MATH 45 - COLLEGE ALGEBRA/BUSN - PRACTICE EXAM # - FALL 00 - DR. DAVID BRIDGE MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the simple interest. Round to the nearest cent. ) $50 at 5% for years Interest = $9.75 Interest = $9. Interest = $. Interest = $.0 ) $60 at % for 0 months Interest = $4. Interest = $4.00 Interest = $600.00 Interest = $6.00 Find the present value of the future amount. Assume simple interest. Round to the nearest cent. ) $6,000 for 0 months; money earns 9% $6. $4,9.9 $4,.7 $4,67.90 4) $,000 for 9 months; money earns.5% $7,95.00 $6,9.7 $6,59.6 $7,04.70 Solve the problem. Assume simple interest. 5) Allan borrowed $500 from his father to buy a car. He repaid him after 0 months with interest of 4%. Find the total amount he repaid. $599. $5974.00 $60.00 $9. 6) A company has ordered 5 new personal computers at a cost of $900 each. They will not be delivered for 4 months. What amount should the firm deposit in an account paying 7.% to have enough money to pay for them? $4,07.5 $7,97. $7,.6 $7,656.4 Find the compound amount for the deposit. Round to the nearest cent. 7) $9,000 at % compounded annually for 4 years $9,55. $4,640.00 $,906.7 $50,90.00 ) $5000 at 7% compounded semiannually for years $590.9 $700.00 $654.05 $669.9 9) $900 at 0% compounded quarterly for 4 years $7.79 $0.56 $097.4 $660.00 Find the compound interest earned by the deposit. Round to the nearest cent. 0) $5,000 at 5% compounded annually for 5 years $444. $000.00 $750.00 $.59 ) $00 at % compounded quarterly for 6 years $79.00 $044.50 $4. $0.5 Find the effective rate corresponding to the given nominal rate. Round results to the nearest 0.0 percentage points. ) % compounded semiannually.00%.57%.0%.46% ) % compounded monthly.04%.0% 0.4%.0%
Find the amount that should be invested now to accumulate the following amount, if the money is compounded as indicated. 4) $500 at 7% compounded annually for yr $9.97 $0.0 $560.4 $7.7 5) $6600 at 6% compounded quarterly for 4 yr $50.00 $57. $75.0 $99.00 Solve the problem. Round to the nearest cent. 6) If inflation is 4% a year compounded annually, what will it cost in years to buy a house currently valued at $5,000? $,5.7 $,99.76 $,9. $,65. 7) June made an initial deposit of $5400 in an account for her son. Assuming an interest rate of % compounded quarterly, how much will the account be worth in 4 years? $6,6.9 $6,047.5 $959.56 $6,9.00 ) Sumi Kato's savings account has a balance of $5. After 6 years what will the amount of interest be at.5% compounded annually? $95.00 $5.0 $55.0 $504.0 Solve the problem. 9) A bank gives you two options to choose from for your investments: Option A: % annual interest rate compounded yearly; and Option B: 7.9% annual interest rate compounded quarterly. Decide which is the better investment at the end of years. Option A Option B 0) Mark and Kate are establishing a fund for their son's college education. What lump sum must they deposit in an account that gives % annual interest rate, compounded monthly, in order for them to have $60,000 in the fund at the end of 0 years? $7,0.4 $,607.4 $,.4 $9,5.4 Find the value. s ) 5 0.04 45.04.5 0.04.9 Find the future value of the ordinary annuity. Interest is compounded annually, unless otherwise indicated. ) R = $00, i = 0.06, n = 6 $64.0 $56.7 $697.5 $.04 ) R = $7500, i = % interest compounded semiannually for 9 years $,79.9 $56,79.9 $,596.60 $54,747.70 Find the periodic payment that will render the sum. 4) S = $6,000, interest is % compounded quarterly, payments are made at the end of each quarter for 5 years $9.77 $797. $0.95 $95.60 5) S = $55,000, interest is 4% compounded annually, payments made at the end of each year for 5 years $0,54.50 $447.66 $04.0 $570.
Solve the problem. 6) Lou has an account with $0,000 which pays % interest compounded annually. If to that account, Lou deposits $5000 at the end of each year for 4 years, find out the amount in the account after the last deposit. $,50.56 $5,70.56 $,50.56 $6,5.45 7) At the end of every months, Teresa deposits $00 into an account that pays 6% compounded quarterly. After years, she puts the accumulated amount into a certificate of deposit paying.5% compounded semiannually for year. When this certificate matures, how much will Teresa have accumulated? $47. $0. $40.54 $55.4 ) Mark wants to start an IRA that will have $450,000 in it when he retires in 7 years. How much should he invest quarterly in his IRA to do this if the interest is % compounded quarterly? $05.9 $6.6 $565.7 $57.7 Find the value. a 9) 0 0.0 9.5 9.6004 47.066 0.0004 a 0) 7 0.0 4.69 5.7466 5.064 9.796 Find the present value of the ordinary annuity. ) Payments of $490 made annually for years at 6% compounded annually $46.6 $47. $4554.55 $40.06 ) Payments of $9 made quarterly for 0 years at % compounded quarterly $7.09 $7. $94. $450.66 Find the lump sum deposited today that will yield the same total amount as this yearly payment (made at the end of each year for 0 years at the given interest rate, compounded annually). ) $9500 at 4% $4,77.05 $9,0. $,77.40 $9,079.5 Find the payment necessary to amortize the loan. 4) $000; 6% compounded annually; 7 annual payments $0. $79. $6.04 $0.6 5) $00; % compounded quarterly; quarterly payments $5.9 $5.4 $6.70 $66.96 Find the monthly house payment necessary to amortize the following loan. 6) In order to purchase a home, a family borrows $0,000 at % for 0 yr. What is their monthly payment? $7. $74.09 $76.6 $4.44 Solve the problem. 7) Tasha borrowed $5,000 to purchase a new car at an annual interest rate of 0%. She is to pay it back in equal monthly payments over a year period. What is her monthly payment? $44.0 $567.7 $4.67 $5.00
) Julio buys a bike which has a cash price of $50. He agrees to take a one-year loan for the entire amount at 7%, payable in installments. After of the payments, he gets some birthday money and decides to pay off his loan. Find the unpaid balance. $.7 $90. $59.7 $.00 Determine whether the given ordered set of numbers is a solution of the system of equations. 9) (, ) x + y = 7 x + y = No Yes 40) (-6, 4) 4x + y = - x + 4y = - No Yes Solve the system of two equations in two variables. 4) x + y = 5 4x + 7y = 0 (-, ) (, ) (-, ) No solution 4) x + 4y = 6 -x + 5y = 0 (, ) (0, 4) (-4, 0) No solution 4) -6x + 4y = 0 7x - 5y = - (, ) (, 6) (-4, -) No solution Multiply both sides of each equation by a common denominator to eliminate the fractions. Then solve the system. 44) x + y = - x - y = -7 (-6, ) (5, ) (-5, ) No solution 45) x - y 5 = 0 4x 7 + 4y 5 = 7 5, 4, 4 4, 4, Solve the problem by writing and solving a suitable system of equations. 46) Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $05 for days and 00 miles, while Mary was charged $4 for 5 days and 600 miles. What does Best Rental charge per day and per mile? $6 per day and 9 cents per mile $7 per day and 0 cents per mile $9 per day and 6 cents per mile $5 per day and 0 cents per mile
47) A shopkeeper orders 56 pounds of cashews and peanuts. If the amount of cashews he orders is 0 pounds less than the amount of peanuts, how many pounds of peanuts did he order? pounds 4 pounds 6 pounds pounds 4) Carole's car averages 5. miles per gallon in city driving and 5.5 miles per gallon in highway driving. If she drove a total of.9 miles on 9 gallons of gas, how many of the gallons were used for city driving? 4 gallons 0 gallons 6 gallons 5 gallons 49) If 40 pounds of tomatoes and 0 pounds of bananas cost $9 and 0 pounds of tomatoes and 50 pounds of bananas cost $ 5, what is the price per pound of tomatoes and bananas? tomatoes: $0.50 per pound; bananas: $0.0 per pound tomatoes: $0.60 per pound; bananas: $0.0 per pound tomatoes: $0.40 per pound; bananas: $0.4 per pound tomatoes: $0.60 per pound; bananas: $0.7 per pound Find the dot product. 50) -4 5 50 6-6 5-0 40-4 Does not exist 5) 5-4 6 50-6 5-0 40-4 Does not exist 5) 7-5 4-66 4-0 -6 5-7 - -5 Does not exist Solve the problem. 5) What is the size of the matrix? 4 5-4 - x 6 x 54) What is the size of the matrix? - 7 x 4 4 4 x 55) What is the size of the matrix? 9-5 5 x 4
56) What is the size of the matrix? 4 4-0 Perform the indicated operation where possible. -9 6 57) + 5 - - 4 5 4 0 4 9 Not defined 5) 4 + 4 Not defined 59) - 0 4 9-4 - 7 0 6-7 4-7 0-6 6 - -7 0 6-6 Not defined 60) - 7-4 -5 7 0-5 4-5 4 0 Not defined Perform the indicated operation. 6) Let B = - 6 6 -. Find -B. - 4 4-5 - - 6 6 6 - - -6 6) Let C = -4 6 6 -. Find C. - 6 - - 4 6) Let C = -6 4 - and D = - -. Find C - D. - 9-6 - - -9 6
64) Let A = -5 and B = 0. Find A + B. - -7 4-0 4-9 4 Solve the problem. 65) Barnes and Able sell life, health, and auto insurance. Sales for May and June are given in the matrices. M = Life Health Auto 0,000 5,000 000 0,000 0 7,000 Able Barnes J = 70,000 0 0,000 0,000 5,000,000 Able Barnes Find the matrix that would give total sales for the months of May and June. 90,000 0,000 40,000 40,000 7,000 50,000 0 49,000 90,000 5,000,000 50,000 5,000,000 90,000 5,000,000 50,000 5,000 49,000 66) Carney and Dobler sell home and mortgage insurance. Their sales for the months of May and June are given in the matrices. M = Home Mortgage,000 45,000 Carney 7,000 7,000 Dobler J = 5,000 44,000 4,000,000 Carney Dobler Find the matrix that would give the change in sales from May to June. 000-000 -000-6000 -000 000 000 6000-6000 7000 6000-7000 67) The matrix shows the average number of wax and buff treatments each of workers in a car wash can do in a day. Give the matrix that shows what each worker can do in 4 days. Wax Buffs 6 0 T = 9 5 4 40 6 0 Ford Morton Porter 64 4 5 40 4 6 0 4 40 6 0
Find the dimensions of the matrix product AB and the product BA, whenever the product exist. 6) A is x, B is x. AB is x, BA is x. AB is x, BA is x. AB is 6 x, BA is 6 x. AB is x 6, BA is x 6. 69) A is x, B is x. AB is nonexistent, BA is x. AB is x, BA is x. AB is x, BA is nonexistent. AB is x, BA is x. 70) A is x, B is x. AB is x, BA is x. AB is nonexistent, BA is x. AB is x, BA is x. AB is x, BA is nonexistent. 7) A is 4 x, B is 4 x. AB is x 4, BA is 4 x. AB is 4 x, BA is x 4. AB is 4 x 4, BA is x. AB is nonexistent, BA is nonexistent. Given the matrices A and B, find the matrix product AB. - - 0 7) A =, B = Find AB. - 4 0-4 4-6 - 6 4-6 6-6 4 7) A = 0 - -6-4, B = - 0 - Find AB. 0 - - - - -4-74) A = - 4, B = 0-4 - Find AB. AB is not defined. -7 4-4 4-7 -4 0-6 - 75) A = - 0 4 -, B = 5 0 - Find AB. AB is not defined. 5-0 5-6 6-5 5-6 -0 6 5-5 5 0 0 Determine whether the two matrices are inverses of each other by computing their product. 5-76) and - 5 Yes No
77) 0 0 and - 0-0 Yes No 7) -5-7, - 7-5 Yes No Find the inverse, if it exists, of the given matrix. 5 79) 5 5 - - 5 5 5-5 - - -5-5 -5 0) A = - - 5-5 - 5 5-5 - 5-5 5-5 - 5-5 - 5 5-5 - 5-5 - 5 5 ) A = - - - -6 - No inverse - 6 6 6 6-6 6 - Solve the problem. ) Three different high schools plan to order the same three text books. School A plans to order 0 of book, 50 of book, 0 of book. School B plans to order 40 of book, 70 of book, 0 of book. School C plans to order 00 of book, 90 of book, 0 of book. The cost of book is $5 per copy, the cost of book is $0 per copy, and the cost of book is $5 per copy. What matrix product displays the cost to each school of buying the textbooks? Display the two matrices which must be multiplied and their product. 5 0 5 5 0 5 0 50 0 40 70 0 00 90 0 50 0 90 = 450 4400 00 5 0 5 = 50 400 50 5 0 5 0 40 00 50 70 90 0 0 0 90 40 0 = 900 750 4050 = 50 00 5500
) Three different clothing stores order the following amounts of clothing by a certain designer: Jackets Shirts Suits Store : 0 0 0 Store : 0 40 50 Store : 0 40 50 The unit prices of each product are given below for two suppliers: Supplier A Supplier B Jacket 5 90 Shirt 0 0 Suit 0 00 What matrix product displays the cost to each store of buying the clothes from each supplier? Display the two matrices which must be multiplied and their product. 0 0 0 5 0 0 0 5 90 50 9000 0 40 50 0 40 50 0 0 = 4950,050,750 0 40 40 0 50 50 0 0 0 00 = 0,00,000,50,400 0 0 0 0 40 50 0 40 50 5 90 0 0 0 00 = 4950 500,050,00,750,900 0 0 0 0 40 50 0 40 50 5 90 0 0 0 00 = 0,50,50 6,650 Solve the matrix equation for X. 5-6 4) A =, B = 5 -, AX = B -6-5 -4 4 - -6 40
Answer Key Testname: MATH 45 - PRACTICE EXAM # ) A ) D ) C 4) B 5) A 6) C 7) A ) D 9) B 0) A ) D ) C ) A 4) B 5) A 6) D 7) A ) C 9) B 0) A ) C ) C ) A 4) A 5) A 6) D 7) A ) D 9) B 0) C ) B ) B ) B 4) B 5) A 6) C 7) A ) B 9) B 40) A 4) A 4) B 4) C 44) C 45) A 46) A 47) B 4) A 49) A 50) B 5) No Correct 5) D 5) C 54) B 55) A 56) D 57) A 5) D 59) C 60) D 6) B 6) D 6) D 64) B 65) D 66) A 67) D 6) A 69) D 70) D 7) D 7) D 7) C 74) B 75) A 76) A 77) B 7) A 79) A 0) A ) C ) B ) C 4) B