# ACT Form 72F Math Answer Explanations

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1. If 4/y = 0.4, then y ?

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2. A motel manager’s costs are 24% higher this year than they had been when the room rate was $60.00. If the room rate had increased by the same percent as the manager’s costs, what would the room rate be this year?

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3. Louis earns his regular pay of $10.00 per hour for up to 40 hours of work in a week. For each hour over 40 hours of work in a week, Louis is paid 12 times his regular pay. How much does Louis earn for a week in which he works 47 hours?

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4. 3x^9 5x^9 is equivalent to:

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5. The total surface area, T, of any right circular cone with a radius r and a slant height s, such as the cone shown below, can be determined by using the. formula T = pi y^2 + pi rs. If a cone has a 3-inch radius and a 5-inch slant height, what is its total surface area, in square inches?

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6. In the Figure below, C lies on both AE and BD, AB and DE are parallel, and congruent, and 2 angle measures are given. What is the measure of ACB ?

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7. What is the least common denominator of the fractions 4/35, 1/28 and 3/8?

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8. Which of the following polynomial equations has solutions —2 and 5 ?

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9. The combined length of 3 pieces of a board is 60 inches. The lengths of the pieces are in the ratio 3:5:7. What is the length, in inches, of tie longest piece?

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10. Zoe programs her calculator to evaluate a linear funttion, but she doesn’t say what the function is. When 9 is entered, the calculator displays the value 6. When 12 is entered, the calculator displays the value 8. Which of the following expressions represents what the calculator will display when any number, n, is entered?

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11. Points C(2,5) and D(8,11) lie in the standard (x,y) coordinate plane. What is the midpoint of CD ?

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12. A rectangular box that is 1/9 foot deep, 1 foot wide, and 1 foot long has a volume of how many cubic feet?

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13. Which of the following expressions is equal to (3x^2-4x-5)-(-x^2+6x+7) for all real values of x ?

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14. For all positiVe integers a, let if E represent the sentence “a is even” and let P represent the sentence “a is prime.” When a = 22, which of the following statements is true?

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15. |6(-7) + 4(8)| =?

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16. In the standard (x,y) coordinate plane, what is the slope of the line 11x + 6y = 3?

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17. A function g is defined as g(x,y,z)=4xy-3xz^2. What i g(2,4,-3)?

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18. A family plans to remodel their kitchen. They have a total budget of $45,000 to cover expenses in 6 categories. Not all the budget has been assigned. The budget amounts that have been assigned are shown in the table below. In a circle graph illustrating the 6 budget amounts in the table, what should be the measure of the central angle of the Flooring sector?

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19. The amount budgeted for Appliances is the sum of the prices of 5 appliances-1 refrigerator, 1 dishwasher, 1 built-in cooktop, and 2 ovens (1 conventional and 1 microwave). What is the average price per appliance?

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20. Suppose a bar graph will be constructed illustrating the amounts of the assigned expenses. The length of the bar for Lighting should be what fraction of the length of the bar for Cabinets?

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21. Which of the following percents is closest to the percent of the total budget that remains to be assigned?

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22. In the figure below, 5 angle measures are given. The angle marked with a measure of y° is an exterior angle. What is the value of y ?

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23. What is the area, in square coordinate units, of parallelogram ABCD shown in the standard (x,y) coordinate plane below?

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24. Right triangle ABC is shown below. The side lengths are given in centimeters. What is tan C?

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25. The system of equations below has 1 solution(a,b). What is the value of b?

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26. For his job delivering pizzas, Albert uses his own car and buys his own gas. He joined the local station’s Frequent Fueler program that earns him points towards free gas each time he buys gas. Points are earned according to the following chart.

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27. The first 2 rectangles of a sequence of rectangles are shown below. The 1st rectangle is 4 inches long and 1 inch wide. The dimensions of the 2nd rectangle, and of each successive rectangle after the 2nd, are determined by continuing the following pattern: the length is 3 inches longer than the length of the previous rectangle, and the width is 1 inch longer than the width of the previous rectangle. What is the perimeter, in inches, of the 6th rectangle in the sequence?

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28. Which of the expressions below is a factor of the polynomial 2x^3 + x^2 – 6x ?

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29. Shown below, a circular dartboard has 4 sectors (red, white, blue, and green) whose areas are in the ratio of 1:2:3:4, respectively. Brad will throw 1 dart at the dartboard, and it will hit the dartboard at a random point contained in 1 of the sectors. What is the probability that the sector the dart hits is NOT the blue sector?

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30. The dimensions of equilateral triangle ABC are given in centimeters in the figure below. What is the value of y?

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31. For right triangle LMN below, cos L =17/6. What is sin N?

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32. When a store sets the price of birdseed at $3.50 per pound, the store sells 2,500 pounds of birdseed eer week. With each $0.25 increase in the $3.50 prie per pound, the store sells 100 pounds less birdseed per week. Let n be the number of $0.25 increases in the price per pound. Which of the following expresions best represents the dollar amount of the store’s weekly sales of birdseed?

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33. The circumference of a circle is 20 cm. What is the length, in centimeters, of the radius of the circle?

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34. You’re on a salvage ship in the Pacific Ocean when your ship’s sonar locates a shipwreck at an angle of depression of 60, as shown in the figure below. After your ship travels 500 meters on the surface of the water to be directly over the wreck, how many meters down would you have to dive to reach the wreck?

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35. What is the length, in meters, of AC ?

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36. The perimeter of 1 of the 25 congruent squares is how many meters?

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37. Point M starts at A and is rotated counterclockwise (k)) about P a total of 450°. After the rotation, M is at the same location as which of the following points?

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38. Suppose ABCD is in the standard (x,y) coordinate plane such that BC is on the x-axis, the midpoint of BC is at the origin, A has positive coordinates, and 1 coordinate unit is equal to 1 meter. What are the coordinates of D ?

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39. For what value of x is the equation /3x-9 + 10 = 13 true?

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40. Ten years ago, Tara invested $2,000 at 6% interest compounded monthly. Which of the following expressions represents today’s value of the investment?

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41. Which of the following is the decimal equivalent to 2/7? (Note: A bar indicates a digit pattern that is repeated.)

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42. Ms. Simons made a bar graph of the 20 scores on the last math test, as shown below. Which of the following statements about the mean of the 20 scores is true?

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43. To plan orders for a party, a caterer uses the formula P = 64G/S, where P is the number of people, G is the number of gallons of punch, and S is the size of the cups in ounces. Which of the following gives the number of gallons of punch to order for a party of 200 people when 5-ounce cups will be used?

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44. Linh has $3.67 in quarters ($0.25), dimes ($0.10), nickels ($0,05), and pennies ($0,01). She arranges these coins in rows and notices that there are 5 more dimes than quarters, 1 more nickel than quarters, and 25 more pennies than quarters. How many pennies does Linh have?

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45. Consider the transformation of the standard (x,y) coordinate plane- that maps each point (x,y) to the point (kx,ky) for a certain positive constant, k. particular, this transformation maps (3,9) to (1,3). This transformation maps (9,24) to which of the following points?

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46. Lindsay is designing a 5-foot-by-8-foot rectangular poster for her art class. She will cover both diagonals of the poster with straight lengths of yellow rope. Which of the following values is closest to the total length, in feet, of the 2 yellow ropes Lindsay will need for the poster?

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47. Robert writes a check for $20. When he records the check in his check register, he accidentally adds $20 to his balance instead of subtracting $20, which causes a discrepancy between what Robert’s check register shows and what it should show, Because of his mistake, Robert’s check register shows:

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48. For a certain location in Grand Canyon National Park, the highest temperature on record is 120°F and the lowest temperature on record is -18°F. Which of the statements below is necessarily true about the temperatures on record for this location?

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49. The graph of y = 2x in the standard (x,y) coordinate plane has a vertical asymptote with equation x = ?

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50. What fraction of a 6-inch-diameter pizza contains the same amount of pizza as 1 slice of a 12-inch-diameter pizza of the same thickness cut into 12 equal slices?

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51. For what real valve of x is true?

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52. What are all real values of m, if any, such that any line through the points (3,7) and (3,m) will be vertical when graphed in the standard (x,y) coordinate plane?

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53. Green Camp and Blue Camp lie on opposite sides of Red Lake. A boat dock is located 1,000 yards from Green Camp. The campers estimated the angles between these 3 locations to be as shown on the map below. Using these estimates, which of the following expressions gives the distance, in yards, between Green Camp and Blue Camp?

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54. The graphs of the functions y =f(x) = (x — 3)^2 + 2 and y = g(x) = 1/2 x + 1/2 are shown in the standard (x,y) coordinate plane below. Which of the following is NOT true?

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55. When 3 <= x <= 5 and 7 <= y <= 9, the smallest possible value for 2/(y-x) is:

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56. In the standard (x,y) coordinate plane below, 0 is the radian measure of any angle in standard position with the point (r, c) on the terminal side. Which of the following points is on the terminal side of the angle in standard position having radian measure m – 0 ?

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57. Which of the following matrices is equal to the matrix product

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58. In the figure below. BC is parallel to AD. E is the midpoint of A , F is the midpoint of CD, G is the midpoint of AE, and II is the midpoint of ED. The lengths marked are in inches. What is the length of GH in inches?

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59. Suppose that a will be randomly selected from the set {-3, —2, —1, 0, 1} and that b will be randomly selected from the set (-2, -1, 0, 1). What is the probability that ab > 0 ?

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60. Distinct points A, B, C, and D are collinear, and B is between A and C. For D to be between A and C such that AD + DB + BC = AC, which of statements I—IV below must be true? (Note: If B is between A and C, then AB + BC = AC.)

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