Test Bank for Differential Equations and Boundary Value Problems: Computing and Modeling, 5th Edition

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Chapter 1 Form AName___________________________________MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers thequestion.Answer the question or solve the problem.1) I'm thinking of a positive number. The number is even. The number is less than98. The number is divisible by 7. The sum of its digits is divisible by 10. What isthe number?A) 91B) 70C) 28D) Not enough information to know1)Use the pattern in the sequence or chart to find the missing number.2) 6, 12, 18, 30, 48,?A) 78B) 20C) 22D) 182)Solve the problem.3) If one must always move downward or to the right in the grid shown, how manypaths are there from the top left corner to the bottom right corner?A) 24B) 20C) 15D) 643)Use the pattern in the sequence or chart to find the missing number.4) Use the 100 chart to find the missing number.32A) 62B) 63C) 35D) 454)Solve the problem.5) How many rectangles are in a figure made by 6 square tiles lined up in a row?Use the pattern below to solve.A) 15B) 21C) 13D) 235)1

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Count the number of items asked for in the problem.6) Squares (of any size)A) 9B) 12C) 8D) 116)Solve the problem.7) Find the 13th pentagonal number that corresponds to the following dot sequence.A) 260B) 91C) 169D) 2477)8) Who am I? If you multiply me by 12 and add 21, the result is 117.A) 8B) 1425C) 1656D) 728)Provide an appropriate response.9) Look for a pattern in the sequence of figures shown below. How many trianglesare needed for the 4th figure? The nth figure?A) 14, 4n-2B) 12, 3nC) 12, 4n-4D) 14, 3n+29)Solve the problem.10) How many different amounts of money can you pay if you use two coinsincluding only nickels, dimes, and quarters?A) 5 amountsB) 6 amountsC) 7 amountsD) 4 amounts10)Answer the question.11) A cell has at least 3 and at most 47 nuclei. How many cells must a scientist viewunder his microscope to be certain that at least two cells have the same number ofnuclei?A) 44 cellsB) 47 cellsC) 45 cellsD) 46 cells11)2

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Provide an appropriate response.12) Look for a pattern in the sequence of figures shown below. How many squares areneeded for the 4th figure? The nth figure?A) 14, 4n+3B) 13, 4n-3C) 13, 3n+1D) 12, 4n-212)Solve the problem.13) Find the number of terms in the following arithmethic progression:-4,3, 10 , . . . , 157A) 25B) 23C) 22D) 2413)Provide an appropriate response.14) Look for a pattern in the sequence of figures shown below, and use yourreasoning to draw the next figure.A)B)C)D)14)Solve the problem.15) Arrange 5 square tiles so that they make a solid pattern with the smallestperimeter possible. The tiles are equal in area and touch at least one other tilealong an entire edge.A)B)C)D)15)3

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16) Place the numbers 9, 11, 12, 13 and 14 in the circles to make the sum across andvertically equal to 34.A)131411912B)141291311C)13129141116)4

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D)131112149Guess the rule used to change one number into another.17) Number Chosen34567Number Given Back1118273851A) n2+nB) n2+2C) 4n-1D) None of the above is the correct rule.17)Solve the problem.18) The numbers on the right in the equations below are the hexagonal numbers. Usethe sequence of equations to find a formula for hn, the nth hexagonal number.1=11+5=61+5+9=151+5+9+13=28..............A) hn=n(2n-1)B) hn=2n(n-1)C) hn=(n-1)(2n+1)D) hn=n(2n+1)18)Provide an appropriate response.19) Consider the following 1×1, 2×2, and 3×3 match stick designs.How many match sticks are needed for a 7×7 design?A) 53B) 112C) 98D) 5619)5

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Solve the problem.20)The number sequence that corresponds to the figures above is 1, 6, 15, 28, . . . .These are the hexagonal numbers H1, H2, H3, H4, . . . .Use inductive reasoning to find a formula for the nth hexagonal number, Hn.A) Hn=n(2n-1)B) Hn=(n+1)(2n-1)C) Hn=5n-4D) Hn=2n(n-1)20)6

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Answer KeyTestname: CHAPTER 1 FORM A1) C2) A3) B4) D5) B6) D7) D8) A9) A10) B11) D12) B13) D14) A15) C16) B17) B18) A19) B20) A7

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CHAPTER 1 FORM BName___________________________________MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers thequestion.Use the pattern in the sequence or chart to find the missing number.1) 3, 2, 1, 0,-1,?A) 1B)-3C)-2D) 01)Solve the problem.2) Find the 36th term in the number sequence that corresponds to this dot sequence:A) 39B) 110C) 108D) 1072)3) Use the sequence of equations to find the unknown sum.1=0+11+3+1=1+41+3+5+3+1=4+9. . . . . . . . . . . . . . .1+3+5+. . .+ 15+. . .+5+3+1=?A) 36+ 49=85B) 7+ 8=15C) 49+ 64=113D) (8+ 7)2=2253)4) Use the sequence of equations to find a general rule.1=0+11+3+1=1+41+3+5+3+1=4+9. . . . . . . . . . . . . . .Fill in the blank to complete the equation:1+3+5+. . . (2n+1)+. . .+5+3+1=?A) (n - 1)2+(n + 1)2B) n2+(n - 1)2C)n - 122+n + 122D) n2+(n + 1)24)5) Who am I? If you multiply me by 14 and add 28, the result is 98.A) 1400B) 5C) 9D) 65)1

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6) Find the 16th triangular number that corresponds to the following dot sequence.A) 257B) 136C) 128D) 1206)Answer the question.7) An average newspaper contains at least 16 pages and at most 87 pages. Howmany newspapers must be collected to be certain that at least two newspapershave the same number of pages?A) 70 newspapersB) 72 newspapersC) 73 newspapersD) 71 newspapers7)Solve the problem.8) Anthony has 11 coins consisting of dimes, nickels, and pennies. The total value ofthe coins is 63 cents. What coins does Anthony have?A) 4 d, 4 n, 3 pB) 3 d, 6 n, 3 pC) 4 d, 3 n, 8 pD) 3 d, 6 n, 2 p8)9) How many different amounts of money can you pay if you use two coinsincluding only nickels, dimes, and quarters?A) 6 amountsB) 5 amountsC) 7 amountsD) 4 amounts9)Guess the rule used to change one number into another.10) Number Chosen56789Number Given Back2630343842A) 4n+6B) n2+10C) 3n+8D) None of the above is the correct rule.10)Solve the problem.11) Who am I? If you multiply me by 4 and subtract 9, the result is 59.A) 104B) 8C) 17D) 3211)2

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12) Place the numbers 4, 5, 6, 7 and 9 in the circles to make the sum across andvertically equal to 20.A)49657B)76594C)46957D)7645912)Answer the question.13) Use the mathematical machine to find the input corresponding to an output of 19.A) 57B) 6.8C)-1.5D) 3.813)3

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Answer the question or solve the problem.14) Jesse forgot in which chapter she has math homework. She knows it is withinchapters 3 to 7 and deals with exponents. She knows that her homework is notfrom chapter 3. Last month they worked on chapter 4 so they're at least twochapters ahead by now. The final will not be for another month. She estimates thatthey do two chapters a month and the book has 8 chapters. When the final comes,they will have just finished the entire book. Which chapter should Jesse look in todo the homework assignment?A) Chapter 5B) Chapter 6C) Chapter 7D) Chapter 414)Solve the problem.15) How many posts does it take to support a straight fence 140 feet long if posts areplaced every 10 feet?A) 15B) 14C) 13D) 1615)Use the pattern in the sequence or chart to find the missing number.16)-2,-4,-8,-16,-32,?A)-48B)-64C) 48D) 6416)Solve the problem.17) How many cuts are needed to divide a pole 16 feet into 2-foot sections?A) 2B) 3C) 7D) 817)18)The number sequence that corresponds to the figures above is 1, 6, 15, 28, . . . .These are the hexagonal numbers H1, H2, H3, H4, . . . .Use inductive reasoning to find a formula for the nth hexagonal number, Hn.A) Hn=(n+1)(2n-1)B) Hn=n(2n-1)C) Hn=5n-4D) Hn=2n(n-1)18)Provide an appropriate response.19) A pet shop has a total of 15 dogs and birds. Altogether there are 42 feet. Howmany dogs are there and how many birds?A) 6 dogs and 9 birdsB) 5 dogs and 10 birdsC) 7 dogs and 8 birdsD) 8 dogs and 7 birds19)4

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Answer the question.20) How many people must be in a room to be sure that at least two were born in thesame month of the year?A) 2 peopleB) 13 peopleC) 3 peopleD) 12 people20)5

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Answer KeyTestname: CHAPTER 1 FORM B1) C2) D3) C4) D5) B6) B7) C8) A9) A10) A11) C12) C13) D14) B15) A16) B17) C18) B19) A20) B6

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CHAPTER 1 FORM CName___________________________________SHORT ANSWER. Write the word or phrase that best completes each statement or answers thequestion.Find all possible solutions to the problem.1) The sum of two whole numbers is 67. Their difference is less than five.What are the possibilities for the two numbers?1)Solve the problem.2) In how many ways can you exactly cover the last two diagrams with"dominoes" that are just the size of two small squares?2)Find all possible solutions to the problem.3) When Beth made a purchase, she received 27 cents in change. What arethe possible combinations of coins she could have received?3)1

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Solve the problem.4) The figure below shows an addition pyramid, in which each number isthe sum of the two numbers immediately below.1789354For the incomplete addition pyramid below, show that the values in thesquare can be determined by forming and solving an equation in theunknown variable shown.39x1294)2

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