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Numbers & Operations (Reporting Category A) M11.A.1.1.1 Find the square root of an integer to the nearest tenth using either a calculator or estimation. M11.A.1.1.3 Simplify square roots. (e.g., 24 = 26) 1. The square root of which of the following numbers is between 5 and 6? A. 15 B. 29 C. 40 D. 48 2. What is the best estimate for 5? A. 1.7320... B. 2.0037... C. 3.1209... D. 2.2360... 3. Simplify: 225 A. 18 B. 21 C. 15 D. 17 4. What is the best estimate for 97? A. 9.8488... B. 9.6436... C. 9.2195... D. 10.0995... 5. What is the best estimate for 111? A. 12.9862... B. 11.3884... C. 7.2111... D. 10.5356... 6. The square root of which of the following numbers is between 10 and 11? A. 90 B. 137 C. 120 D. 123 7. What is the best estimate for 15? A. 2.8284... B. 3.1622... C. 4.1231... D. 3.8729... 8. Simplify: 294 A. 49 6 B. 7 6 C. 6 49 D. 7 36 9. What is the best estimate for 2? A. 0.4142... B. 1.7320... C. 1.4142... D. 3.1415... 10. The square root of which of the following numbers is between 6 and 7? A. 47 B. 35 C. 50 D. 21 Answers 1. B 2. D 3. C 4. A 5. D 6. C 7. D 8. B 9. C 10. A M11.A.1.1.2 Express numbers and/or simplify expressions using scientific notation (including numbers less than 1). 1. How do you write the number 0.00664 x 1015 in scientific notation? A. 6.64 x 1013 B. 66.4 x 1012 C. 6.64 x 1012 D. 6.64 x 1014 2. How do you write the standard number 49,250 in scientific notation? A. 4.925 x 102 B. 49.25 x 103 C. 4.925 x 106 D. 4.925 x 104 3. Which shows the expression below simplified? (1.43 x 108) ÷ (1.3 x 103) A. 1.1 x 106 B. 1.1 x 103 C. 1.1 x 104 D. 1.1 x 105 4. How do you write the 8.711 x 10-3 in standard form? A. 8.711 B. 0.000008711 C. 0.08711 D. 0.008711 5. How do you write the 1.254 x 103 in standard form? A. 125.4 B. 12.54 C. 12,540 D. 1,254 6. How do you write the standard number 0.0006298 in scientific notation? A. 6.298 x 10-6 B. 6.298 x 10-3 C. 6.298 x 10-4 D. 62.98 x 10-5 7. Which shows the expression below simplified? (4.3 x 1017) + (2.9 x 1016) A. 7.2 x 1017 B. 4.1037 x 1019 C. 4.329 x 1017 D. 4.59 x 1017 8. How do you write the number 2,537 x 10-11 in scientific notation? A. 2.537 x 10-8 B. 2.537 x 10-7 C. 2.537 x 10-10 D. 2.537 x 10-9 9. Which shows the expression below simplified? (5.3 x 104) x (7.1 x 10-5) A. 3.763 x 10-1 B. 12.4 x 10-1 C. 3.763 x 100 D. 3.763 x 10-2 10. Which shows the expression below simplified? (8.5 x 10-4) - (3.4 x 10-7) A. 8.49966 x 10-4 B. 8.466 x 10-5 C. 8.466 x 10-4 D. 8.4966 x 10-4 Answers 1. C 2. D 3. D 4. D 5. D 6. C 7. D 8. A 9. C 10. D M11.C.3.1.1 Calculate the distance and/or midpoint between 2 points on a number line or on a coordinate plane (formula provided on the reference sheet). M11.A.1.3.1 Locate/identify irrational numbers at the approximate location on a number line. Number Lines 1. 10 11 12 13 14 15 16 What is the distance of the red line segment on the number line? A. 4 1/4 B. 2 1/2 C. 2 1/4 D. 1 1/2 2. 4 5 6 7 At what position on the number line is the red dot located? A. 60 B. 40 C. 20 D. 30 3. 1 2 3 4 What position on the number line is the red dot located? A. 2 B. 16 C. 12 D. 8 4. -1 0 1 2 What position on the number line is the red dot located? A. 1 B. 0.75 C. 0 D. 0.5 5. 3 4 5 What position on the number line is the red dot located? A. 3.6 B. 3.4 C. 3.2 D. 4 6. -6 -5 -4 -3 -2 -1 0 What is the distance of the red line segment on the number line? A. 2.5 B. 1 C. 2 D. 0.5 7. 9 10 11 What position on the number line is the red dot located? A. 9 3/5 B. 9 1/2 C. 9 2/5 D. 9 4/5 8. 0 1 2 3 What position on the number line is the red dot located? A. 6 B. 7 C. 3 D. 2 9. 9 10 11 12 What position on the number line is the red dot located? A. 10 B. 10 1/4 C. 10 3/4 D. 10 1/2 10. What position on the number line is the red dot located? A. 2 B. C. D. 5 Answers 1. B 2. D 3. D 4. D 5. A 6. C 7. C 8. C 9. B 10. C M11.A.1.2.1 Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials. GCF & LCM of Monomials 1. Look at the two monomials below. 18x4y4 10x3y What is the least common multiple (LCM) of the monomials shown above? A. 2x4y4 B. 90x4y4 C. 90x3y D. 2x3y 2. Look at the two monomials below. 18x3y2 10xy4z3 What is the least common multiple (LCM) of the monomials shown above? A. 2xy2 B. 90xy2 C. 90x3y4z3 D. 2x3y4 3. Look at the two monomials below. 2u4v2w4 22u3v2w4 What is the greatest common factor (GCF) of the monomials shown above? A. 3u2vw3 B. 2u4v2w4 C. 2u3v2w4 D. 6u2vw3 4. Look at the two monomials below. 9u2v3w 15u3v4w4 What is the least common multiple (LCM) of the monomials shown above? A. 45u2v3w B. 3u2v3w C. 3u3v4w4 D. 45u3v4w4 5. Look at the two monomials below. 39x3y 33x3y2 What is the greatest common factor (GCF) of the monomials shown above? A. 3x3y B. 33x3y C. 3x3y2 D. 33x3y2 6. Look at the two monomials below. 9xyz4 15x4y4z3 What is the least common multiple (LCM) of the monomials shown above? A. 3xyz3 B. 45xyz3 C. 3x4y4z4 D. 45x4y4z4 7. Look at the two monomials below. 78xy4z3 66xy3z3 What is the greatest common factor (GCF) of the monomials shown above? A. 6xy4z3 B. 6xy3z3 C. 66xy4z3 D. 66xy3z3 8. Look at the two monomials below. 26x4yz 10xy2 What is the greatest common factor (GCF) of the monomials shown above? A. 2x4y2 B. 2xy C. 2xyz D. 10xy 9. Look at the three monomials below. 27x2y2z 15x4y2z4 5x3y What is the least common multiple (LCM) of the monomials shown above? A. 3x4y2z4 B. 3x2y2z C. 135x4y2z4 D. 135x2y2z 10. Look at the three monomials below. 3x2y3 15x2y 3x3y2 What is the greatest common factor (GCF) of the monomials shown above? A. 5x3y3 B. 4xy C. 3x2y3 D. 3x2y Answers 1. B 2. C 3. C 4. D 5. A 6. D 7. B 8. B 9. C 10. D M11.A.1.3.2 Compare and/or order any real numbers (rational and irrational may be mixed). Compare & Order Real Numbers 10 3 1. Identify the missing symbol: /6 ? /2 A. > B. < C. = 2. Which list of numbers is in order from least to greatest? A. 9 4/8 , 10 , 9.31 B. 10 , 9.31 , 9 4/8 C. 9.31 , 10 , 9 4/8 D. 9.31 , 9 4/8 , 10 3. Which list of numbers is in order from least to greatest? A. 420.37 , 420.237 , 427.03 , 427.023 B. 420.237 , 420.37 , 427.023 , 427.03 C. 427.03 , 420.237 , 420.37 , 427.023 D. 420.237 , 420.37 , 427.03 , 427.023 4. Which list orders the percentages from least to greatest? A. 0.76%, 0.97%, 1.21%, 1.35%, 1.48% B. 0.76%, 0.97%, 1.35%, 1.21%, 1.48% C. 0.76%, 0.97%, 1.35%, 1.48%, 1.21% D. 0.76%, 1.21%, 1.35%, 0.97%, 1.48% 5. Which list of numbers is in order from least to greatest? A. 2,1,2, 16 B. 1 , 2 , 2, 16 C. 1 , 2,2, 16 D. 16 , 2 , 2,1 6. Which list of numbers is in order from least to greatest? A. -7,000 , -7,008 , -7,080 , -7,800 B. -7,800 , -7,080 , -7,000 , -7,008 C. -7,800 , -7,008 , -7,080 , -7,000 D. -7,800 , -7,080 , -7,008 , -7,000 1 7. Identify the missing symbols: /4 ? 1/6 ? 1/7 A. < and > B. > and < C. > and > D. < and < 2 8. Identify the missing symbol: /3 ? 4/6 A. = B. < C. > 9. Which list of numbers is in order from least to greatest? A. (9/12) , (13/16) , (7/8) B. (13/16) , (7/8) , (9/12) C. (7/8) , (13/16) , (9/12) D. (9/12) , (7/8) , (13/16) 10. Which list of numbers is in order from least to greatest? A. -846.08 , -840.86 , -846.078 , -840.786 B. -846.08 , -846.078 , -840.786 , -840.86 C. -840.86 , -840.786 , -846.08 , -846.078 D. -846.08 , -846.078 , -840.86 , -840.786 Answers 1. A 2. D 3. B 4. A 5. C 6. D 7. C 8. A 9. A 10. D M11.A.2.1.1 Solve problems using operations with rational numbers including rates and percents (single and multi-step and multiple procedure operations) (e.g., distance, work and mixture problems, etc.). Rates, Work & Percent Problems 1. Ace Window Service has a contract to wash windows at the school. There are 96 windows on the first floor and 32 on the second floor. Ace brings along two helpers. He can wash 17 windows per hour. His first helper can wash 14 windows in three hours. The second worker can wash 16 windows in two hours. How long will it take to wash all the windows? A. 4.31 hours B. 4.71 hours C. 5.12 hours D. 5.05 hours 2. Sara is mixing together a fruit punch for a party. She’s made 4 gallons of punch with a mixture of 50% juice. But her mother tells her to change it to a mixture of 65% juice. How much fruit juice should be added to make the mixture 65% fruit juice (round to the nearest hundredth)? A. 0.67 gallons B. 1 gallons C. 1.71 gallons D. 0.5 gallons 3. Mark went rock climbing on Saturday on Mt. Rockytop. He started at 10:00 a.m. and climbed at the rate of 2 miles per hour. His friend Paul began climbing at noon, climbing at a rate of 3 miles per hour. At what time would Paul catch up to Mark? A. 8:00 p.m. B. 4:00 p.m. C. 3:00 p.m. D. 6:00 p.m. 4. Ed, Jason and Michael volunteered to wash cars for the annual class car wash. They’ve been asked to wash 100 cars. Ed can wash 2 cars per hour. Jason can wash 5 in two hours. And Michael can wash 5 in two hours. How long will it take to wash 100 cars? A. 14 2/7 hours B. 12 1/2 hours C. 13 1/3 hours 13 D. 11 /17 hours 5. Mrs. Carter owns a shop specializing in obscure blends of tea. She has combined 1 pound of Darjeeling with 4 pounds of Earl Grey, for a 5-pound mixture that is 20% Darjeeling. After tasting it, she decided to change the mixture to 40% Darjeeling. How much Darjeeling does she need to add to bring it up to the 40%? A. 2 lb. B. 5 lb. C. 1 2/3 lb. D. 5/7 lb. 6. Two runners left the school and ran in opposite directions on the main street. If one runner averaged 4 mph and the other averaged 7 mph, how long was it before they were 23.1 miles apart? A. 2.8 hours B. 7.7 hours C. 2.1 hours D. 2.6 hours 7. Hal is mixing bug spray for his roses. He has one gallon with a mixture of 90% water and 10% chemical. However he needs a mixture that is 97% water. How much water should be added to the mixture to make it 97% water? A. 3 gallons B. 1.86 gallons C. 9 gallons D. 2.33 gallons 8. Pat and Joe have volunteered to help the kindergarten teacher get her class ready before school starts. One of the tasks they have to do is sorting out all the crayons into color groups. Pat can sort 500 crayons in an hour. Joe can sort 750 crayons in three hours. At that rate how long will it take them to sort 8000 crayons? A. 7.27 hours B. 6.67 hours C. 10.67 hours D. 7.62 hours 9. Tom and Jerry have to sort and organize all the nails on their father’s workbench. Tom can sort 200 nails in 2 hours. Jerry can sort 180 nails in 3 hours. How long will it take them to sort 700 nails if they work together (round to the nearest hundredth)? A. 3 hr B. 4.38 hr C. 3.33 hr D. 2.42 hr 10. Brett is on the school's track team. He runs at a speed of 6 miles per hour on the track after school. His friend Tom is also on the team, and runs at 8 miles per hour. When Tom arrives one day, Brett has already been running for 30 minutes. How long will it take for Tom to catch up with Brett? A. 1 1/2 hours B. 2 1/2 hours C. 1 hours D. 3/8 hours Answers 1. A 2. C 3. B 4. A 5. C 6. C 7. D 8. C 9. B 10. A M11.A.2.1.2 Solve problems using direct and inverse proportions. M11.A.2.1.3 Identify and/or use proportional relationships in problem solving settings. Proportional Relationships 1. For an object falling freely from rest (disregarding air resistance), the distance the object falls varies directly as the square of the time. If an object is dropped from a 784 foot cliff and hits the ground in 7 seconds, how far did it fall in the first 4 seconds? A. 240 feet B. 289 feet C. 448 feet D. 256 feet 2. Boyle's Law states that the pressure P of a sample of a gas at a constant temperature varies inversely with the volume V. The pressure of a gas in a balloon with a volume of 6 in3 is 9 psi. If the volume of the balloon is increased to 15 in 3, then what is the new pressure of the gas? A. 4.5 psi B. 22.5 psi C. 3.6 psi D. 2.7 psi 3. As an architect, Duane was hired by So-Low Discount Tire to design a new shop. He is making a model of the new design on a 12-inch square piece of wood. The dimensions of the new shop measure 48 feet long by 36 feet wide. Which scale should Duane use to make the largest model possible that will still fit on his wood base? A. 1 inch = 3 feet B. 1 inch = 6 feet C. 1 inch = 4 feet D. 1 inch = 5 feet 4. A building is 392 feet tall. For a class project, Kari is to make a scale model of the building to place in the front hall display case. The display case is 22 inches tall. Which scale will allow her to make the tallest model that will fit in the display case? A. 1 inch = 25 feet B. 1 inch = 20 feet C. 1 inch = 10 feet D. 1 inch = 30 feet 5. The weight W that can be safely supported by a 2 by 4 piece of lumber varies inversely with its length l. The maximum weight a 8 foot cedar 2 by 4 can support is 900 pounds. What is the maximum weight that can be safely supported by a length of 20 feet? A. 330 pounds B. 315 pounds C. 360 pounds D. 2,250 pounds 6. In a layout of Joe's backyard, the ratio is 1 centimeter = 10 meters. The length of the deck on the layout is 5 cm and the width is 4 cm. What is the perimeter of Joe’s deck? A. 18 meters B. 90 meters C. 20 meters D. 180 meters 7. The weight of an object on earth is directly proportional to the weight of that same object on the moon. A 210-pound man would weight 33.6 pounds on the moon. How much would a 120-pound woman weigh on the moon? A. 19.2 pounds B. 22.4 pounds C. 16 pounds D. 17.6 pounds 8. The dimensions of Cube B are twice the dimensions of cube A. The surface area of cube B is 256. What is the surface area of cube A? A. 1,024 B. 128 C. 32 D. 64 9. Ryan is building a storage shed in his back yard for his lawnmower. The scale drawing of the shed is drawn so that 1 cm = 1 ft. If the drawing shows the area of shed to be 51 square cm, what is the actual area of the shed? A. 51 square feet B. 51 feet C. 102 feet D. 102 square feet 10. Chris looked at a map of an amusement park that used a scale of 1 inch = 1 meter. On the map the roller coaster was 6 inches from the ice cream stand. When Chris gets off the roller coaster, how far will she have to walk to get to the ice cream stand? A. 6 meters B. 4 meters C. 6 inches D. 7 inches Answers 1. D 2. C 3. C 4. B 5. C 6. D 7. A 8. D 9. A 10. A M11.A.2.2.1 Simplify/evaluate expressions involving positive and negative exponents, roots and/or absolute value (may contain all types of real numbers - exponents should not exceed power of 10). M11.A.2.2.2 Simplify/evaluate expressions involving multiplying with exponents (e.g. x 6 * x7 = x13), powers of powers (e.g., (x6)7=x42) and powers of products (2x2)3=8x6 (positive exponents only). Simplify & Evaluate Expressions 1. Evaluate the following expression when r = 4 and t = 2. 5r t + 46 A. 91 B. 126 C. 66 D. 158 2. Evaluate the following expression when n = 2. |2n - 8| + |-3| A. 7 B. 1 C. -7 D. -1 3. Evaluate the following expression when r = 4 and t = 3. (3 + r)t - 23 A. 193 B. 320 C. 332 D. 169 4. Evaluate the following expression when r = 4 and t = 2. 7r t + 84 A. 112 B. 228 C. 147 D. 196 5. Evaluate the following expression when n = 3. |n - 7| - |2 - n| A. 5 B. -5 C. 3 D. -3 6. Evaluate the following expression when n = 3. |3n - 7| + |-2| A. 0 B. 11 C. 2 D. 4 7. Evaluate the following expression when n = 8. 6|2 - n| - |-9| A. -27 B. 27 C. -45 D. 45 8. Evaluate the following expression when n = -2. 3|n + 4| A. 5 B. -6 C. 18 D. 6 9. Simplify: (2mn2)3 × (2mn)4 A. 212m8n9 B. 27m7n14 C. 212m12n24 D. 27m7n10 10. Evaluate the following expression when n = -3. -5|n + 7| A. -20 B. -1 C. -50 D. 20 Answers 1. B 2. A 3. B 4. D 5. C 6. D 7. B 8. D 9. D 10. A M11.A.3.1.1 Simplify/evaluate expressions using the order of operations to solve problems (any rational numbers may be used). Order of Operations 1. 6×2-5 2 9+4×2 -13 A. /17 -1 B. /2 -19 C. /17 37 D. /17 2. If N = 8 - 1 × 5 + 22, then the value of N is A. -1 B. 39 C. 6 D. 7 3. (6 + 5) - 4 ÷ 4 A. 10 B. 9 C. 4 D. 13 E. 7 4. 17 - (10 - 2 × 52) A. 57 B. 77 C. -23 D. 107 5. (-12 + 4) × (-4) 19 - 3 A. 2 B. 4 C. -2 D. -8 6. 1/2 × 8 + (12 ÷ 4 × 7) A. 20 B. 25 C. 32 D. 14.5 7. 85 - 5 × (9 - 7)3 A. 45 B. -12 C. 22 D. -6 8. 8 × 22 + 9 - (3 + 11) A. 80 B. 49 C. 27 D. 251 9. 16 ÷ 4 + 32 × 2 - 6 A. 20 B. 14 C. 104 D. 16 10. 3 × 22 + 5 ÷ 5 - (6 + 7) A. 14 B. 0 C. 2 D. 24 Answers 1. A 2. D 3. B 4. A 5. A 6. B 7. A 8. C 9. D 10. B M11.A.3.2.1 Use estimation to solve problems. Estimate Solutions 1. A lumber company is able to clear about 4 acres of dense forest each day. Assuming that, on average, each acre of forest contains 971.4 large sized trees, what is a good estimate of the number of large trees that the company could clear in 3 days? A. 13,500 trees B. 10,800 trees C. 13,200 trees D. 12,000 trees 2. Jim likes to go fishing on Lake Chippewa every Saturday. He usually catches between 8 and 12 fish. If only half of those fish are big enough to keep, then about how many fish does Jim take home in 9 weeks? A. 90 fish B. 57 fish C. 37 fish D. 45 fish 3. Samson's Fishing Depot has $62,850.71 in net income each month to give out to 9 employees. Five employees are classified as Level 1, and 4 employees are Level 2. Each Level 1 employee earns 5% of the net income each month, whereas each Level 2 employee earns 6% of the net income. Which is the best estimate of how much more a Level 2 employee earns each month than a Level 1 employee? A. $2,130.00 B. $1,380.00 C. $630.00 D. ($170.00) 4. Everyday Sammy goes to lunch and buys one sandwich for $1.36 and a soft drink for $0.67. Which is a reasonable amount that Sammy would spend on 60 sandwiches and 45 soft drinks? A. $255 B. $105 C. $205 D. $55 5. It costs a lumberyard $3.17 per cubic foot of lumber. If they sell the lumber back to their customers for $5.83 per cubic foot and sell an average of 150 cubic feet of lumber per month, what is the approximate profit made by the lumberyard per year? A. $1,800.00 B. $3,600.00 C. $450.00 D. $5,400.00 6. Marcus has a part-time job at the water park. He makes between $70.97 and $76.18 a day. Which is a reasonable amount of money that Marcus makes for working 5 days a week for 11 weeks? A. $4,021 B. $4,248 C. $4,243 D. $3,843 7. Lily bought 25.15 pounds of grapefruit. The lightest grapefruit weighed 1.2 pounds. The heaviest grapefruit weighed 1.8 pounds. Which is the best estimate of how many grapefruits she purchased? A. 10 grapefruits B. 19 grapefruits C. 50 grapefruits D. 17 grapefruits 8. At the start of the month, Suzanne's clothing store website had 8,305 hits. At the end of the month, it had 90,166 hits. If each hit lasted 1 1/2 minutes, then what was the approximate total number of minutes on the website for this month? A. 126,000 B. 1,500 C. 96,000 D. 123,000 9. A computer company has a special going in which all customers receive a free monitor and scanner with the purchase of a new computer. It costs the company $397.46 to make each computer, $259.98 to make each monitor, and $43.72 to make each scanner. The computers are then sold for $1,156.85 each. Approximately how much profit will the company make if 417 customers take advantage of their special? A. $960,000.00 B. $100,000.00 C. $260,000.00 D. $200,000.00 10. A cake recipe calls for between 5 1/4 and 5 3/4 cups of flour for 4 servings. If 55 cups of flour are used, which of the following is a reasonable number of servings that can be made? A. 40 B. 25 C. 50 D. 30 Answers 1. D 2. D 3. C 4. B 5. D 6. A 7. D 8. D 9. D 10. A

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