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

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