Math Level 7 (Pre Alg2) Issue 1. Super Mathter

Transcription

1 Super Mathter December 30, 2005 : Fax: For class info, visit Direct your questions and comments to programs@mathenglish.com Sample Only EQUATIONS IN 3 TERMS...2 PROBLEM SOLVING...4 OPERATION OF NUMBERS...9 MATH OLYMPIA...11 ASSESSMENT TEST

2 Equations in 3 Terms 7. -4t = 20 Solve the following equations x - 10 = y = t = x - 8 = t = z = x + 4 = x - 7 = z = = 7-2y 6. 5x + 8 = -12 2

3 13. -9x - 9 = -36 Math Level 7 (Pre Alg2) Issue x - 3 = = 9 + 4y s = x - 6 = x - 7 = b = x = -3 3

4 Problem Solving Given A board 20 feet long is to be cut into two (a) Find the GCF and LCM for 72 and 96. pieces so that one piece is 8 feet longer than the other. How long should the (b) Find the sum in the lowestest terms. shorter piece be? 22. A school has 8 classes of 32 pupils and 7 classes of 33 pupils. The school has room for 520 pupils. How many additional pupils can the school admit? 26. A highway noise barrier that is 120 m long is constructed in two pieces. One piece is 45 m longer than the other. Find the length of each piece. 23. An airplane flying at an altitude of 25,000 ft dropped 4000 ft in 25 sec and rose 2500 ft in the next 15 sec. What was the altitude of the airplane after the 40 sec? 27. A gas tank can hold 15 gallons. If the tank is I full, how many gallons of gas are in the tank now? 24. Joe has 5 times as many joke books as Deloris. Deloris has H as many joke books as Glen. If Glen has 32 joke books, how many does Joe have? 28. A student s college education costs $8,500 per year. His father agrees to pay 1 of it. He saves $1,200 while working during the summer. How much does the student still need? 4

5 29. At the Megalopolis Zoo they make a special feed to provide to their exotic birds. It is 2 super meal, I commercial birdseed, and 7 cracked corn. The rest is made up of Nutro Feedofill. How much commercial birdseed is required to make 152 kilograms of the special feed? 33. If B of a number is 24, what is 2 of this number? 34. If 16 I A = 15 32, then A = Question set [30-32] Find the ratio as a fraction in the lowest terms. 30. The number of weekdays to the number of weekend days (Saturdays and Sundays) in the month of February (not in a leap year) 35. If 3 pints of yogurt cost $1, how much will 1 gallon cost? 31. The number of weekdays in the month of February (in a non-leap year) to the number of days in February 36. If 5 apples cost $1.15, how much will 16 apples cost? 37. If 5 oranges sell for 95, what is the cost of 12 oranges? 32. The number of days to the number of Sundays in the month of February (in a non-leap year) 5

6 38. If rain is falling at a rate of 2 inches per hour, how many inches will fall in 12 minutes? 42. Janice wants to buy some brocade ribbon to make bookmarks. She wants to make one bookmark 7I inches long and the other 9H inches long. How many inches of the brocade ribbon should Janice buy? 39. In 1960, only about $12 billion was spent on advertising. About 7 of that was spent on television. How much was spent on television? 43. Linda bought 4 tires for her car at a total cost of $264. How much would 5 tires cost at the same price? 40. In 1997, total advertising expenditures were about $54 billion for Cyber Venture Co. The expenditures of advertising through direct mail were about $6 billion. What fraction of the total expenditures were sent through direct mail? 44. Ms. Cheung had $1,200. She bought a desk for $160, and spent half of what she had left for a used car. How much did she have left? 41. In a creek bed, 5 of the gravel is less than 5 cm in diameter and 2 of it is between 5 and 10 cm in diameter. What fraction of the gravel is greater than 10 cm in diameter? 45. Pete s test results are listed below. Test 1: got 10 correct out of 12 problems. Test 2: got 12 correct out of 14 problems. On which test did he do better? 6

7 46. Sandy lives 1.5 miles from school. Her friend lives 2.7 miles from school in the opposite direction. If Sandy rode her bike to school, visited her friend, and then returned home, how many miles would she ride? 50. If the perimeter is 64 cm, find the width and the length. 47. Some sea turtles can swim 100 times faster than tortoises can walk. A sea turtle can swim at a rate of 25 mph, how fast can some tortoises walk? 51. Building A is 47 yards high and building B is 139 ft. Which one is taller? (Hint: 1 yard = 3 feet) 48. The Kidmans pay $160 per quarter for auto insurance. How much is their insurance for 3 years? 52. Jessica leaves her house at 10:00 A.M. she walks steadily at a speed of 3 miles per hour toward her grandma s house, 12 miles away. What time will she arrive? Question set [49-50] The ratio of the length of a rectangle to its width is 5: If the width is 24 cm, find its length. Percentages refer to fractions of a whole; that is, whatever you re looking at, the percentage is how much of the whole thing you have. For instance, 50% means 1 ; 25% means 3 ; 40% means 52 ; etc. Often you will need to figure out what percentage of something another thing is. For instance, if a class has 26 students, and 14 are female, what percentage of the students are 14 female? It is 14 out of 26, or 26 = , or about 54%. (For more information on percent word problems, look at the Percent of lesson.) Percent is actually per cent, meaning out 7

8 of a hundred. (I think it s Latin.) You can use this fact, along with the fact that fractions mean division, to convert between fractions, percents, and decimals. 53. A baseball park has 40,000 seats of which 26,000 are box seats and the rest are reserved seats. What percent of the seats are reserved? 57. A real estate agent collected $5,000 in rents. She gave the owner $4,000 and retained the balance as commission. What was her rate of commission? (Hint: The commission rate is the ratio of the commission and the original price.) 54. A baseball team won 34 games out of its first 85. What percent of the games did the team win? 58. A service contract offered by a washing machine manufacturer can be purchased for 15% of the price of a washing machine. If a certain washer costs $660, what is the price of the service contract? 55. A basketball player made 45 out of 75 free-throw shots. What percent of the free throws did she make? 59. A town has a population of 153,000. There are 50,490 telephones in the town. What is the number of telephones per 100 people? 56. A programmable robot manufactured by Lego was sold at $200 last year. It is sold at $240 this year. What is the percent increase of the price over the last year? 8

9 Operation of Numbers = = = %( ) = 62. 1( ) + 2( ) = 68. 1B 3H = 63. (0.2) 2 + (0.3) 2 = = = = = 2 (True or False) 71. (-3) 2 = 9

10 72. 2 ( 3 2 ) = Math Level 7 (Pre Alg2) Issue = = 10

11 Math Olympia Math Level 7 (Pre Alg2) Issue A container half full with water weighs 12 pounds. One-third of the water in the container is poured out. The container and the remaining water weighs 91 pounds. What is the weight of the container when empty? 79. In a 3-hour examination of 320 questions, there are 40 questions on science. Twice as much time is given to each science question as to the other questions. How much time is allotted to the 40 science questions? (A) 40 min (B) 60 min (C) 80 min (D) 120 min 76. How many whole numbers between 200 and 699 have no digits repeated within the number? 77. The first number is four more than two times the second number. The sum of the two numbers is ninety seven. Find the numbers. 78. A man purchases some 2-cent and some 15-cent stamps at the same time. He pays $1.56 for all the stamps. There are 10 more 2-cent stamps than 15-cent stamps. How many of each kind did he buy? 11

12 Assessment Test Math Level 7 (Pre Alg2) Issue The distance from Asheville to Wilmington is 327 miles. In traveling from Asheville to Wilmington and back to Asheville, what would be the total distance expressed in scientific notation? (A) mi (B) mi (C) mi (D) mi 84. Which of the following is true? (A) 3 > 1 (B) -4 < -5 (C) -51 > 31 (D) -1 < Which number sentence below models the problem shown on the number line? 81. The length of the orbit for Jupiter is km. What is this distance written in standard form? (A) 112,000 km (B) 1,120,000 km (C) 11,200,000 km (D) 112,000,000 km 82. Earth is about 93,000,000 miles from the sun. What is this distance expressed in scientific notation? (A) mi (B) mi (C) mi (D) mi 83. The circumference of the Earth is about kilometers. What is the circumference of the Earth in meters? (A) 400,000,000 m (B) 40,000,000 m (C) 4,000,000 m (D) 40,000 m (A) (B) (C) (D) The current temperature of 10 degrees below zero (Fahrenheit) is 24 degrees below the high temperature for the day. What was the high temperature for the day? (A) 34 F (B) 24 F (C) 14 F (D) -14 F 87. In Siberia, a record high temperature of 98 F has been reported. The record low temperature is 192 degrees lower than the record high temperature. What was the coldest Siberian temperature? (A) -290 F (B) -94 F (C) 94 F (D) 106 F 12

13 88. The thermometers below show the Celsius temperatures of four different solutions. What is the range of the temperatures of the solutions? Math Level 7 (Pre Alg2) Issue A truck has traveled 75 miles in 1.5 hours. Which proportion can be used to determine how long, T (in hours), it would take the truck to travel 325 miles, assuming it is moving at the same speed? (A) 325 = T (B) 1. 5 = T (C) 75 = T (D) 325 = T 91. Mr. Williams mixes white and brown paint in the ratio of 8:2. If he uses 15 quarts of white paint, how many quarts of brown paint will he need? (A) 3.25 (B) 3.5 (C) 3.75 (D) 4 (A) -5 C (B) 5 C (C) 20 C (D) 35 C 89. A city s daily low temperatures in January fluctuated between -7 F and 2 F. What was the temperature range? (A) 2 F (B) 5 F (C) 7 F (D) 9 F 92. Mrs. Patterson purchased 5 trays of flowers to plant in the school s flowerbeds. The total cost was $ Each tray contained 2 dozen individual plants. After planting all of the flowers, Mrs. Patterson decided she needed an additional 18 plants. If the plants are priced individually, about how much should she expect to pay for the additional flowers? (A) $7 (B) $8 (C) $9 (D) $10 13

14 93. A cereal box contains 499 grams of cereal. If one serving is equal to 27 grams, which proportion could be used to find the number of servings per box? x 1 (A) 499 = 27 x 27 (B) 499 = (C) 27 = x (D) x = According to these two circle graphs, which statement is correct? 94. Betty s mother bought a house for $79,500. She had enough money for a 15% down payment. How much of the $79,500 did she have to borrow from the bank to pay for the house? (A) $67,575 (B) $69,575 (C) $78,000 (D) $91, A department store is having a 50%-off sale on tennis shoes. If the original price of a pair of shoes was $78, what is the sale price of the shoes? (A) $28 (B) $39 (C) $50 (D) $78 (A) The same number of boys and girls play the flute. (B) The flute is played by more girls than boys. (C) The number of boys playing either the tuba or the clarinet is the same as the number of girls playing the tuba or the clarinet. (D) Fifty girls play the flute. 97. The photo lab for the Cary News reduces each side of a photograph by 20%. The original size of the photo is 8 inches 10 inches. What are the dimensions of the reduced photo? (A) 6 inches 8 inches (B) 6.4 inches 8 inches (C) 7.4 inches 8 inches (D) 7.8 inches 9.8 inches 14

15 98. Christopher s square sandbox has 36 square feet of playing space. It was constructed using 4 boards. One of the sandbox s boards needs to be replaced. What length board should Christopher s father cut to repair the side of the sandbox? (A) 3 feet (B) 6 feet (C) 9 feet (D) 12 feet 99. A 6-ounce box of strawberry gelatin costs $.90 and a 3-ounce box costs $.42. What is the difference in cost per ounce between the larger and the smaller boxes? (A) $0.04 (B) $0.03 (C) $0.01 (D) no difference 15

16 Answer Key Equations in 3 Terms 1. x = 2 2. t = 3 3. t = 3 4. x = z = 4 6. x = t = y = x = z = x = y = x = y = x = x = b = x = x = s = -3 Problem Solving = = 6 ft = = 33 pupils = ft 24. D = 32 H = 24 J = 5 24 = = = 24 4 GCF(72, 96) = 24 LCM(72, 96) = = = 288 = = = = 82.5 m = 37.5 m I = 5N gal 28. 1(8500) = = $3, I = 19 3 = 57 kg = gallon = 4 quarts 1 quart = 2 pints 1 gallon = 8 pints It costs 38 = $2B = = $ minutes = 4 hour = 5 in 16

17 = 1.5 (billion) / = 0.33 = 33% 40. 6/54 = = I + 9H = 177 in = 5 66 = $ ( ) = $ He did better on Test = < 14 = ( ) = 8.4 mi = 3 mph 48. (160 4) 3 = $ cm The length must be longer, so it is = 40 cm. 50. L=20 cm, W=12 cm 64 2 = (5 + 3) = = 20 (length) 4 3 = 12 (width) 51. Building A is taller 1 yard = 3 ft Building A: 47 yards = 141 ft Building B: 139 ft = 4 (hr) 10: hrs = 2:00 P.M ,000 40,000 = = = 0.35 = 35% = 0.4 = 40% = 3 5 = 0.6 = 60% 56. percent increase = = 0.2 = 20% /5000 = 20% increase = original price Operation of Numbers = = = ( ) + 2( ) = (0.2) 2 + (0.3) 2 = = = 7( ) = /12 = False = = ( ) = 0.2(25) = B 3H = = 76/27 = = (-3) 2 = ( 3 2 ) = = = 1/200 Math Olympia (pounds) Pouring out 2 of 1 of water makes a difference of = 21 pounds. Therefore, the water in the container s full capacity weighs (12-91) (1 2) = 15 pounds. Now that the water that half fills the container weighs 1 15 = 71 pounds. The weight of the container is = 2 (pounds) = $

18 76. Let abc represent the three-digit number 81. B from 200 to 699, with no digits repeated. Range # choices 82. A a a digit from 2 to B b a digit from 0 to 9, D but not a again c a digit from 0 to 9, D but not a or again 86. C = and 66 Let x = the second number. Let 4 + 2x = the first number. x x = 97 3x = 93 x = (2 -stamps) and 8 (15 -stamps) = (2 + 15) = 8 (stamps of each kind) = 18 (2-cent) 79. A = = 180 1( ) = minutes for science questions and 140 minutes for others. Assessment Test 80. C 87. B 88. D 89. D 90. D 91. C 92. B 93. A 94. A 95. B 96. A 97. B 98. B 99. C 18