Mathematics Practice Test 2

Transcription

1 Mathematics Practice Test 2 Complete 50 question practice test The questions in the Mathematics section require you to solve mathematical problems. Most of the questions are presented as word problems. The Mathematics section questions are from three skill factors: (1) estimation, measurement, and statistical principles; (2) computation and problem solving; and (3) numerical and graphic relationships. Approximately 30 percent of the questions from this section are drawn from the estimation, measurement, and statistical principles area; approximately 35 percent are drawn from the computation and problem-solving area; and approximately 35 percent are drawn from the numerical and graphic relationships area. Use of calculators is prohibited on this examination Scaled Scores The scaled scores used for reporting the results range from 20 to 80 for each of the three sections (Reading, Mathematics, and Writing) of the test. The passing score on each section is a scaled score of 41. A total score (the sum of Reading, Mathematics, and Writing scaled scores) of 123 is required for passing status. It is possible to pass the test with a scaled score on one or two sections as low as 37, provided that the total score is 123 or higher. It is not possible, however, to pass the test if any section score is below 37, regardless of how high the total score may be. 1

2 Question Number Your Response Question Number Your Response

3 1. What is the value of 18 + (-14)? a. 4 b. -4 c. 32 d. -32 e A rectangle is 7 inches wide and 10 inches long. If the width is doubled, what is the perimeter of the resulting rectangle? a. 17 inches b. 34 inches c. 48 inches d. 68 inches e. 51 inches 3. Carol has an initial balance of $4,300 in her checking account. She makes a deposit of $350, then writes two checks, one for $67, the other for $247. Carol then makes a deposit of $150. What is her new balance? a. $4650 b. $4486 c. $4336 d. $4351 e. $4450 3

4 Use the graph below to answer the following questions 4 to What is the total amount Karen has budgeted for savings? a. $14 b. $140 c. $274 d. $300 e. $ What two items in her monthly budget are in equal amounts? a. Utilities and Food b. Other and Food c. Savings and Utilities d. Clothes and Other e. Other and Savings 4

5 6. If Karen spends $120 on entertainment for a certain month, how does this compare to the actual amount she has budgeted? a. Exactly what she has budgeted. b. $5 over budget c. $5 under budget d. $10 over budget e. $10 under budget 7. If Karen sticks to this budget, how much will her savings increase over a 3 month period? a. $322 b. $42 c. $644 d. $966 e. $ What is the value of x if x = ? a. -12 b. 12 c. -32 d. 32 e. 14 5

6 9. Which of the following is equivalent to 1/2? a. 13/27 b. 14/29 c. 26/52 d. 32/66 e. 50/ Which of the following is the least in value? a..06 b. 2/3 c. 5/10 d. 7.5% e. 4/ Which of the following is equivalent to 0.25? a. 4/10 b. 25/50 c. 8/32 d. 4/8 e. 4/25 6

7 12. Which of the following is the closest approximation to 7/9? a b c d e A piece of wood is 4.5 yards long. What is the length expressed in inches? a. 162 b. 450 c. 54 d e Which of the following is a true statement? a. 14 > 15 b. -3 < -4 c. 63 > ( 9 x 8) d. 15 < (3 x 5) e. -15 > -16 7

8 15. In Mr. Hall's class, any grade below 60% is failing. If 27 out of 36 students have average scores greater than or equal to 60%, what is the percentage of the class that is failing? a. 27% b. 36% c. 60% d. 9% e. 25% 16. If x = 3, which of the following is a true statement? a. x + 4 > x + 5 b. - x = - x + 3 c. 2x > 3x d. x + 5 > x e. x - 3 = x + 3 8

9 17. Use the information below to answer the question that follows. 4 quarts = 1 gallon 1 gallon = 3.8 liters Approximately how many liters of water would fit in a container that held 2 quarts? a. 0.5 liters b. 1 liter c. 1.9 liters d. 7.2 liters e. 2.7 liters 18. A proposed road is to be 3.4 miles long. How many feet long would the road be? (1 mile = 5280 feet) a feet b feet c feet d feet e feet 9

10 19. What is the value of 9 - (-8) + 5? a. 12 b. 22 c. 6 d. -12 e. -22 Use the following table to answer questions The following table represents information based on reported scores from a standardized mathematics test. *Please note: The information is fictional and represents no real school, real data, or any real graph. 10

11 20. What would be the appropriate range to put in the empty box in the percentile column? a b c d e What value should be placed in the empty box in the last row? a. 561 b. 461 c. 361 d. 261 e How many 6th graders scored at or above the 50th percentile? a. 151 b. 161 c. 145 d. 125 e

12 23. What value should be in the empty box in the 7th grade column? a. 11 b. 21 c. 31 d. 41 e. 51 Use the following graph to answer questions

13 24. Between which months in 2000 was there virtually no difference in sales? a. February and March b. March and April c. May and June d. November and December e. June and July 25. Which month appears to have the greatest difference in revenue between 1999 and 2000? a. January b. June c. December d. October e. April 26. Approximately what was the total revenue for the month of December of 2000? a. 45,000 b. 40,000 c. 30,000 d. 20,000 e. 25,000 13

14 27. Which of the following months had lower revenue in 2000 as compared to 1999? a. December b. August c. October d. January e. July 28. The temperature at 3 pm was 25 degrees F (above zero). By 5 pm, the temperature had dropped 17 degrees. At 10 pm, the temperature was recorded as being 20 degrees below zero (-20 degrees F). How far had the temperature dropped between 5 pm and 10 pm? a. 17 degrees b. 25 degrees c. degrees d. 28 degrees c. 42 degrees 29. A school will put no more than 32 students in a classroom. If there are 549 total students, what is the least number of classrooms needed? a. 17 b. 18 c. 19 d. 20 e

15 30. 3 out of every 11 students at an elementary school would like to take band. If there are 704 total students, how many want to take band? a. 192 b. 64 c. 33 d. 640 e Which of the following values for x satisfies the statement: 10 < x + 5? Please note: There should be a line under the < symbol. If it does not show up, please regard it as there! a. 1 b. 2 c. 3 d. 4 e A hot air balloon is at an altitude of 237 feet. It descends 56 feet, climbs 75, then descends for 43 feet before leveling off. At what altitude is the balloon now at? a. 237 feet b. 174 feet c. 16 feet d. 371 feet e. 213 feet 15

16 Use the following information to answer question # 33. When open for business in the morning, a women's shoe store had: 123 pairs of athletic shoes 45 pairs of boots 67 pairs of sandals 76 pairs of dress shoes At the end of the business day, the store had reported selling 87 pairs total of footwear. They also now had on hand 60 pairs of sandals. Which of the following would you be able to calculate? a. The number of boots sold. b. The number of sandals sold. c. The number of athletic shoes left. d. The number of customers that bought shoes. e. The number shoes returned. 34. A bag contains 4 red balls, 7 green balls, and 9 yellow balls. What is the probability of taking out a red or a green ball? a. 1/5 b. 7/20 c. 9/20 d. 11/20 e. 13/20 16

17 35. Jennifer works in a grocery store part-time at $8.25 per hour. She works at least 25 hours per week. Her employer does not allow her to work more than 30 hours in one week. Her work week is Sunday to Thursday. If you know she had worked a total of 17 hours as of the end of Tuesday, which of the following do you know to be true? a. She will work at least 8 more hours for the week. b. She will not work 13 hours more for the week. c. She will work 8 hours on Wednesday. d. She will not work on Thursday. e. She did not work on Sunday. 36. A 6th grade teacher is ordering pencils, crayons, and markers for her classroom. The prices are as follows: Pencils: $0.27 per dozen Crayons: $0.48 per box of eight. Markers, set of 6 different colors: $0.96 She orders 72 pencils, 20 boxes of crayons, and 10 sets of markers. How much (before tax) is the total cost? a. $20.82 b. $38.44 c. $1.71 d. $16.20 e. $

18 37. Carl and Joe are driving in separate cars to a city 320 miles away. Both of them are leaving from the same place. Joe leaves at 9 am and does an average of 60 mph. Carl leaves at 9:30 am and catches up to Joe at 12 noon. How fast is Carl's average speed? a. 60 mph b. 72 mph c. 65 mph d. 62 mph e. 80 mph Use the following to answer questions 38 to 40 The following report on a student was sent home regarding standardized testing. *Note: It is totally fictitious! Name: John Doe Current Grade Level: 4th Grade Equivalent: 5.7 National Norm: 3.7 Raw Score: 26 National Norm: 17 Percentile: 80th 38. What was the number of correct answers this student had on this test? a. 80 b. 17 c. 5.7 d. 3.7 e

19 39. What is the average number of correct answers given by all students tested? a. 57 b. 26 c. 17 d. 84 e Which of the following is valid conclusion on the above student? a. Student should skip one grade. b. Student is above average for a 4th grader. c. Student is average for a 4th grader. d. Student should be held back one grade. e. Student has a very high IQ. 41. Convert Fahrenheit to Celsius: If F = 77, what is C? Use the formula: C = 5/9(F - 32) a. 25 b. 35 c. 45 d. 55 e

20 42 Convert Celsius to Fahrenheit: If C = 15, what is F? Use the formula: F = (9/5) C + 32 a. 19 b. 29 c. 39 d. 49 e The price of a newspaper subscription was $40. The new price is $43. What percent was the price increased? a. 3% b. 6% c. 7.5% d. 8% e. 9.5% 44. Solve for x in the following equation. (1/3)X + 8 = 17 a. 11 b. 17 c. 9 d. 27 e

21 45. What is the perimeter of the figure below? a. 36 b. 52 c. 48 d. 28 e green marbles, 13 red marbles, and 12 purple marbles are in a box. What is the probability of taking out a green marble? a. 13/30 b. 2/5 c. 1/6 d. 5/6 e. 1/5 21

22 47. The sum of 2 numbers is 54. The difference in the 2 numbers is 12. What is the value of the smaller number? a. 32 b. 21 c. 52 d. 42 e Which of the following would come between 1/3 and 0.6? a. 1/5 b. 4/10 c d. 1/4 e Which of the following has a larger value? a. 5/9 b. 6/11 c. 7/10 d. 9/15 e. 6/13 22

23 50. John works in a camera store. He must work at least 25 hours a week, but no more than 38. If he has worked 9 hours so far in the current week, which of the following is true? a. He must work 29 more hours. b. He can work 16 hours more. c. He cannot work more than 20 hours more. d. He cannot work 20 hours more. e. He must work at least 9 more hours. 23

24 Answers a Just the same as If you are adding signed numbers, each positive will cancel out a negative. Since we have 4 more positives than negatives, the answer is positive 4. No need for a sign on positive numbers. 2. c. The width was 7, now 14. The perimeter is now = b. Calculate to get e. 14% of 2300 is 322. Do.14 x 2300 or 14 x d. 6. b. Calculate the amount she has budgeted and compare x 2300 or 5 x 23 = is 5 over. 7. d. Use the figure you got in # 4 and multiply it by 3. * Test taking hint: why recalculate numbers you already did? Look back! 24

25 8. a. We have 22 negatives and 10 positives. That's 12 more negatives, so -12 is the answer. 9. c. Other answers are close, but c reduces down exactly. 10. a. Start at ones you know and compare. You should be able to tell that b, c, and e are all more than a and d. Then realize 0.06 is 6%, so it is the least. 11. c. You need a fraction that reduces to 1/4th. 8/32 = 1/ c. Learn 9ths. Each 9th is a repeating decimal. It repeats the number on top. 1/9 = /9 = /9 = And so on. Round as needed. 7/9 = , so the closest is a. 3 feet to a yard, so 4.5 yards = 3 x 4.5 = 13.5 feet. 12 inches to a foot, so 13.5 feet = 13.5 x 12 = 162 inches. 14. e. Negative numbers get smaller as the number gets bigger. d can be eliminated because the 2 values are equal. The inequality signs always points to the smaller number. Think: Small point, smaller number. Wide side, larger number. 25

26 15. e. 9 students are failing out of 36. This reduces to 1/4 or 25% 16. d. All other choices give false statements shown in the following a becomes > or 6 > 8 which is false. b becomes -3 > or -3 > 0 which is false. c becomes 2 x 3 > 3 x 3 or 6 > 9 which is false. e becomes 3-3 > or 0 > 9 which is false. Answer d is > or 8 > -3 which is true. 17. c. 2 quarts is half a gallon. 1 gallon is 3.8 liters, so half a gallon would be 1.9 liters. 18. a. Multiply 3.4 x 5280 to get You could have added to get But you know it is about a half mile more. Logical choice would be a. 19. b. Getting rid of a negative is a "positive" thing. equation becomes = 22. So, it is just like adding the same number. The You could do the positives first, to get 14. You know you either add or subtract 8 to get 22 or 6. Think logically, is 9 - (-8) the same as 9-8? No! Of course you logically need to realize that -(-8) = a. 26

27 All groups go from the 0 to the next 9. It should be obvious which one is missing. 21. d. The last row is the total of students in the column. Here it is the 8th grade column. It all adds up to c. Add all boxes in the 6th grade column that are from on up. This would be = b. The total for the column is 310. All other boxes in this column add to = c. We are looking at 2000, the dark line. It appears flat between May and June. * You need to realize the first letter of the month is how they are written at the bottom. The first J stands for January. 25. e. Look at each month and decide which gap appears largest. April is by far the largest gap. 26. a is the dark line and it should be clear it is about half way between and You can always use a corner of your test book to fold up to get a straight line. 27. b. Look only at the months listed. Find one where the dark line is below the shaded line. August works. 27

28 28. d. At 5 pm the temperature was 8 degrees. (25-17). To get to -20, you need to go 8 degrees to get to 0, then 20 more. Total of 28 degrees. 29. b. 549 divided by 32 is 17 and a little more. We need 1 extra classroom for that. Total 18 classrooms. Don't worry how your school does it or if this is the best way. 30. a. Divide 704 by 11 then multiply by 3. Or solve the equation 3/11 = x/704. Which number on top of 704 would reduce to 3/11? You could work backward and try all answers to get one that works. 31. e. If there is a line under the inequality sign, it means it is okay for both sides to be equal as well. The only number listed that works is e. Calculate to get b. Each choice is reasoned through below: a. We have no idea how many boots are left. b. We know we started with 67 and now have 60 We CAN assume 7 were sold. c. We have no idea how many athletic shoes are left. d. We cannot assume each customer bought only 1 pair of shoes. Some may have bought more. e. We have no idea how many were returned. 28

29 34. d. We don't care whether it is red or green. Either one will do. If this is confusing, think of the question as being "What are the chances of NOT taking a yellow ball?" It is the same question. Either way you get 11/ a. Her hourly wage is extra information and does not figure into the problem. Each choice is reasoned through below: a. If she works at least 8 hours, she will work her minimum of 25 hours. This is true. b. She could indeed work 13 hours more. c. How do we know how many hours she will work on a day? d. How do we know she will not work on Thursday? e. How do we know she did not work on Sunday? 36. a. Calculate as follows: 72 pencils = 6 dozen, 6 x 0.27 = boxes of crayons = 20 x 0.48 = sets of markers = 10 x.96 = 9.6 Total = = b. At 12 noon, Joe has been traveling for 3 hours at an average speed of 60 mph. Therefore, he has driven 180 miles (3 x 60). Carl catches up to him at this time, which means Carl has done 180 miles in 2.5 hours. Divide 180 by 2.5 to get 72. Or you could work backwards and multiply each answer by 2.5 and see which one gives a value of 180. a. 2.5 x 60 = 150 b. 2.5 x 72 = 180 c. 2.5 x 65 =

30 d. 2.5 x 62 = 155 e. 2.5 x 80 = e. Raw score is how many answers were correct. 39. c. National Norm is the average for all students who took the test (nationally). 40. b. Grade Equivalent is grade level the student tests at. 5.7 means 5th grade, 7th month. IT IS NOT meant for comparing students to other grades. It does not mean student can do 5th grade work, nor should be skipped ahead. The only valid conclusion is above average for a 4th grader. It says nothing about a student's IQ. 41. a. Do what is inside the parentheses first. Substituting 77 for F we get = 45. Then multiply by 5/9. You can do this many ways. The easiest way is to multiply 45 x 5, then divide by 9. This would give 225/9 which is 25. You could have divided 45 by 9 first, then multiplied by 5. You could have also noted that 5/9 is about.56, so multiply 45 by.56 to get Closest answer would be e. Here we need to multiply (9/5) x 15. (On most tests the 9/5 would not be in parentheses) 9/5 = 1.8, so multiply 15 b 1.8 to get 27. Then add 32 to get 59. *You do not add first. These are not in parentheses! You must multiply first. Another way to multiply 9/5 x 15 would be (9 x 15)/5. 30

31 Another way to multiply 9/5 x 15 would be to divide 15 by 5, then multiply by 9. In all cases you get c. Compare the increase to the original price. 3/40. This is the percent increase. 3/40 means divide 3 by 40 to get or 7.5% You could also reason your way through it as follows: We are looking at 3 out of % of 40 = 4, so we know it is less than 10% 5% of 40 = 2, so we know it is more than 5% This now eliminates answer a. 1% of 40 =.4, so 6% = 2.4, 7 % = = 2.8, 8% = = 3.2 But now we have gone too far. It is between 7% and 8%. The only choice is c. 44. d. You are looking for a number that when you take 1/3 of it and add it to 8 you get 17. The only number when added to 8 to give 17 is 9. But the answer cannot be 9 because we are looking at a third of a number to be 9. 9 is 1/3 of 27. So, x = 27. You could work backwards, checking each answer. However, because we are finding a third, the answer must be divisible by 3. That eliminates answers a,b, and e. 9 looks attractive because = 17. But (1/3)9 + 8 = = 11 and (1/3) = = is the only one that works. 31

32 45. b. Assume all angles are right angles. We know we have = 36. But we are missing 2 sides. The bottom side will be = 14 (Look at the top sides. See how they correspond to the bottom length?) The missing side between the 8 and 6 must be 2. (Look at the left side. It is 12. Look at the right side. It is 10. The missing length must be added to 10 to get 12. So, it has to be 2) Perimeter = = c. 5 of the 30 marbles are green. The fraction 5/30 reduces to 1/ b. We need 2 numbers to total up to 54. Many combinations work, but only one where 1 number is 12 more than the other one. Work backward. Remember, we are looking for the smaller number, not the larger. Reason through the answers as follows: a. If 32 is the smaller, then 44 is the larger. But = 76, not 54. b. If 21 is the smaller, then 33 is the larger. And = 54. c. If 52 were the smaller, then 64 is the larger. Way too big. d. Same as c. e. same as c. 48. b. You need to think of both values in terms of fractions and decimals. 1/3 is about.33, and 0.6 is 6/10. The range is between 1/3(.33) and 6/10(.6) Look at each answer: a. 1/5 =.2 32

33 b. 4/10 =.4 c..05 = 5/100 d. 1/4 =.25 e. 0.7 = 7/10 The only answer that fits between the given values is b, d. Glance through the answers and see if you can eliminate some right off. All are more than 1/2 except e, so eliminate e. 7/10 is.7 or 70%. This should let you see that it is bigger than a and b. We now need to compare 7/10 to 9/15. To compare 2 fractions, multiply the denominator of one by the numerator of the other. Multiply bottom to top, placing the product above that fraction that you multiplied the top by. Look at the diagram. 10 x 9 is 90, put 90 above the x 7 = 105, put 105 above the 7. The side that now has the larger number is the larger fraction. Since 105 is larger than 90, it is on the side of the larger fraction. So, the larger fraction is 7/10. Use this technique to compare any fractions. 50. b. Reason out each answer as follows: a. He could work 29 more hours. but does not have to. The word "must" implies he has too. b. 16 more would give him 25. Yes, he could work 25. c. He could indeed work 20 hours more. d. See answer c. e. He could work 9 more hours, but does not have too. 33