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Objective 1: Numbers, Operations, and Quantitative Reasoning 8.1A: Compare and order rational numbers in various forms, including integers, percents, and positive and negative fractions and decimals. 2003 #42: A librarian arranged some books on the shelf using the Dewey decimal system. Choose the group of book numbers that is listed in order from least to greatest. F G H J* 549.010, 549.101, 549.02, 549.3 392.4, 397.46, 399.53, 399.062 101.2, 101.04, 104.21, 110.0 834, 834.19, 834.2, 834.29 2004 #25: Which fraction is between A 1 2 B 3 5 C* 5 7 D 7 8 2 3 and ? 3 4 2006 #31 2 1 7 Several stores are having sales. The prices are reduced by 62.5%, , 75%, , and . 3 2 10 Which list shows the price reductions from greatest to least? A B* C D 1 2 7 75%, 62.5%, , , 2 3 10 7 2 1 75%, , , 62.5%, 10 3 2 7 1 2 75%, , 62.5%, , 10 2 3 7 2 1 75%, , 62.5%, , 10 3 2 1 Objective 1: Numbers, Operations, and Quantitative Reasoning 8.1B: Select and use appropriate forms of rational numbers to solve real-life problems, including those involving proportional relationships. 2003 #2: A bag of mixed Yummy Gummies contains 26% green, 34% red, 24% blue, and 16% yellow gummies. Carla put 250 mixed gummies in a bowl. Which proportion can be used to find y, the total number of yellow gummies in the bowl? F 16 250 = 100 y G* 16 y = 100 250 H 100 y = 16 250 J 16 150 = 100 y 2003 #45: An electronic device counted 3,962 vehicles passing through an intersection during a 7-hour period. If the number of vehicles passing through this intersection per hour remains the same, which proportion can be used to find x, the number of vehicles that would be counted by the device during a 9-hour period? A x 7 = 3,962 9 B* 3,962 x = 9 7 C 7 9 = x 3,962 D 16 7 = 3,962 x 2 Objective 1: Numbers, Operations, and Quantitative Reasoning 2004 #40: Carlos, Jackie, Lester, and Margie ate lunch at a restaurant. The total amount of the bill, 1 including tax and tip, was $44.60. Carlos paid $15.00, Jackie paid of the bill, Lester 4 paid 20% of the bill, and Margie paid the rest of the bill. Who paid the greatest part of the bill? F* G H J Carlos Jackie Lester Margie 2006 #27 The Texas state flag is rectangular and has a width-to-length ratio of 2:3. Which of the following can be used to find l, the length of a Texas state flag with a width of 28 inches? A B* C D 2 + 28 = 3 + l 2 l = 28 3 2 28 = 3 l 2 · 28 = 3 · l 3 Objective 1: Numbers, Operations, and Quantitative Reasoning 8.1C: Approximate mentally [and with calculators] the value of irrational numbers as they arise from problem situations. ( , 2 ) 2003 #30: The area of a square is 125 square meters. Which best represents the length of a side of the square? F G* H J 10.8 m 11.2 m 11.9 m 12 m 2004 #42: Mr. Harrington wrote four irrational numbers on the board and asked Jared to choose the number closest to 3. Which irrational number should Jared choose? F 6 G* 10 H 12 J 14 2006 #18 The area of a square is 83 square meters. Which of these is closest to the length of each side of the square? F* G H J 9.1 m 9m 8.9 m 8m 4 Objective 1: Numbers, Operations, and Quantitative Reasoning 8.1D: Express numbers in scientific notation, including negative exponents, in appropriate problem situations. 2003 #46: A certain bacterium measures approximately 0.000015 millimeter in length. How is this length expressed in scientific notation? F* G H J 1.5 × 10-5mm 1.5 × 10-4 mm 0.15 × 105 mm 15 × 104 mm 2004 #3: The diameter of a blood cell is measured in micrometers. A micrometer is 0.000001 meter. Which expression represents this number in scientific notation? A B C* D 1.0 × 107 1.0 × 106 1.0 × 10-6 1.0 × 10-7 2004 #43: The sun’s core temperature reaches close to 2.7 × 107 degrees Fahrenheit. Which of the following represents this temperature in standard notation? A B C* D 270,000°F 2,700,000°F 27,000,000°F 270,000,000°F 2006 #13 Mr. Loya stated that the circumference of Earth at the equator is 24,902.4 miles. Which expression represents this number in scientific notation? A* B C D 2.49024 × 10 4 24.9024 × 10 4 249.024 × 10 4 2.49024 × 10 5 5 Objective 1: Numbers, Operations, and Quantitative Reasoning 8.2A: Select and use appropriate operations to solve problems and justify the selections. 2003 #9: Jasmine has an average of 95 on 15 quiz grades. If her teacher drops Jasmine’s lowest grade, a 72, which equation can be used to find n, Jasmine’s new quiz average? A n= 95 72 14 B* n= (95 15) 72 14 C n= (95 15) 72 15 D n= 95(72 15) 14 2004 #6: The Webster Junior High faculty includes 37 teachers. The principal’s and teachers’ annual salaries total $1,266,140. If the principal’s salary is $54,250, which equation can be used to find s, the average salary for a teacher at Webster Junior High? (1,266,140 54,250) 37 F s= G s = 1,266,140 + 54,250 37 H s = 1,266,140 − 54,250 37 J* s= (1,266,140 54,250) 37 6 Objective 1: Numbers, Operations, and Quantitative Reasoning 2006 #16 A water tank contains 2,500 gallons. A faucet ttached to the tank releases water at a constant rate of 5 gallons per minute. If the faucet is left open for 1 hour and no other water is released, which equation can be used to find r, the number of gallons of water remaining in the tank? F G H* J r = 2,500 ÷ 5 r = 2,500 − 60 r = 2,500 − 60(5) r = 2,500 ÷ 60(5) 2006 #47 1 1 yards of fabric and 6 yards of trim. 2 4 If the fabric costs $2.79 per yard and the trim costs $1.19 per yard, which equation can be used to find c, the total cost of covering the bulletin board? To cover his bulletin board, Mr. Adams needs 1 A B* C D c = (2.79 + 1.5) + (1.19 + 6.25) c = (2.79 · 1.5) + (1.19 · 6.25) c = (2.79 + 1.5) − (1.19 + 6.25) c = (2.79 · 1.5) − (1.19 · 6.25) 7 Objective 1: Numbers, Operations, and Quantitative Reasoning 8.2B: Add, subtract, multiply, and divide rational numbers in problem situations. 2003 #21: Three roommates agreed to split the cost of food and rent evenly. Last month they spent a total of $349.66 for food and $365 for rent. Find the amount that each of the 3 roommates paid. Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value. 2004 #35: On Friday the low temperature in Nome, Alaska, was −12°F, and the high temperature was 23°F. How much warmer was the high temperature than the low temperature? A B C D* −35°F −11°F 11°F 35°F 2004 #47: 2 1 ounces of chocolate candy, 4 ounces of hard candy, and 4 3 2 ounces of dried fruit. What is the total weight of the contents of the gift basket? A gift basket contains 6 A 11 1 oz 6 B 14 1 oz 2 C 14 3 oz 5 D* 15 1 oz 6 8 Objective 1: Numbers, Operations, and Quantitative Reasoning 2006 #11 1 1 1 cups of milk, 2 cups of flour, and 1 cups of other 2 4 3 ingredients. How many cups of milk, flour, and other ingredients are needed to make 36 waffles? A recipe for 12 waffles calls for 1 A B* C D 1 cups 3 1 15 cups 4 1 12 cups 4 1 51 cups 12 20 9 Objective 1: Numbers, Operations, and Quantitative Reasoning 8.2C: Evaluate a solution for reasonableness. 2003 #11: Ms. Gonzalez’s monthly electricity bills for March through June were $97.09, $103.96, $114.73, and $121.82. She estimated that the electricity cost a total of $400.00 over these 4 months. Which best describes her estimate? A* B C D Less than the actual amount because she rounded to the nearest $100 Less than the actual amount because she rounded to the nearest $10 More than the actual amount because she rounded to the nearest $100 More than the actual amount because she rounded to the nearest $10 2003 #26: Rae’s recipe for lemon-lime punch calls for the following ingredients: 1 quart of apple juice 2 3 cups of lemon-lime soda 4 64 ounces of pineapple juice 2 quarts of cold water 1 cup of lemon juice 4 What is the smallest container that will hold all the ingredients? F G H* J A 4-quart container A 5-quart container A 6-quart container A 7-quart container 2004 #16: Cody’s parents bought a big-screen television for $1,099.99 and a DVD player for $99.99, including tax. Cody’s parents plan to pay the total amount in 18 equal monthly payments. What is a reasonable amount for each monthly payment? F G H J* $50.00 $150.00 $113.00 $67.00 10 Objective 1: Numbers, Operations, and Quantitative Reasoning 2006 #20 Sean is planning a trip of 1,450 miles. He plans to drive between 250 and 300 miles each day. At this rate, which is a reasonable number of days it will take Sean to complete his trip? F G* H J Less than 4 days Between 4 and 6 days Between 6 and 8 days More than 8 days 2006 #43 Anthony helps his father with his lawn-mowing service. His father charges from $25.00 to $50.00 per lawn depending on the size of the lawn to be mowed. Last Saturday, 1 Anthony and his father spent 6 hours mowing 3 lawns. If Anthony’s father actually 2 charged $25.00 for the smallest lawn and $50.00 for the largest lawn, about how much could Anthony’s father have charged for all 3 lawns? A B C* D $75 $95 $110 $150 11 Objective 1: Numbers, Operations, and Quantitative Reasoning 8.2D: Use multiplication by a constant factor (unit rate) to represent proportional relationships for example, the arm span of a gibbon is about 1.4 times its height, a = 1.4h. 2004 #37: The Childress family went on a camping trip. They paid $28.00 for a 2-night stay at a campground that allows a maximum stay of 30 nights. Which equation can they use to find c, the cost of camping at this campground for the maximum number of nights? A B C D* c = 60 · 56 c = 30 · 28 c = 28 · 28 c = 30 · 14 2006 #40 Which equation can be used to find m, the number of minutes in h hours? F G H J* m = 60 − h m = h + 60 m = h ÷ 60 m = 60h 12