Arith1
- 1. CPT Mathematics Review The College Entry-Level Placement Test (CPT) for mathematics will be used to determine your placement into a mathematic class. The test begins at the elementary algebra level. If your algebra skills are strong enough, you will be branched into the college-level mathematics test for course placement. If your algebra skills are weak, you will be branched down into the arithmetic section of the test. The arithmetic portion of the test will measure your ability to work with whole numbers, fractions, decimals, percents, and word problems that can be solved without using algebra. If your arithmetic skills are strong enough you will be placed into Elementary Algebra; if not you will be placed into Pre-Algebra. College-level Mathematics Test and Placement Elementary Algebra Test Elementary Algebra Placement Arithmetic Test Pre-Algebra Placement The attached sample tests are representative of the type and style of questions that you will see on the CPT. If you have difficulty with a type of question, such as a fraction question, you should study that concept more thoroughly. The Learning Support Centers and libraries on each campus will have additional textbooks available for you to use to review for the CPT. These tests are intended to function as a review of skills, not a substitution for knowledge. Simply memorizing how to do these specific problems will not guarantee that you will pass the CPT. Good luck as you prepare for this most important placement test. CPT Review 4/17/01 1
- 2. Arithmetic Review Read all questions carefully. Make sure you are answering the question that is being asked. Work problems out completely. Try not to guess. 1. How many three foot wide pieces of fencing are needed to surround the perimeter of a yard that is 15 feet long and 24 feet wide? A) 13 B) 26 C) 39 D) 78 2. Mary’s savings account contained $2,491. On Monday she withdrew $725 and on Thursday she deposited $984. How much was in her savings account after these transactions? A) $782 B) $2232 C) $2750 D) $4200 3. The Smith family moved into a new home and had to buy new kitchen appliances. Estimate the cost to the nearest hundred dollars for the purchase of a dishwasher $695, stove $999, and refrigerator $1599. A) $3290 B) $3293 C) $3200 D) $3300 4. A movie theater has seats arranged in 25 rows with 30 seats in each row. How many seats are in the theater? A) 55 B) 110 C) 750 D) 562,500 CPT Review 4/17/01 2
- 3. 3 1 1 5. A train carryington of coal drops off ton in Pittsburgh, then drops off ton in 4 3 6 Buffalo. How much coal is the train carrying after it leaves Buffalo? 1 A) ton 3 1 B) ton 4 1 C) ton 12 7 D) ton 12 1 2 6. Find the sum in lowest terms. 1 +3 4 5 1 A) 4 10 1 B) 4 3 13 C) 4 20 3 D) 4 20 3 7. Jennifer borrowed $720 for a new TV. She has paid of the debt. How much does 4 she still owe? A) $180.00 B) $540.00 C) $719.25 D) $960.00 8. Which of the following is the best approximation for the product of 42.081 × 99.91? A) 42 B) 420 C) 4200 D) 42000 CPT Review 4/17/01 3
- 4. 1 3 9. 6 − 2 5 5 2 A) 4 5 2 B) 3 5 3 C) 3 5 3 D) 4 5 16 10. ÷5 5 A) 3 16 B) 25 C) 16 D) 31 11. Which of the following cannot be true about the statement 0.9 < X < 1.5 ? A) X = 0.95 B) X = 0.145 C) X = 1.13 D) X=1 1 12. If a recipe calls for 2 cups of flour and you want to make five times the recipe, how 2 much flour do you need? 1 A) 10 cups 2 1 B) 7 cups 2 1 C) 12 cups 2 5 D) 2 cups 2 CPT Review 4/17/01 4
- 5. 13. Find the average of the following list of data: 14.2, 18.3, 9.6, 11.4, and 7 A) 11.9 B) 10.1 C) 12.1 D) 12.3 14. Write 0.68 as a fraction in lowest terms. 19 A) 25 33 B) 50 17 C) 25 16 D) 25 15. There are 40 women and 35 men in the drama club. Find the ratio (in lowest terms) of women to the total number of students in the club. 7 A) 8 7 B) 15 8 C) 7 8 D) 15 16. A basketball player makes 6 free throws in his first 10 attempts. If he continues at the same rate, how many free throws will he make in 25 attempts? A) 9 B) 12 C) 15 D) 18 CPT Review 4/17/01 5
- 6. 17. Which of the following cans/bottles of Coca-Cola has the lowest cost per ounce? A) 12 oz for 55¢ B) 16 oz for 75¢ C) 32 oz for $1.09 D) 48 oz for $1.69 18. 17 is what percent of .17? A) 1% B) 100% C) 1000% D) 10000% 1 19. Mary and her five children are to inherit a total of $12,400. Mary is to receive of 4 the money and the children are to evenly split the remaining moneys. How much money will each child receive? A) $1860 B) $2480 C) $3100 D) $9300 20. Jill is buying new appliances. The cost of the dishwasher is $459 and the cost of the microwave is $289. What is the total price including the sales tax rate of 7%? A) $52.36 B) $800.36 C) $748.00 D) $700.36 21. A watch loses 15 seconds every hour. How many minutes will the watch lose in a day? A) 360 B) 24 C) 96 D) 6 22. If John has test scores of 90 and 76 with one test remaining to be taken, what score must he make on the last test to end up with an 86 average. A) 96 B) 86 C) 92 D) 84 CPT Review 4/17/01 6
- 7. 23. Dr. Peebles wants to buy tickets for the Oceanography Class to attend a Marine Science Center fieldtrip. If the tickets cost $32 each and the department has $3408 budgeted for the trip, what is the greatest number of tickets that can be purchased? A) 107 tickets B) 106 tickets C) 16 tickets D) 10 tickets 24. Which of the following is NOT a true statement? A) .04 = .02 1 1 B) ÷ =2 2 4 C) 13 2 = 169 D) 3.10 ≤ 3.100 25. A bag has one red ball, three blue balls, and twice as many green balls as blue balls. If one ball is drawn (with out looking) from the bag, what are the chances that the ball will be blue? A) 3 in 10 B) 3 in 8 C) 1 in 3 D) 1 in 7 26. All of the following are true statements EXCEPT 135 125 10 A) = + 50 50 50 135 B) = 5 − 2.3 50 135 150 C) = − 0.15 50 50 135 D) = 2 • 1.35 50 27. Find the area of a circle that has a radius of 3.5 cm. Use 3.14 for the value of π . A) 21.98 cm 2 B) 38.465 cm 2 C) 43.96 cm 2 D) 153.86 cm 2 CPT Review 4/17/01 7
- 8. 3 28. For a chemistry experiment of an ounce of a certain chemical is needed. If a 4 bottle of the chemical holds 96 ounces, how many times can the experiment be completed? A) 128 B) 72 C) 24 D) 32 29. Find the area of a triangle with base = 6 m and height = 5 m. A) 15 m 2 B) 26 m 2 C) 30 m 2 D) 105 m 2 3 30. 10 1 6 1 A) 20 9 B) 5 C) 5 9 D) 20 CPT Review 4/17/01 8
- 9. Solutions to Arithmetic CPT Practice perimeter = 2 ×15 + 2 × 24 1. B = 30 + 48 = 78 feet of fencing needed Each section of fencing is 3 feet wide. 78 ÷ 3 = 26 pieces of fencing . 2. C $2491 − $725 + $984 = $2750 When estimating round numbers first. $695 = $700 3. D $999 = $ 1000 $1599 = $1600 Now add $700 + $1000 + $1600 = $3300 4. C 25 × 30 = 750 seats 3 9 5 5 = = 4 12 12 12 1 4 1 2 5. B − = - = 3 12 6 12 5 3 1 = 12 12 4 1 5 1 = 4 20 2 8 6. C +3 = 5 20 13 13 4 =4 20 20 3 7. A $720 × = $540 amount paid. $720 - $540 = $180. 4 CPT Review 4/17/01 9
- 10. 8. C 42.081 × 99.91 ≅ 42 ×100 = 4200 1 6 6 =5 5 5 3 3 − 2 = −2 9. C 5 5 3 3 5 16 ÷5 5 16 1 10. B × 5 5 16 25 11. B First line up the numbers according to their size inserting zeros to the left of the decimal point to help with comparison. 0.145 0.900 given number 0.950 1.000 1.130 1.500 given number The number which does not fit in the range is 0.145 1 2 ×5 2 5 5 12. C × 2 1 25 1 = 12 2 2 CPT Review 4/17/01 10
- 11. 14.2 18.3 9.6 Next divide the total by 5. 13. C 11.4 60.5 ÷ 5 = 12.1 + 7.0 60.5 68 ÷ 4 17 14. C = 100 ÷ 4 25 women 40 ÷ 5 8 15. D Total students 40 + 35 = 75 = = = total 75 ÷ 5 15 6 ? = Now cross multiply 10 25 16. C 150 = 10 × ? Divide both sides of the equation by 10 ? = 15 17. C To calculate cost per ounce you divide the cost of each product by the price of each product. Remember to change $ to ¢ for equal comparisons. 55 ÷ 12 = 4.583 75 ÷16 = 4.6875 109 ÷ 32 = 3.40625 169 ÷ 48 = 3.52083 The least expensive is the 32 ounce container at 3.40625¢ per ounce 17 ? = Now cross multiply .17 100 18. D 1700 = .17 × ? Divide both sides of the equation by .17 ? = 10000 CPT Review 4/17/01 11
- 12. 1 3 19. A Since Mary gets of the total the children will get the remaining to 4 4 1 share. Each child will then get of this amount. 5 3 1 $12400 × × = $1860 4 5 $459 + $289 = $748 20. B $748 × .07 = $52.36 $748 + 52.36 = $800.36 15 seconds × 24 hours in day = 360 21. D 360 ÷ 60 seconds in a minute = 6 minutes 90 + 76 + ? = 86 3 22. C 86 × 3 = 166 + ? 258 = 166 + ? 258 − 166 = 92 You could also do this problem by trial and error. 23. B $3408 ÷ $32 = 106.5 Since you cannot purchase part of a ticket the answer is 106 tickets. 24. A For this problem you must work out each situation. Remember you are looking for the statement that is NOT true. .04 = .2 not .02 since .2 × .2 = .04 This would be the correct choice. 25. A First figure out the total number of balls in the bag. 1 red 3 blue 2 × 3 = 6 green 10 total next set up a ratio of blue to total which is “3 in 10” CPT Review 4/17/01 12
- 13. 150 26. C − 0.15 50 150 15 = − 50 100 300 15 = − 100 100 285 = 100 135 which does not reduce to 50 27. B Area of a circle formula = πr 2 π given as 3.14 r is the radius 3.14 × 3.5 2 3.14 × 3.5 × 3.5 = 38.465cm 2 3 96 ÷ 4 28. A 96 4 × = 128 1 3 1 29. A Area of triangle formula = × Base × Height 2 1 × 6m × 5m = 15m 2 2 3 1 30. B This is a compound fraction which really means ÷ 10 6 3 1 ÷ 10 6 3 6 9 × = 10 1 5 CPT Review 4/17/01 13