |What is the area enclosed by this circle, expressed in square | |A. (-2,0) B. (-2,7) C. (0,7) D. (2,5) E. (5,7) |
| |coordinate units? | | |
| |A. 3 [pic] B. 4 [pic] C. 6 [pic] D. 9 [pic] E. 16 | | |
| |[pic] | | |
| |How many solutions are there to the equation x2 - 15 = 0 ? | |The area of a trapezoid is [pic]h(b1 + b2), where h is the altitude, and b1 and|
|33. |F. 0 G. 1 H. 2 J. 4 K. 15 |34. |b2 are the lengths of the parallel bases. If a trapezoid has an altitude of 5 |
| | | |inches, an area of 55 square inches, and one base 13 inches long, what is the |
| | | |length, in inches, of its other base? |
| | | |F. 9.0 G. 16.8 H. 19.4 J. 45.0 K. 97.0 |
|35. |A circle with center (-3,4) is tangent to the x-axis in the standard |36. |If you have gone 4.8 miles in 24 minutes, what was your average speed, in miles|
| |(x,y) | |per hour? |
| |coordinate plane. What is the radius of this circle? | |A. 5.0 B. 10.0 C. 12.0 D. 19.2 E. 50.0 |
| |A. 3 B. 4 C. 5 D. 9 E. 16 | | |
|37. |In [pic]ABC, if [pic]A and [pic]B are acute angles, and sin A = [pic],|38. |If a and b are any real numbers such that 0 < a < 1 < b, which of the following|
| | | |must be true of the value of ab ? |
| |what is the value of cos A ? | |F. 0 < ab < a G. 0 < ab < 1 H. a < ab < 1 J. a < ab < b K. b < ab |
| |F. [pic] G. [pic] H. [pic] J. [pic] K. [pic] | | |
|39. |What are the values of a and b, if any, where a|b - 2| < 0 ? |40. |In right triangle [pic]ABC below, what is the sine of [pic]A ? |
| |A. a < 0 and b [pic]2 B. a < 0 and b = 2 C. a [pic]0 and b > | |[pic] |
| |2 | |A. [pic] B. [pic] C. [pic] D. [pic] E. [pic] |
| |D. a > 0 and b < 2 E. There are no such values of a and b. | | |
|41. |In a shipment of 1,000 light bulbs, [pic]of the bulbs were defective. |42. |The graph of y = [pic]is shown below. |
| |What is the ratio of defective bulbs to nondefective bulbs? | |[pic] |
| |F. [pic] G. [pic] H. [pic] J. [pic] K. [pic] | |Among the following, which is the best representation |
| | | |of y = [pic]? |
| | | |F. [pic] J. [pic]G. [pic]K. [pic]H. [pic] |
ACT PRACTICE PROBLEMS [2012/2013]
PAGE 1: 1. F 2. E 3. K 4. J 5. G 6. C 7. J 8. C 9. A or B 10. A
11. C 12. D 13. 21 (correct answer is missing) 14. A 15. E 16. A 17. C 18. C
PAGE 2: 19. B 20. C 21. K 22. H 23. A 24. D 25. J 26. E 27. C
28. K 29. F 30. K 31. D 32. B 33. H 34. F
PAGE 3: 35. B 36. C 37. F 38. J 39. A 40. D 41. G 42. F
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.