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Name: ________________________ Class: ___________________ Date: __________ ID: A Math II Chapter 2 test Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. The four best scores from an amateur golf tournament sponsored by a local golf club are given in the table. Since the lowest score wins, which golfer won the tournament? Player Score Mr. Benitez 2 Mr. Hill –3 Mr. Williams –8 Mr. Hayashi 8 a. b. ____ ____ ____ ____ Mr. Hayashi Mr. Benitez c. d. Mr. Hill Mr. Williams 2. Find the sum –37 + (–25). a. –12 b. 12 c. d. 62 –62 3. Evaluate p − q for p = –13 and q = –50. a. 37 b. –63 c. d. 63 –37 4. Find the product 6 • (–9). a. 3 b. –54 c. d. 54 –3 5. Find the quotient 130 ÷ 2. a. 128 b. –65 c. d. 132 65 ____ 6. A submarine started at the surface of the water and was moving down at –15 kilometers per minute toward the ocean floor. The submarine traveled at this rate for 48 minutes before coming to rest on the ocean floor. What is the depth of the ocean floor? a. –720 kilometers c. –708 kilometers d. 33 kilometers b. –732 kilometers ____ 7. Tell whether the number 75 is prime or composite. a. prime b. composite ____ 8. It takes 120 drops of water to fill a teaspoon. Write the prime factorization of 120 using exponents. a. 2 2 • 3 • 5 c. 2 3 • 3 • 5 b. 2 • 3 • 5 d. 2 3 • 15 1 Name: ________________________ ____ ID: A 9. Ramon would like to plant a garden where each row has the same combination of plants. If Ramon has 27 tomato plants, 15 cucumber plants, and 6 basil plants, what is the greatest number of rows the garden can have if Ramon uses all of the plants? a. 2 rows c. 9 rows b. 3 rows d. 5 rows ____ 10. Find the least common multiple (LCM) of 7, 10, and 20. a. 200 c. 20 b. 140 d. 70 ____ 11. Lauren visits the park every 3 days and goes to the library every 10 days. If Lauren does both of these today, how many days will pass before Lauren gets to do them both on the same day again? a. 13 days c. 30 days b. 60 days d. 7 days ____ 12. Write the fraction 21 24 in simplest form. a. 24 21 c. −7 8 b. 7 24 d. 7 8 ____ 13. Tell whether the fractions a. 8 4 76 and 38 are equivalent. equivalent b. not equivalent 5 9 c. 69 2 d. 73 60 9 ____ 14. Write a. 7 b. 63 as a mixed number. 7 2 3 ____ 15. Write 2 4 as an improper fraction. a. 7 4 c. 11 4 b. 23 8 d. 2 1 ____ 16. Victoria and Anne are sisters who both take piano lessons. Each day, Victoria practices piano for 2 3 and Anne practices piano for 1 hours. Do the sisters practice piano for the same amount of time? a. No ____ 17. Write the fraction a. b. 0.55 1.83 b. 22 12 Yes as a decimal. If necessary, round your answer to the nearest hundredth. c. d. 2 22.12 2.03 5 3 hours, Name: ________________________ ID: A ____ 18. Write the decimal 0.51 as a fraction in simplest form. 1 51 a. 2 c. 1 100 b. 1 51 d. 51 100 ____ 19. Write the decimal 1.71 as a mixed number in simplest form. 71 71 c. 1 100 a. 100 b. 7 1 10 d. 1 71 ____ 20. During a review game, Mr. Pai’s class correctly answered 69 questions on the first try. If there were 72 questions in the game, at what rate were questions answered correctly on the first try? Express your answer as a decimal. Round to the nearest hundredth. a. 0.958 c. 0.042 b. 1.043 d. 0.096 ____ 21. Compare the fractions a. 3 10 2 ? 6 . Write < or >. < b. > ____ 22. Compare the decimals 0.22 __?_ 0.79. Write < or >. a. < b. > ____ 23. Order –0.985, –0.95, 3 4 from least to greatest. a. –0.95, –0.985, 3 4 c. 3 4 b. –0.985, 4 , –0.95 d. –0.985, –0.95, 3 , –0.95, –0.985 3 4 Numeric Response - PICK ONE! 24. Two classes compete in a science fair. Each class splits into smaller groups, but every group, both classes included, must be the same size. The first class has 176 students, and the second class has 128 students. What is the greatest number of students each group can have? 1 1 25. A restaurant uses 47 3 cups of rice to make its daily pot of rice. Write a fraction that shows how many 6 -cups are used to cook rice each day at the restaurant. 3 Name: ________________________ ID: A Matching Match each vocabulary term with its definition. a. opposite e. b. integers f. c. absolute value g. d. multiple mixed number prime number composite number ____ 26. the distance of a number from zero on a number line, shown by | | ____ 27. the set of whole numbers and their opposites ____ 28. a number that is the same distance from 0 on a number line as a given number ____ 29. the product of any number and a whole number ____ 30. a number made up of a whole number that is not zero and a fraction Match each vocabulary term with its definition. a. equivalent fractions e. b. improper fraction f. c. nonterminating decimal g. d. rational number terminating decimal mixed number repeating decimal ____ 31. fractions that name the same value ____ 32. a decimal number that comes to an end ____ 33. a decimal in which one or more digits repeat infinitely ____ 34. a fraction in which the numerator is greater than or equal to the denominator ____ 35. any number that can be expressed as a ratio of two integers 4 Name: ________________________ ID: A Match each vocabulary term with its definition. a. least common multiple (LCM) e. b. prime number f. c. greatest common factor (GCF) g. d. mixed number composite number multiple prime factorization ____ 36. a number written as the product of its prime factors ____ 37. the smallest number, other than zero, that is a multiple of two or more given numbers ____ 38. a number greater than 1 that has more than two whole-number factors ____ 39. the largest common factor of two or more given numbers ____ 40. a whole number greater than 1 that has exactly two factors, itself and 1 Short Answer 41. The highest temperature recorded in the town of Westgate this summer was 100°F. Last winter, the lowest temperature recorded was –1°F. Find the difference between these extremes. 42. Miguel spends $35 a day for 4 days. He earns $21 a day for 5 days. Does Miguel end up with more or less money than he started with? By how much? 43. This morning at 8:00, the temperature was –7°F. Yesterday morning, the temperature was 6°F colder. What was yesterday’s temperature? 44. One way to factor the number 270 is 1 • 270. This number can be factored several other ways. Factor 270 the following ways: a. Use a factor tree to show the prime factorization of 270. b. Show a factorization of 270 that is not prime. 2 1 45. Consider the numbers 5 5 , 5.2, 5.02, 5 4 , and 5.333. a. b. Order the numbers from least to greatest. Write each of the fractions as a decimal, and each of the decimals as a fraction in simplest form. 5 ID: A Math II Chapter 2 test Answer Section MULTIPLE CHOICE 1. ANS: D Graph each player’s score on a number line. Mr. Williams’ score is farthest to the left, so it is the lowest score. Therefore, Mr. Williams is the winner of the tournament. DIF: Advanced TOP: 2-1 Integers KEY: integer | compare | order 2. ANS: D To add two integers with the same sign, find the sum of their absolute values and use the sign of the two integers. To add two integers with different signs, find the difference of their absolute values and use the sign of the integer with the greater absolute value. DIF: Average REF: Page 83 TOP: 2-2 Adding Integers KEY: addition | integers 3. ANS: A Substitute –13 for p and –50 for q. Then, find the difference. To subtract an integer, add its opposite. DIF: Average REF: Page 89 TOP: 2-3 Subtracting Integers KEY: evaluate | expression | integers | subtraction 4. ANS: B In multiplying integers, if the signs are the same, the product will be positive. If the signs are different, the product will be negative. DIF: Average REF: Page 95 TOP: 2-4 Multiplying and Dividing Integers KEY: integers | multiplication 5. ANS: D In dividing integers, if the signs are the same, the quotient will be positive. If the signs are different, the quotient will be negative. DIF: Average REF: Page 95 TOP: 2-4 Multiplying and Dividing Integers KEY: integers | division 6. ANS: A Multiply the rate per minute by the number of minutes. −15 • 48 = −720 DIF: Average REF: Page 95 TOP: 2-4 Multiplying and Dividing Integers 1 ID: A 7. ANS: B A number is prime if it is divisible by only 1 and itself; otherwise, it is composite. DIF: Basic REF: Page 106 KEY: divisibility | prime | composite 8. ANS: C 120 = 2 3 • 3 • 5 TOP: 2-6 Prime Factorization DIF: Advanced TOP: 2-6 Prime Factorization 9. ANS: B Find the GCF of the three numbers by either listing the factors, using prime factorization, or using a ladder diagram. DIF: Average REF: Page 111 TOP: 2-7 Greatest Common Factor KEY: GCF | greatest common factor | problem solving 10. ANS: B List multiples of 7, 10, and 20. Find the smallest number that is in all the lists. DIF: Basic REF: Page 114 TOP: 2-8 Least Common Multiple KEY: LCM | least common multiple 11. ANS: C Find the LCM of both numbers by either listing the multiples or using prime factorization. DIF: Average REF: Page 115 TOP: 2-8 Least Common Multiple KEY: LCM | least common multiple 12. ANS: D Find the GCF of 21 and 24. Divide the numerator and denominator by the GCF, 3. 21 21 ÷ 3 7 = 24 ÷ 3 = 8 24 DIF: Average REF: Page 120 TOP: 2-9 Equivalent Fractions and Mixed Numbers KEY: equivalent | fraction 13. ANS: A Find a common denominator and compare the numerators. If both fractions can be written with a common denominator and the numerators are equal, then the fractions are equivalent. DIF: Average REF: Page 121 TOP: 2-9 Equivalent Fractions and Mixed Numbers KEY: equivalent | fraction 14. ANS: B Divide the numerator by the denominator. Use the quotient and the remainder to write the mixed number. DIF: Average REF: Page 121 TOP: 2-9 Equivalent Fractions and Mixed Numbers KEY: convert | improper fraction | mixed number 2 ID: A 15. ANS: C Multiply the denominator and the whole number, and then add the numerator. Write the result over the denominator. DIF: Average REF: Page 121 TOP: 2-9 Equivalent Fractions and Mixed Numbers KEY: convert | improper fraction | mixed number 16. ANS: B Write the improper fraction as a mixed number. 5 2 = 13 3 Compare the mixed numbers. 2 2 13 = 13 Yes, the sisters practice piano for the same amount of time DIF: Advanced TOP: 2-9 Equivalent Fractions and Mixed Numbers 17. ANS: B To write a fraction as a decimal, divide the numerator by the denominator. DIF: Average REF: Page 124 TOP: 2-10 Equivalent Fractions and Decimals KEY: convert | decimal | fraction | rational number 18. ANS: D Use the place value of the last digit to the right of the decimal point as the denominator of the fraction. DIF: Basic REF: Page 125 TOP: 2-10 Equivalent Fractions and Decimals KEY: decimal | fraction | mixed number 19. ANS: C Use the place value of the last digit to the right of the decimal point as the denominator of the fraction. DIF: Average REF: Page 125 TOP: 2-10 Equivalent Fractions and Decimals KEY: decimal | fraction | mixed number 20. ANS: A Divide the number of questions in the game by the number correctly answered on the first try. DIF: Average REF: Page 125 TOP: 2-10 Equivalent Fractions and Decimals KEY: convert | decimal | fraction | rational number 21. ANS: A If the fractions have different signs, the negative fraction is less than the positive fraction. When both fractions have the same sign, write them with a common denominator. Then, compare the numerators to determine which fraction is greater. DIF: Basic REF: Page 128 KEY: compare | fraction TOP: 2-11 Comparing and Ordering Rational Numbers 3 ID: A 22. ANS: A Line up the decimal points. Compare the tenths place. If the tenths are the same, then compare the hundredths place. 0.22 < 0.79. DIF: Average REF: Page 129 TOP: 2-11 Comparing and Ordering Rational Numbers 23. ANS: D Write all of the numbers as decimals with the same number of places. Then, compare the decimals. DIF: Average REF: Page 129 TOP: 2-11 Comparing and Ordering Rational Numbers KEY: compare | decimal | fraction | order NUMERIC RESPONSE 24. ANS: 16 DIF: 25. ANS: DIF: Advanced TOP: 2-7 Greatest Common Factor 284 6 Advanced TOP: 2-9 Equivalent Fractions and Mixed Numbers MATCHING 26. ANS: C DIF: Basic REF: Page 77 27. ANS: B DIF: Basic REF: Page 76 28. ANS: A DIF: Basic REF: Page 76 KEY: integers | opposite | number line 29. ANS: D DIF: Basic REF: Page 114 30. ANS: E DIF: Basic REF: Page 121 TOP: 2-9 Equivalent Fractions and Mixed Numbers KEY: convert | improper fraction | mixed number 31. ANS: TOP: 32. ANS: TOP: KEY: 33. ANS: TOP: 34. ANS: TOP: KEY: 35. ANS: TOP: KEY: A DIF: Basic REF: Page 120 2-9 Equivalent Fractions and Mixed Numbers E DIF: Basic REF: Page 124 2-10 Equivalent Fractions and Decimals convert | decimal | fraction | rational number G DIF: Basic REF: Page 124 2-10 Equivalent Fractions and Decimals B DIF: Basic REF: Page 121 2-9 Equivalent Fractions and Mixed Numbers convert | improper fraction | mixed number D DIF: Basic REF: Page 129 2-11 Comparing and Ordering Rational Numbers convert | decimal | fraction | rational number 4 TOP: 2-1 Integers TOP: 2-1 Integers TOP: 2-1 Integers TOP: 2-8 Least Common Multiple KEY: equivalent | fraction ID: A 36. 37. 38. 39. 40. ANS: ANS: ANS: ANS: ANS: G A E C B DIF: DIF: DIF: DIF: DIF: Basic Basic Basic Basic Basic REF: REF: REF: REF: REF: Page 106 Page 114 Page 106 Page 110 Page 106 TOP: TOP: TOP: TOP: TOP: 2-6 Prime Factorization 2-8 Least Common Multiple 2-6 Prime Factorization 2-7 Greatest Common Factor 2-6 Prime Factorization SHORT ANSWER 41. ANS: 101°F Subtract the lowest temperature from the highest temperature. DIF: Average REF: Page 89 TOP: 2-3 Subtracting Integers KEY: integers | subtraction 42. ANS: Miguel ends up with $35 less than he started with. Miguel spends $35 a day. You can write this as −35. Multiply first, and then add. −35 • 4 + 21 • 5 = −140 + 105 = −35 DIF: Advanced 43. ANS: –13°F TOP: 2-4 Multiplying and Dividing Integers –7 – 6 = –13 Scoring Rubric: 4 The solution is correct, and all of the work is shown as above. or A different logical method is used to find the correct solution. 3 The solution is correct, but not all of the work is shown. 2 The solution is incorrect, but the work shows understanding of the concept. 1 The solution is incorrect, and the work shows no understanding of the concept. DIF: Average TOP: 2-3 Subtracting Integers KEY: integers | subtraction | Performance Assessment 5 ID: A 44. ANS: a. 270 ìî 10 • 27 ìî ìî 2•5 •3• 9 ì ì ì ìî 2 • 5 • 3 • 3 • 3 The prime factorization of 270 is 2 • 3 • 3 • 3 • 5 or, 2 • 3 3 • 5 270 b. ìî 10 • 27 ìî ìî 2•5 • 3•9 Another factorization is 2 • 3 • 5 • 9. (There are several other possibilities.) Scoring Rubric: 4 The solution is correct, and all of the work is shown as above. or A different logical method is used to find the correct solution. 3 Both solutions are correct, but not all of the work is shown. 2 The solution for part a is correct, but the solution for part b is incorrect. or The solution for part a is incorrect, but the work for part b is correct. 1 Both solutions are incorrect, and the work shows no understanding of the concept. DIF: Average TOP: 2-6 Prime Factorization KEY: factor tree | factorization | Performance Assessment | prime factorization 6 ID: A 45. ANS: a. 5.02, 5.2, 5 1 , 5.333, and 5 2 4 b. 5 2 5 5 = 5.4 1 5.2 = 5 5 1 5.02 = 5 50 1 5 4 = 5.25 1 5.333 = 5 3 Scoring Rubric: 4 The solution is correct, and all of the work is shown as above. or A different logical method is used to find the correct solution. 3 Both solutions are correct, but not all of the work is shown. 2 The solution for part a is correct, but the solution for part b is incorrect. or The solution for part a is incorrect, but the work for part b is correct. 1 Both solutions are incorrect, and the work shows no understanding of the concept. DIF: Average TOP: 2-11 Comparing and Ordering Rational Numbers KEY: compare | convert | decimal | fraction | order | Performance Assessment 7