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Estimation 1. In RST shown below, RS RT , and the measure of R is 40. What is the measure of S ? A. B. C. D. E. 2. 20 40 50 70 Cannot be determined from the given information A recipe calls for 23 cup sugar to make 24 two-inch cookies. According to this recipe, how many cups of sugar should be used to make 60 two-inch cookies? A. B. C. D. E. 5 9 1 1 15 1 23 3 16 3. In the figure below, F and E are points on GD . What is the ratio of the area of square ABEF to the area of the parallelogram ACDG ? A. B. C. D. E. 4. 1:14 1:7 7:1 7:2 2:7 The scales on both axes of the standard (x,y) coordinate plane below are the same. Of the following, which is the best estimate for the slope of AB ? A. 4 B. 34 C. 14 D. - 14 E. -4 5. In the regular hexagon below, vertices B, C, and D are labeled; OA is perpendicular to CD ; A is the midpoint of CD ; and O is the midpoint of BC . What is the degree measure of AOC ? F. G. H. J. K. 6. 15 20 30 45 60 Theo polygon below was a square with 12-inch sides before a triangle was cut off. What is the perimeter, in inches, of this polygon? F. G. H. J. K. 41 43 46 48 53 7. In triangle ABD below, points D, C, and B are collinear, AD is perpendicular to DB , and AC bisects DAB. If the measure of CBA is 40, what is the measure of ACB ? F. G. H. J. K. 8. 115 112.5 110 107.5 105 The area of the trapezoid below is 16 square inches, the altitude is 2 inches, and the length of one base is 3 inches. What is the length, b, of the other base, in inches? A. 2 23 B. 5 C. 11 D. 13 E. 15 9. The radio station WEST is erecting a new transmitting tower that is 280 feet tall. A support wire will be attached to the ground at point A and to the tower 250 feet up at point B, as shown below. The wire must be at least as long as AB . Which of the following expresses the length of AB , in feet? F. 250 cos 70 G. 250 sin 70 H. 250 tan 70 J. cos250 70 K. 250 sin 70 10. In the diagram shown below, lines m and n are parallel. The lengths of AB and AC are equal, and one angle measures 70, as shown. What is the measure of ACD ? F. G. H. J. K. 110 130 140 150 160 11. In the figure below, PQ is perpendicular to QR , and points Q, R, and S are collinear. If the measure of PRS is 145, what is the measure of QPR ? F. G. H. J. K. 27.5 35 45 55 72.5 12. In trapezoid ABCD below, BAD and ADC are both right angles. If AB is 10 units long, DC is 15 units long, and AD is 12 units long, how many units long is BC ? A. B. C. D. E. 119 5 5 13 2 61 17 13. In the figure below, OB bisects 70 angle AOC and is perpendicular to AC . What is the degree measure of ACD ? A. B. C. D. E. 105 125 135 140 160 14. (2 - 3 2 )(3 + 2 2 ) = ? A. 6-6 2 B. -6 C. 6 - 11 2 D. -6 - 5 2 E. -16 15. In right triangle ABD below, AC is perpendicular to the hypotenuse BD . If the length of AD is 6 units and that of AB is 8 units, then how many units long is AC ? A. 10.0 B. 7.5 C. 6.4 D. 4.8 E. 2.4 16. In the figure below, m is parallel to n and the measures of angles are as marked. What is the measure, in degrees, of x ? A. B. C. D. E. 80 75 65 55 35 17. Two transversals intersect at R, a point between the 2 parallel lines m and n. The measures of angles are as marked on the figure below. What is the measure, in degrees, of PQR ? F. G. H. J. K. 76 54 46 44 32 18. In the figure below, all distances are in centimeters and all angles are right angles. A straight line drawn from point A to point D would be how many centimeters long? F. G. H. J. K. 5 12 13 16 17 19. A ramp goes from the edge of a dock to the edge of a ship’s deck. If the ramp is 25 feet long and the deck of the ship is 7 feet above the dock, how many feet away from the dock is the ship? A. 674 B. 576 C. 674 D. 24 E. 18 20. In the figure below, Q lies on PR , PQS and PSR are each right angles, and the measure of QRS is 30. If PS is 4 units long, how many units long is QS ? F. 2 3 3 G. 4 3 3 H. 3 J. 2 3 K. 4 21. In a certain rural school district, exactly 60% of the students live on farms. If there are 7,345 students in the district, how many do NOT live on farms? F. 294 G. 447 H. 2,938 J. 4,407 K. 6,898 22. Given: m and n are parallel lines t is a transversal crossing lines m and n a measures 30 What is the measure of f below? A. 30 B. 60 C. 120 D. 130 E. 150 23. In the figure below, where the 3 lines intersect at the indicated angles, x = ? F. G. H. J. K. 25 52.5 65 70 75 24. In the figure below, AB and CD bisect each other at E. The measure of CAE is 80 and the measure of BDE is 60. What is the measure of CEA ? F. G. H. J. K. 10 30 40 60 Cannot be determined from the given information 25. At a certain company, 240 of the employees belong to a union while the other 160 do not. What percent of the company’s workers are nonunion? F. G. H. J. K. 25% 33 13 % 40% 60% 66 23 % 26. A circle has a circumference of 10 inches. What is the radius, in inches, of the circle? 5 A. 10 B. C. 10 D. 20 E. 100 27. What is the area, in square inches, of the figure shown below? F. G. H. J. K. 18 30 36 44 60 28. If the lengths of the sides of the triangle below are shown in inches, how many inches long is side AB ? F. G. H. J. K. 12 40 70 4 3 4 5 29. Two 30-60-90 triangles are shown below. The hypotenuse of the larger triangle is 18 centimeters long. If the perimeter of one triangle is 3 times that of the other triangle, how many centimeters long is the shortest of the 6 sides? A. B. C. D. E. 3 3 3 6 9 9 3 30. In the diagram below, AED and BCD each measure 135, DF is an altitude of CDE and ABCE is a rectangle. What is the area, in square meters, of pentagon ABCDE ? A. 28 + 8 2 B. 96 C. 112 D. 120 E. 140 31. A line passes through the points (2,4) and (3,8) in the standard (x,y) coordinate plane. What is the value of y if (6,y) is also on this line? A. B. C. D. E. 12 13 16 20 32 32. Below, in right triangle ABC, AB is 4 inches long and BC is 5 inches long. What is the area, in square inches, of square ACDE ? F. 9 G. 41 H. 82 J. 4 41 K. 41 33. In the figure below, rectangle CDFG is contained in rectangle ABCD. If equilateral triangle CDE divides FG into 3 equal-length segments FT , TW , and WG , what is the ratio of the widths of these rectangles (that is, FD:AD) ? A. B. C. D. E. 1:3 1:2 1: 3 1:1 2:3 34. The figure below is a regular pentagon. What is the measure of A ? F. G. H. J. K. 72 108 120 135 144 35. It is estimated that, from the beginning of 1980 to the end of 1986, average milk consumption in the United States decreased from 30 gallons per year to 22 gallons per year. During the same time period, soft drink consumption rose from an average of 24 gallons per year to 34 gallons per year. Assuming that in each case the change was linear, during what year were the 2 consumption rates equal? A. B. C. D. E. 1981 1982 1983 1984 1985 36. In a group of 64 students, 40 are freshmen. What percentage of the group are freshmen? A. B. C. D. E. 1.6% 16% 25% 40% 62.5% 37. Of the 50 people in a music store, 35 of them own a cassette tape player. If 1 of those 50 people is randomly selected to win a cassette tape, what is the probability that the person chosen will already own a cassette tape player? A. B. C. D. E. .70 .65 .35 .30 .15 38. The volume of a certain gas at constant pressure is equal to a fixed number multiplied by the absolute temperature. If that gas occupies 500 cubic centimeters when the absolute temperature is 300, what is the volume, in cubic centimeters, when the temperature rises 30 and the pressure kept constant? F. G. H. J. K. 18 50 198 550 883 1/3 39. Given the information in the diagram below, including the fact that BCD is isosceles, how many feet long is AB ? F. G. H. J. K. 5 6 10 10 2 10 3 20 40. A parabola can be defined as the set of points equidistant from a focus point and a directrix line. What is the distance, in units, between the focus F and the point P that are graphed in the standard (x,y) coordinate plane below? A. B. C. D. E. 4 2 5 6 4 5 20 41. If the radius of the circle below is 4 feet, what is the area of the shaded portion of the circle, in square feet? F. G. H. J. K. 4 6 8 12 16 42. Points A, B, C, and D are on the circle below with center at X and radius of 12 inches. The length of DB equals the length of XB . What is the length, in inches, of arc DCB? A. B. C. D. E. 4 8 20 24 48 43. In the figure below, A lies on CQ , P lies on QB , and AP is parallel to CB . If AP is 5 units long, PQ is 3 units long, and CB is 15 units long, how many units long is PB ? F. G. H. J. K. 5 6 9 12 15 44. In the figure below, l1 is parallel to l2, l3 is parallel to l4, and the lines intersect as shown. What is the measure of angle z? A. B. C. D. E. 110 120 130 140 Cannot be determined from the given information 45. What is the number of degrees the hour hand of a clock moves in 10 hours? A. B. C. D. E. 100 120 150 220 300 46. In the standard (x,y) coordinate plane below, POQ and SRQ are isosceles right triangles with equal areas. Points O, P, Q, and R are located on the axes as shown. Which of the following could be the coordinates of point S? F. G. H. J. K. ( 0,14) ( 7, 0) ( 7,14) (14, 0) (14, 7) 47. Two strips of tape are to be used to wrap a box, as shown below. Both strips must go completely around the box. What is the minimum length of tape, in centimeters (cm), required to wrap the box? F. G. H. J. K. 102 112 144 204 244 48. In the figure below, 3 parallel lines are crossed by 2 transversals as shown. the points of intersection and some distances, in inches, are labeled. What is the length, in inches, of YX ? F. 1 G. 2 H. 3 J. 32 K. 52 49. The figure below shows square OABC and also shows the circle centered at O with radii OC and OA . If the area of the square is 36 square units, what is the area of the circle, in square units? A. B. C. D. E. 12 18 36 72 81 50. A forest begins 300 feet from the center of the base of a vertical television tower, across level ground. If the tower is 400 feet tall, how many feet is it from the top of the tower to the nearest edge of the forest at ground level? A. B. C. D. E. 100 7 200 3 500 700 120,000 51. Trapezoid ABCD below is isosceles, with side lengths as marked. Its diagonals intersect at E. What is the ratio of the length of AE to DE ? F. x y G. xz H. 1 J. yz K. zy 52. Vivian made 63 throws out of 89 attempts during the basketball season. What percentage, to the nearest percent, of her free throws did she make during this season? A. B. C. D. E. 41% 63% 71% 89% 98% 53. In the triangle shown below, what does the x represent? F. G. H. J. K. 42 64 69 74 Cannot be determined from the given information. 54. If all angles in the figure shown below are right angles and each dimension given is in inches, then what is the area of the figure, in square inches? A. B. C. D. E. 35 44 62 83 96 55. The dimensions of parallelogram ABCD, shown below, are given in centimeters. What is the area, in square centimeters, of parallelogram ABCD ? F. G. H. J. K. 25 36 40 50 80 56. On the number line below, what is the coordinate of the point between A and B that is twice as far from point A as from point B ? 57. Two lookout towers are located about 7 miles apart, at the same elevation. A fire is sighted at angles of 37 and 42 from the line of sight between the towers, as indicated in the diagram below. Which of the following expressions, if any, gives the approximate distance, in miles, between the fire and tower A ? (Note: The law of sines states that the ratio between the length of the side opposite an angle and the sine of that angle is the same for all interior angles in the same triangle) F. G. H. J. K. The distance cannot be approximated without more information. 37 2 42 2 7 cos 42 cos101 7 tan 42 7 sin 42 sin101 58. In the figure below, the perpendicular bisectors of XY and XW meet at P. Given the information above, a circle with center P and radius PX must pass through which of the labeled points? A. B. C. D. E. X only W and X only Y and X only W, X, and Y only W, X, Y, and Z 59. to keep up with rising expenses, a motel manager needs to raise the $40.00 room rate by 22%. What will be the new rate? F. G. H. J. K. $40.22 $42.20 $48.00 $48.80 $62.00 60. The total cost of renting a car is $30.00 for each day the car is rented plus 28 ½ ¢ for each mile the care is driven. What is the total cost of renting the car for 5 days and driving 350 miles? (Note: No sales tax is involved.) A. B. C. D. E. $ 104.75 $ 159.98 $ 249.75 $ 300.00 $1,147.50 61. In the isosceles right triangle below, AB = 10 feet. What is the length, in feet, of AC ? A. B. C. D. E. 5 10 20 20 10 2 62. In the standard (x,y) coordinate plane, a line segment has its endpoints at (3,6) and (9,4). What are the coordinates of the midpoint of the line segment? A. B. C. D. E. ( 3, -1) ( 3, 1) ( 6, 2) ( 6, 5) (12,10) 63. The lengths of the corresponding sides of 2 similar right triangles are in the ratio of 2:5. If the hypotenuse of the smaller triangle is 5 inches long, how many inches long is the hypotenuse of the larger triangle? F. 2 G. 2.5 H. 7 J. 10 K. 12.5 64. In the figure below, ABCD is a square. Points are chosen on each pair of adjacent sides of ABCD to form 4 congruent right triangles, as shown below. Each of these has one leg that is twice as long as the other leg. What fraction of the area of square ABCD is shaded? A. B. C. D. E. 1 9 2 9 4 9 5 9 8 9 65. In ABC, shown below, the measure of B is 41, the measure of C is 34, and AB is 25 units long. Which of the following is an expression for the length, in units, of BC ? (Note: The law of sines states that, for any triangle, the ratios of the sines of the interior angles to the lengths of the sides opposite those angles are equal.) A. B. C. D. E. 25 sin105 sin 41 25 sin105 sin 34 25 sin 75 sin 41 25 sin 41 sin105 25 sin 34 sin 75 66. In the pentagon ABCDE, shown below, A measures 50. What is the total measure of the other 4 interior angles? F. G. H. J. K. 130 200 310 432 490