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Practice Test Problems (Sections 7.1-7.3 10.1-10.5) Name___________________________________ Express the ratio in simplest form. 1) $80 to $104 15) Matt bought a 32 oz can of fuel additive for $43.52. Roger bought the 16 oz size for $26.24. Who made the better buy? What was the lowest price per ounce? 2) 24 inches to 15 inches 16) Which is the better buy: one yard of ribbon for $0.67 or three feet of ribbon at $0.36 per foot. 3) The ratio of wins to games played if a baseball team wins 25 games and loses 60 games Solve the proportion. 10 6 17) = x x + 20 4) 6 feet to 60 inches 5) 8 minutes to 3 hours 18) 6) 14 hours to 96 days 1 1 7) 3 days to 5 weeks 2 2 5 x - 10 = 3 10 Use a proportion to solve the problem. Round answers to the nearest tenth if necessary. 19) Dr. Wong can see 9 patients in 2 hours. At this rate, how long would it take her to see 72 patients? Solve the problem. 8) The ratio of staff to patients at Lakeview is 4 to 7. If total staff plus patients is 1430 people, how many staff are at Lakeview? 20) The 12th hole at the Riverwoods Golf Course is 440 yards long. How long would it be on a model with a scale of 0.5 inches to 100 yards? 9) Carl wants to make some furniture stripper. The stripper is a mixture of chemicals A and B in the ratio of 11 to 4. How many ounces of chemical A are needed to make 150 ounces of stripper? 21) Jim drove 336 miles in 7 hours. If he can keep the same pace, how long will it take him to drive 1392 miles? 10) The ratio of the distances a pitching wedge and an 8-iron will drive a golf ball is 4 to 5. If a golfer averages 137 yards with a pitching wedge, how far should she average with an 8-iron? 22) In a sample of 94 widgets, 2 were defective. How many defective widgets would you expect in a sample of 188 widgets? Use a proportion to solve the problem. 23) If a spring stretches 8 meters when a weight of 3-kilograms is attached to it, how much will it stretch when a weight of 21-kilograms is attached to it? 11) The trim for a costume costs $11.25 for 4.5 yd. Find the unit price in dollars per yard. 12) A 3-lb package of ground beef costs $5.37. What is the unit price in cents per ounce? Round to the nearest hundredth of a cent. 24) The ratio of the lengths of strings that play the notes F and G is 9 to 8. If a string 80 centimeters long plays a G, what is the length of the string that plays an F? 13) Find the best buy. Brand X 8 oz for $0.56 Brand Y 6 oz for $0.36 25) On a map of the Fox River, 1 centimeter represents 7 kilometers. If a trail by the river is actually 28.00 kilometers long, what is the length of the river on the map? 14) Find the best buy. Brand A 20 oz for $14.60 Brand B 24 oz for $17.76 1 38) 366% Provide an appropriate response. 26) Explain the process you would use to determine the best buy. 2 39) 38 % 3 27) Suppose that Jody drove 80 miles in 2 hours. Dividing 80 by 2 tells us how many miles Jody drove in each hour. The units for this rate are miles per hour (mi/hr). If we divide 2 by 80 what information would this give us? Give an 2 interpretation of the rate = 0.025. What units 80 40) 4 % 9 41) 0.04% would be used for this rate? Solve the problem. 42) On a biology test, a student got 25 questions correct but did not pass. On a second attempt, the student got 34 questions correct. What was the percent of increase? Find the percent of the figure that is shaded. 28) 43) Enrollment in a business seminar increased from 62 people to 81 people. What was the percent of increase? 44) By switching service providers, a familyʹs telephone bill decreased from about $50 a month to about $45. What was the percent of decrease? 29) 45) All 33 of the students in a mathematics class attended class on Monday. On Tuesday only 25 students attended. What was the percent of decrease? Write the ratio as a percent. 7 30) 36 31) 46) A carpeted living room and dining room area measures 32 ft by 13 ft. Mark decides to install wood flooring in the 15 ft by 13 ft dining room. By what percent has he reduced the area that is carpeted? 25 40 Solve the problem. If the answer is an amount of money, round to the nearest dollar. 47) The parking lot at a grocery store has 64 cars in it. 75% of the cars are blue. How many cars are blue? 8.36 32) 7.82 Write as a percent. 33) 0.47 48) The Perrones have saved $20,400 for a down payment. If a 31% down payment is required, what price house can they buy? 34) 0.953 49) Alex and Juana went on a 100-mile canoe trip with their class. On the first day they traveled 26 miles. What percent of the total distance did they canoe? 35) 4.8 36) 1 Write the percent as a fraction in the lowest terms. 37) 6% 2 50) Which is the best investment for three consecutive years? a. A growth of 2% followed by a growth of 4% followed by a growth of 6% b. A growth of 6% followed by a growth of 4% followed by a growth of 2% c. Three years of growth at 4% per year. 59) What is the vertex of ∠DEI? Describe the figure. 60) A) Simple nonconvex polygon B) Nonsimple closed curve C) Simple polygon D) Simple closed curve 51) If a number is increased by 11%, by what percent must it be decreased to obtain the original number? Round to the nearest hundredth if necessary. 61) Use the following figure to verify if statement is true or false. A) Simple closed curve B) Simple curve C) Closed curve D) None of the above 62) 52) AB and GF are skew lines. A) Simple polygon C) Closed polygon 53) AB and CG are intersecting lines. B) Convex polygon D) All of the above 63) 54) AK and EK are perpendicular to the plane BEF. 55) AD and BC are coplanar lines. Refer to this figure to answer the question. A) Simple convex polygon B) Nonconvex polygon C) Nonsimple polygon D) Convex polygon 64) A) Simple closed curve B) Closed curve C) Simple curve D) None of the above 56) What are the endpoints of HI ? 57) What are the endpoints on DE ? Decide whether the figure is convex or not convex. 65) 58) Are HD and HA the same line? 3 66) 72) Classify the triangle as equilateral, isosceles, or scalene. Then classify it as right, obtuse, or acute. 67) 73) 10 8 4 68) 74) 6 5 3 69) 15 Find the requested angle. 75) Complement of 3° 15 76) Supplement of 68.5° 15 27 70) 19 77) Supplement of 129° 19 1 78) Complement of 41 ° 2 Classify the polygon by name. 71) Decide whether or not the network is traversable. 79) 80) 4 81) Given the floor plan, determine whether a person could traverse through each unit by passing through each door only once. 85) 82) 86) Give an appropriate answer. 83) Use the following graph to find a traversable path that begins with vertex A. 87) A) A → C → D → A → B → D B) No traversable path exists. C) B → A → D → C D) A → B → D → C 84) Use the following graph to find a traversable path that begins with vertex B. A) B → A → C → D B) B → A → D → C C) B → A → D → C → A → B D) No traversable path exists. Give the appropriate answer. 88) What is the name for the point where the three medians are concurrent? 89) Can a triangle be both obtuse and scalene? 90) Decide whether the statement is true or false. Two lines in the same plane are called skew. 5 91) Decide whether the statement is true or false. The three angles of a triangle are always supplementary. 96) Identify all pairs of alternate interior angles. 92) Decide whether the statement is true or false. In every triangle, the centroid, orthocenter, and circumcenter are collinear. Refer to the figure and provide an appropriate name for the indicated angles. 97) Identify all pairs of alternate interior angles. 93) ∠6 and ∠7 A) Right angle B) Alternate interior angles C) Supplementary angles D) Complementary angles 94) ∠3 and ∠7 A) Alternate exterior angles B) Alternate interior angles C) Supplementary angles D) Complementary angles Refer to this figure to answer the question. Line DH is parallel to line IM. Line BO is perpendicular to line DH. Identify the specified angles. 95) Identify all pairs of corresponding angles. 98) m∠IJN is 59°. What is the measure of ∠DEA? 99) m∠IJN is 54°. What is the measure of ∠DEJ? 100) Are ∠MLG and ∠FGC supplementary? 101) Choose the true statement. 6 Use the properties of parallel lines to solve the problem. 102) If p q and m∠8 = 59°, what are the measures of the other angles? 105) In the figure, GH DE . Identify any pairs of congruent angles. 103) In the figure, AB CD . Identify all pairs of congruent angles. Solve the problem. 106) Find the measure of the indicated exterior angle. ∠x = (5n - 17)°, ∠y = (n + 9)°, ∠z = (157 - 5n)° 107) Find the measure of the indicated exterior angle. 104) In the figure, BC DE . Identify any pairs of congruent angles. ∠x = (198 - 5n)°, ∠y = (6n + 8)°, ∠z = (n + 10)° 108) What is the angle sum of a regular polygon with 4 sides? 109) What is the angle sum of a regular polygon with 10 sides? 110) If each angle of a regular polygon measures 108°, how many sides does it have? 111) If each angle of a regular polygon measures 150°, how many sides does it have? Answer the question. 112) What is the measure of the central angle of a regular polygon with 16 sides? 113) How many triangles are formed in a polygon with 15 sides? 7 119) Answer the question. Figures not drawn to scale. 114) Find the measure of ∠P 60° 140° 115) Find the measure of ∠P 200° 120) 70° 121) 12 116) Find the measure of ∠P 8 8 260° 12 100° 122) 117) Find the measure of ∠P Find the missing length in the right triangle. If necessary, round to the nearest tenth. 123) 50° 5 cm Which property (if any), should be used to show that the pair of triangles is congruent? 118) 12 5 8 cm 124) 13 cm 9 cm 5 125) 7 12 18 in. 7 20 in. 8 132) The length of a rectangle is 72 meters, and the width is 21 meters. Find the measure of the diagonal of the rectangle. 72 meters 126) 10 mi 5 mi 21 meters Find d in simplest radical form. 127) Find d in simplest radical form. 133) 3 3 128) 7 2 134) 2 2 Cube 12 Solve the problem. Give the answer to the nearest thousandth if necessary. 129) A long-distance runner runs 3 miles south and then 9 miles east. How far is the runner from the starting point? 135) 7 2 South ↓ 3 mi East --9 mi--> 130) A boat travels 4 miles south and then 8 miles east. How far is the boat from its starting point? 136) South ↓ 4 mi 2 2 East --8 mi--> 131) A painter leans a ladder against one wall of a house (as shown below). The ladder is 29 ft long. The base of the ladder is 23 ft from the house. How high is the wall? 29 ft ? 23 ft 9 140) PM = 32 and LP = 46. Find the length of each diagonal. Find the measures of the indicated sides, angles, or diagonals of the given parallelogram. 137) Find the measures of the angles of the parallelogram when m∠D = 61°. Answer the question. 141) What type of figure is formed by joining the midpoints of the sides of a kite? 138) Two side lengths of a parallelogram are given. Find the lengths of the other sides of the parallelogram. 142) Choose the word ʺparallelogram,ʺ ʺrectangle,ʺ ʺsquare,ʺ or ʺrhombusʺ that could be used in the blank to make the statement true. If none of the words can be used, write ʺnone.ʺ A quadrilateral is a ___ if and only if all of its diagonals bisect its angles. 19 10 143) Choose the word ʺrectangle,ʺ ʺsquare,ʺ or ʺrhombus,ʺ that could be used in the blank to make the statement true. If none of the words can be used, write ʺnone.ʺ A parallelogram is a ___ if and only if its diagonals are congruent. 139) One side length of a parallelogram is given. The perimeter of ▱HIJK is 75. Find the lengths of the other sides of the parallelogram. 15 144) Choose the word ʺrectangle,ʺ ʺsquare,ʺ or ʺrhombus,ʺ that could be used in the blank to make the statement true. If none of the words can be used, write ʺnone.ʺ A parallelogram is a ___ if and only if it has at least one right angle and four congruent si . 1 2 145) Choose the word ʺrectangle,ʺ ʺsquare,ʺ or ʺrhombus,ʺ that could be used in the blank to make the statement true. If none of the words can be used, write ʺnone.ʺ A parallelogram is a ___ if and only if it has four congruent sides,its diagonals bisect the a . 146) Choose the word ʺrectangle,ʺ ʺsquare,ʺ or ʺrhombus,ʺ that could be used in the blank to make the statement true. If none of the words can be used, write ʺnone.ʺ A parallelogram is a ___ if and only if it has exactly one pair of parallel side. 10 147) Choose the word ʺkite,ʺ ʺtrapezoid,ʺ or ʺparallelogram,ʺ that could be used in the blank to make the statement true. If none of the words can be used, write ʺnone.ʺ A quadrilateral is a ___ if and only if one pair of opposite sides are parallel. 148) Choose the word ʺkite,ʺ ʺtrapezoid,ʺ or ʺparallelogramʺ that could be used in the blank to make the statement true. If none of the words can be used, write ʺnone.ʺ A quadrilateral is a ___ if and only if a pair of adjacent angles are congruent. 149) Does the following condition ensure that a quadrilateral is a parallelogram? One pair of opposite sides are both parallel and con . 150) Does the following condition ensure that a quadrilateral is a parallelogram? One pair of opposite sides are congruent. 11 Answer Key Testname: MTH 232 PRACTICE TEST PROBLEMS (7.1‐7.3, 10.1‐10.5) 1) 10 : 13 2) 8 : 5 3) 5 : 17 4) 6 : 5 5) 2 : 45 6) 7 : 1152 7) 1 : 11 8) 520 9) 110 10) 171.25 yd 11) $2.50 per yd 12) 11.19 cents per oz 13) Brand Y 14) Brand A 15) Matt, $1.36 16) One yard 17) 30 80 18) 3 19) 16 hours 20) 2.2 in. 21) 29 hr 22) 4 widgets 23) 56 meters 24) 90 centimeters 25) 4.0 centimeters 26) Answers will vary. The best buy is the container with the lowest cost per unit. To determine the cost per unit, divide the price of the container by the number of units in it. 27) Answers will vary. The rate 2 = 0.025 tells 80 us how many hours it took Jody to drive each mile. The units are hours per mile (hr/mi). 28) 1% 29) 12% 4 30) 19 % 9 31) 62.5% 32) 106.91% 33) 47% 34) 95.3% 35) 480% 36) 100% 3 37) 50 38) 3 33 50 39) 29 75 40) 1 225 41) 1 2500 42) 36% 43) 30.6% 44) 10% 45) 24.2% 46) 46.9% 47) 48 cars 48) $65,806 49) 26% 50) c 51) 9.91% 52) TRUE 53) FALSE 54) FALSE 55) TRUE 56) H 57) None 58) Yes 59) E 60) D 61) C 62) D 63) B 64) D 65) Not convex 66) Convex 67) Scalene; obtuse 68) Scalene; acute 69) Equilateral; acute 70) Isosceles; obtuse 71) quadrilateral 72) heptagon 73) octagon 74) decagon 75) 87° 76) 111.5° 77) 51° 1 78) 48 ° 2 79) Traversable 80) Traversable 81) Not traversable 82) Traversable 83) A 84) D 85) No 86) No 87) Yes 88) centroid 89) yes 90) False 91) False 92) True 93) D 94) B 95) ∠1 and∠5, ∠2 and∠6, ∠4 and ∠8, ∠3 and∠7 96) ∠4 and∠6, ∠3 and∠5 97) ∠2 and∠6, ∠3 and∠7 98) 121° 99) 54° 100) Yes 101) ∠FGL and ∠GLK are supplementary. 102) m∠2 = m∠4 = m ∠6 = 59°, m∠1 = m∠3 = m∠5 = m ∠7 = 121° 103) ∠ABE and ∠FCD , ∠ABC and ∠BCD 104) ∠ABC and ∠ADE, ∠ACB and ∠AED 105) ∠EDF ≅ ∠GHF, ∠DFE ≅ ∠HFG, ∠DEF ≅ ∠FGH, ∠DFG ≅ ∠EFH 106) 82° 107) 123° 108) 360° 109) 1440° 110) 5 sides 12 111) 112) 113) 114) 115) 116) 117) 118) 119) 120) 121) 122) 123) 124) 125) 126) 127) 128) 129) 130) 131) 132) 133) 134) 135) 12 sides 22.5° 13 100° 65° 80° 50° SSS SAS None SAS HA 9.4 cm 9.4 cm 26.9 in. 8.7 mi 3 2 2 3 9.487 mi 8.944 mi 17.664 ft 75 meters 14 6 3 14 2 3 136) 3 137) m∠F = 61°, m ∠G = m∠E = 119° 138) PS = 10, SR = 19 1 139) HK = 15 , HI = 2 JK = 22 140) LN = 92, MO = 64 141) rectangle 142) rhombus 143) rectangle 144) square 145) rhombus 146) none 147) trapezoid 148) none 149) Yes 150) No