Diagnostic Test This test is designed to determine a student s strengths and weaknesses for the purpose of planning an effective review, thereby using this study guide efficiently. The diagnostic test is issued in five sections: Sets and Logic Arithmetic Algebra Geometry Probability and Statistics Each section of the test has fifteen questions with an allotted time of 25 minutes per section. One may take a break between sections, but not during a section test. Use your time wisely. Do not linger on a question. If you are unsure about the working or the solution to a question, place a star next to it and move onto another question. Give priority to the questions that come easy to you. You can always go back to your starred questions later, if time permits. However, do not leave any questions unanswered; by a process of elimination make a logical choice. The answers to the diagnostic test are provided at the end of the test. The interpretation for the score in each section is: 14 15 correct: Review this chapter at your leisure. 11 13 correct: Review this chapter, but not necessarily first. Below 11 correct: Review this chapter immediately. The recommended order of review for the chapters in this study guide depends on the scores of the diagnostic test. Review the chapters in order of least score to highest score. DO NOT USE A CALCULATOR 1
2 DIAGNOSTIC TESTS Sets and Logic Diagnostic Test 25 minutes 1. Consider the diagram. Which statement is true if all regions are occupied? A C B a) Any element of A is an element of B. b) Any element of B is an element of A. c) Some element of A is an element of C. d) None of the above. 2. Select the rule that directly transforms statement i) into statement ii). i) Not all pens are blue. ii) Some pens are not blue. a) All are not p into Some are not p. b) Not (not p) into p. c) All are not p into None are p. d) If p then q into If not q, then not p. 3. Select the rule that directly transforms statement i) into statement ii). i) It is not true that Jim speaks Spanish or English. ii) Jim does not speak Spanish and does not speak English a) Not (p or q) into Not p and not q. b) Not (p and q) into Not p or not q. c) None are p into All are not p. d) None of the above.
DIAGNOSTIC TESTS 3 4. Negate: Jack will study and he will pass the test. a) Jack will not study and he will not pass the test. b) Jack will not study or he will not pass the test. c) If Jack studies, then he will not pass the test. d) Jack will study or he will pass the test. 5. Find the negation of If loving you is wrong, then I don t want to be right. a) Loving you is not wrong or I want to be right. b) If loving you is not wrong, then I want to be right. c) If I want to be right, then loving you is not wrong. d) Loving you is wrong and I want to be right. 6. Negate: All teachers are intelligent. a) Some teachers are intelligent. b) No teacher is intelligent. c) Some teachers are not intelligent. d) Every teacher is intelligent. 7. Negate: Some students are taking Algebra I. a) All students are taking Algebra I. b) Some students are not taking Algebra I. c) Not all students are not taking Algebra I. d) No students are taking Algebra I. 8. Select a statement that is logically equivalent to If Jerry is tall, then Betty is short. a) If Betty is not short, then Jerry is not tall. b) Jerry is tall and Betty is short. c) If Betty is short, then Jerry is tall. d) If Jerry is not tall, then Betty is short.
4 DIAGNOSTIC TESTS 9. Select the logical equivalent to It is not true that I like mathematics and you like English. a) I do not like mathematics and you do not like English. b) I like mathematics or you like English. c) If I like mathematics, then you like English. d) I do not like mathematics or you do not like English. 10. Select the statement that is logically equivalent to It is not true that if it rains, it pours. a) If it does not rain, then it does not pour. b) It rains and it does not pour. c) It does not rain and it does not pour. d) If it does not rain, then it pours. 11. Consider the following pair of statements and find a valid conclusion, if possible. i) No student likes homework. ii) All teaches like homework. a) Some students are teachers. b) No teachers are students. c) Some students like homework. d) None of the above. 12. Consider the following pair of statements and find a valid conclusion. i) All drivers have a license. ii) Some drivers own a car. a) All drivers own a car. b) All licensed people drive. c) Some licensed people who are not drivers own a car. d) None of the above.
DIAGNOSTIC TESTS 5 13. Select the conclusion to make the argument valid. If I take the bus, then I will arrive late. If I arrive late, then I will work more hours. a) If I work more hours, then I will take the bus. b) I take the bus or I will work more hours. c) If I take the bus, then I will work more hours. d) I take the bus and I arrive late. 14. Consider the following pair of statements and find a valid conclusion. i) If you practice, then you will succeed. ii) You will not succeed. a) You practice. b) You do not practice. c) You practice and you will succeed. d) You do not practice or you succeed. 15. To qualify for a loan of $100,000, an applicant must have a gross income of $40,000 if single or $50,000 if married and the applicant(s) must have assets of at least $20,000. Read the requirements and each applicant s qualifications for obtaining a $100,000 loan. Select the qualified applicant. Mr. A and his wife have assets of $25,000. He makes $32,000 and she makes $23,000. Mr. B is married with five children and makes $53,000. His wife is unemployed. Miss C is single and works two jobs. She makes $28,000 on her day job and $13,000 on her night job. She has assets of $17,000. a) Mr. A b) Mr. B c) Miss C d) No one
6 DIAGNOSTIC TESTS Arithmetic Diagnostic Test 25 minutes 1. 82.965 + 3.47 + 108.2 a) 192.035 b) 194.635 c) 843.94 d) 84.394 2. 2.28 0.012 a) 19 b) 190 c) 1.9 d) 0.19 3. a) b) c) d) 4. 407 % is equivalent to a) 4.07 b) 407 c) 40.7 d) 0.407 5. is equivalent to a) 4.4 % b) 4.4 c) 0.44 % d) 0.44 6. 0.28 is equivalent to a) b) 2.8 % c) d) % 7. 60 is what percent of 40? a) 50 % b) 150 % c) % d) % 8. An item that regularly sells for $80 is on sale for $60. What is the percent decrease? a) 250 % b) 25 % c) 2.5 % d) 0.25 %
DIAGNOSTIC TESTS 7 9. Round to the nearest hundredth: 547.3951 a) 547 b) 547.395 c) 500 d) 547.4 10. Select the expanded form for 27.09. a) b) c) d) 11. An investor buys 203 shares of stock. Each share costs $52.50. What is a reasonable estimate of the purchase? a) $8,000 b) $10,000 c) $12,000 d) $14,000 12. 3 3 + 5 3 is equivalent to a) ( 3 + 5 ) 3 b) ( 3 3 ) + ( 5 3 ) c) ( 3 + 5 ) 6 d) ( 3 3 3 ) + ( 5 5 5 ) 13. Place =, <, or > between the numbers: 9.17? 9. 17 a) > b) < c) = 14. A checking account charges $6 per month plus $0.20 per check. How many checks were written in a month in which the total charges amounted to $22.00? a) 6 b) 140 c) 80 d) 110 15. Find the largest positive integer which is a factor of 24 and 40 and is also a factor of the sum of 24 and 40. a) 4 b) 8 c) 16 d) 32
8 DIAGNOSTIC TESTS Algebra Diagnostic Test 25 minutes 1. Simplify: a) 23 b) 55 c) 70 d) 82 2. Simplify: a) b) c) d) 3. Name the property: - 4(9x) + (- 4)(3) = - 4( 9x + 3) a) associative property c) distributive property b) commutative property d) additive identity 4. a) b) c) d) 5. Solve: 4(x + 2) > 3x + 20 a) x 4 b) x = 4 c) x > 4 d) x < 4 6. Find the solution: a) (-1, 1) b) (1, -1) c) (2, -1) d) (-1, 2) 7. If f (x) = x 2 + 4x 5, find f (-2). a) 1 b) 7 c) 9 d) 17 8. For which statements is 1 a solution? i) t 1 = 0 ii) (x 2)(x 5) 6 iii) r 2 + 4r + 16 = 13 a) i only b) iii only c) none d) all
DIAGNOSTIC TESTS 9 9. Which graph represents 2x + y = -3? a) b) 4 3 2 1-4 -3-2 -1 0 1 2 3 4-1 -2-3 -4 4 3 2 1-4 -3-2 -1 0 1 2 3 4-1 -2-3 -4 c) d) 4 3 2 1-4 -3-2 -1 0 1 2 3 4-1 -2-3 -4 4 3 2 1-4 -3-2 -1 0 1 2 3 4-1 -2-3 -4 10. Identify the conditions that correspond to the shaded region. 4 3 2 1-4 -3-2 -1 0 1 2 3 4-1 -2-3 -4 a) 2x 3y > 6 b) 2x 3y 6 c) 2x 3y 6 d) 2x 3y < 6 11. Which is a factor of 3x 2 + 7x 6? a) (x 3) b) (3x 2) c) (x 2) d) (3x + 3)
10 DIAGNOSTIC TESTS 12. Find the real roots: 2x 2 + 3x = 1 3 ± 17 1 a) b), 1 c) 4 2 3 ± 17 1 d), 1 4 2 13. A machine can do 7 jobs in 4 hours. Which equation can be used to find the number of hours (x) the machine takes to do 11 jobs? 7 11 x 4 a) = b) 4 x 7 = 7 11 7 x c) = d) = 11 x 4 4 11 14. The tension (t) in a spring varies directly with the distance (d) the spring is stretched. If the tension is 42 pounds when the spring is stretched 2 inches, find the tension when the spring is stretched twice as far. a) 4 inches b) 84 inches c) 21 inches d) 44 inches 15. The difference between a number and five more than three times the number is five. What equation should be used to find the number? a) x + (3x 5) = 5 b) x (3x + 5) = 5 c) b) x (5x + 3) = 5 d) x (5x 3) = 5
DIAGNOSTIC TESTS 11 Geometry Diagnostic Test 25 minutes 1.Convert 752.4 mm to cm. a) 7524 cm b) 75.24 cm c) 7.524 cm d) 0.7524 cm 2. Round measurement A to the nearest ½ inch. a) 2 inches b) 2 2 1 inches c) 2 4 3 inches d) 3 inches A 1 2 3 4 5 3. Find the distance around a circular table of radius 1.3 m. a) 1.3 π m b) 1.69 π m c) 1.96 π m 2 d) 2.6 π m 4. The length of a rectangle is 5 feet more than twice the width. If the perimeter is 22 feet. Find the length of the rectangle. a) 2 ft b) 4 ft c) 9 ft d) 18 ft 5. Find the shaded area. 5 m 10 m a) 25 m 2 b) 50 m 2 c) 75 m 2 d) 50 m 6. Find the volume of the cone. 2 cm 9 cm a) 6 π cm 3 b) 36 π cm 3 c) 12 π cm 3 d) 18 π cm 3 Houghton Mifflin Company. All rights reserved.
12 DIAGNOSTIC TESTS 7. Jan is wrapping a cube shaped gift box. The side of the cube is 10 cm. How much paper, in cm 2, does Jan need to cover the gift box? a) 10 cm 2 b) 60 cm 2 c) 100 cm 2 d) 600 cm 2 8. What is the appropriate measure for the amount of water in a pool? a) meters b) square inches c) miles d) liters 9. Find the angle measurements if lines L 1 and L 2 are parallel. L 1 L 2 5x-20 3x a) 25 º b) 25 º, 75 º c) 75 º, 105 º d) 105 º 10. Find the angle measure of x. 110 x a) 90 º b) 70 º c) 110 º d) 180 º 11. Find the height of a flagpole that casts a shadow of 5 feet while a person that is 6 feet tall casts a shadow of 3 feet. a) 2 2 1 feet b) 4 ft c) 8 ft d) 10 ft 12. Find the missing leg of the triangle. 13 cm 5 cm a) 12 cm b) 8 cm c) 144 cm d) 194 cm
DIAGNOSTIC TESTS 13 13. How high up a wall does a 50-foot ladder reach if the foot of the ladder is 30 feet from the wall? a) 30 feet b) 40 feet c) 1600 feet d) 3400 feet 14. What quadrilateral has all sides equal, but no right angles? a) square b) rectangle c) rhombus d) trapezoid 15. Find the value of x. 3x + 10 2x a) 34 b) 68 c) 112 d) 180
14 DIAGNOSTIC TESTS Probability and Statistics Diagnostic Test 25 minutes 1. Jane can have her potato baked or fried. She can have her chicken baked, fried, or barbequed. She can drink soda or water. How many choices does Jane have for a meal? a) 3 b) 12 c) 7 d) 21 2. A student is asked to rank his 5 teachers from best to worst. How many ways can the teachers be ranked? a) 5 b) 25 c) 60 d) 120 3. A committee must consist of two men and two women. How many different committees can be formed if there are four men and three women? a) 18 b) 6 c) 9 d) 3 4. A box has 3 red pens, 2 black pens, and 4 green pens. What is the probability of randomly selecting a black pen? a) b) c) d) 5. The probability that it will rain tomorrow is 47%. What is the probability that it will not rain tomorrow? a) 0.53 b) 0.47 c) 0.92 d) 1 6. A box has 3 red pens, 2 black pens, and 4 green pens. What are the odds in favor of selecting a green pen? a) 5 : 4 b) 4 : 9 c) 4 : 5 d) 9 : 4 7. Seventy percent of the students at a certain community college are taking Math. Eighty percent are taking English, and sixty percent are taking both Math and English. What percent of students are taking either Math or English? a) 70 % b) 80 % c) 90 % d) 150 %
DIAGNOSTIC TESTS 15 8. Using the table below, what is the probability that a nurse received a good evaluation given that she is part-time? (Table shows results from a survey of 200 nurses.) Good Evaluations Bad Evaluations Part-time 38 42 Full-time 84 36 a) b) c) d) 9. A box has six good apples and four bad apples. If two apples are chosen at random with replacement, what is the probability that the first one will be good, and the second one will be bad? a) b) c) d) 10. A toy-store owner wants to determine which electronic game system is the most popular among students in his county. Which procedure is best for obtaining an unbiased sample? a) Survey a sample of students in Art class. b) Survey the first two hundred students who enter his store. c) Survey a random sample of students from the entire student body. d) Survey a random sample of student responses from Pre-K through 6 th graders. For Question 11, use the graph below. Class-Skipping Frequency Bi-weekly 25 30 Weekly Monthly 70 75 Never 11. What percentage of students never skip class? a) 25 % b) 75 % c) 37.5 % d) 125 %
16 DIAGNOSTIC TESTS For Question 12, use the graph below. Yearly Rainfall Rainfall (in inches) 80 60 40 20 0 1991 1992 1993 1994 1995 1996 Year 12. Which year had the greatest rainfall? a) 1993 b) 1994 c) 1995 d) 1996 13. Consider a student s scores for one semester in an English class: {85, 72, 93, 96, 88}. What is the mean score? a) 93 b) 87 c) 88 d) 89 14. More than half of the shirts in the store cost $15.00. Most of the other shirts cost $25.00, and the remaining few cost $35.00. Which of the statements below is true? a) The mean is greater than the mode. b) The median is equal to the mean. c) The median is less than the mode. d) The mean is less than the median. 15. The scores on a placement examination are as follows: Score Percentile Rank 25 99 20 82 15 74 10 45 5 22 What percentage of students taking the examination scored between 10 and 20? a) 37 % b) 45 % c) 82 % d) 127 %
DIAGNOSTIC TESTS 17 Answers to Diagnostic Test Sets and Logic 1 b 4 b 7 d 10 b 13 c 2 a 5 d 8 a 11 b 14 b 3 a 6 c 9 d 12 c 15 a Score: Arithmetic 1 b 4 a 7 b 10 c 13 a 2 b 5 d 8 b 11 b 14 c 3 d 6 c 9 d 12 d 15 b Score: Algebra 1 b 4 a 7 c 10 d 13 a 2 a 5 d 8 b 11 b 14 b 3 c 6 a 9 c 12 a 15 b Score: Geometry 1 b 4 c 7 d 10 b 13 b 2 b 5 a 8 d 11 d 14 c 3 d 6 c 9 c 12 a 15 a Score:
18 DIAGNOSTIC TESTS Probability and Statistics 1 b 4 b 7 c 10 c 13 b 2 d 5 a 8 b 11 c 14 a 3 a 6 c 9 c 12 d 15 a Score: