Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Name:________________________ Math 311 – Fall 2008 Take Home Final Instructions: Because this is a take home final and calculators are allowed as well as your books and notes, it is even more important that you show all your work. Fractions and decimals need to be worked using fractions or decimals respectively, and work for LCD’s, building higher terms and long division and multiplication must always be shown. You are allowed to use any resource except the help of another person. This test is due on Wednesday, December 17, 2008. It needs to be handed in prior to the start of the in-class portion of the final. If it is not received by the end of class and prior to the start of the in-class portion, it will not be accepted. Good luck! 1. a) Write the prime factorization of the following numbers. Write the final answer using exponential notation. Work must be shown. 20 b) 30 c) 24 2. Find the LCD of 20, 30 & 24 Write the answer using exponential notation and then expand and simplify to a number. 3. For 5/24, build the higher term so that the new denominator is 72. 4. a) What are all the factors each of the following. 72 b) 5. Find the GCF of 6. Give the following fraction in lowest terms. Show your work by canceling or division. 72 108 Y. Butterworth 108 72 & 108 Take Home Final – Fall 2008 1 7. Give both the improper fraction and the mixed number that represents the shaded portion of the picture below. Give the 8. Write the following number in words. Watch spelling. 97.043 ________________________________________________________________________ 9. Round 89.945 to each of the specified places. a) ones b) tenths _________________________________ c) hundredths _____________________________ 10. Fill in the following table by making the conversions between decimals, fractions and percentages. Work must always be shown – I have left room below the table for that purpose. Fraction Decimal Percent 4 /9 1.2 67.5% 11. Simplify the following using order of operations. Do not use the distributive property. Show your work for each step in the order of operations. Fractions stay in fractions _________________________________ and decimals stay in decimals. You may use your calculator for calculating intermediate numbers, like parentheses answers and product answers and quotient answers, but I must see intermediate steps. a) (1/4)2 (2 ½ ¾) + 5/7 Y. Butterworth b) Take Home Final – Fall 2008 5 + 0.1(1.5 2.39) 0.1 2 c) 12. 5 + 9(3 + -1) 6 16 4 16 Find the a) b) d) area perimeter 9(-1 + -8) + 34 2 3 5 + 4 of the patio with the following shape 90 feet 70 feet 60 feet 70 feet 40 feet 20 feet 13. The following are word problems and therefore must show setup, an algebraic equation and the solution to that equation solving the problem. a) Billy, June and Joe go to the movies. Each gets a ticket costing $6.50, drinks costing $2.50 each, and Billy and June each have popcorn that costs $4.25 each, Joe buys candy instead. If their total cost is $39, what was the cost of Joe’s candy. This must be set up as a missing addend problem. Note that there are 3 instances of multiplication! Y. Butterworth Take Home Final – Fall 2008 3 b) The difference in the elevation of Mt. Rushmore and Death Valley is 7524 feet, and the elevation of Mt. Rushmore is 7242 feet, what is the elevation of Death Valley. You must use a missing subtrahend setup. c) If the amount of rock in each bag is 3.25kg, how many bags weigh 45.5 kg? This must be set up as a missing factor problem. d) The surface area of the room is 272 square feet. The paint that you have chosen will need two coats, and it covers 150.5 square feet per gallon. How many gallons will you have to buy in order to get two coats of paint on your walls? e) The train travels at 53 mph. How long will it take for the train to travel a distance of 385 miles? (If necessary, round your answer to the nearest tenth of an hour.) You must use a missing factor set-up. Y. Butterworth Take Home Final – Fall 2008 4 f) Susan deposits $2500 in her account which earns 5 1/4 % simple annual interest. If she leaves the money in the account for 2 ¾ years, how much interest should she expect to make at the end of the time? There must be an equation, even if it is very simple and all work must be shown with the decimal conversions. EC) Edgar and Sam each have a state quarter collection. Edgar has collected five less than twice the number of quarters that Sam has collected. Between Sam and Edgar they have $7 in quarters. How many quarters does each boy have? 14. Translate each of the following into expressions or equations. If there is an unknown number let that number be x. Do not simplify. a) The difference of some number and the product of fifteen and the sum of the number and negative 9. b) The quotient of nine subtracted from some number and 27. c) Twenty-three less some number is equivalent to five more than twice that number. d) Three less than some number is divided by the product of the number and nine. Y. Butterworth Take Home Final – Fall 2008 5 15. a) Show all work for full credit. Change decimals to fractions and/or fractions to decimals in order to compare. Too compare fractions build the higher terms and compare numerators, or use the cross product trick shown in class. Use <, > or = to compare. - | - 95| - ( - 45) b) | 918 | | - 918 | c) 5 /8 0.675 d) 0.885 0.889 e) 3 /5 7 f) - 34 (-3)4 g) 280 16. Circle the problem below for which the final answer would be undefined. a) -28 + 28 b) 5 + 30 5 + 30 -28 + 28 17. Solve each of the following. Show all work using distributive property, addition property and multiplication property where needed. Box your final answer. a) 6x 5 + 9x = 7 4x 12 b) 2 3(5x + 2) = 2(3 5x) c) 1.5(x 0.2) + 3 = 2.7x d) 2 Y. Butterworth /12 281 Take Home Final – Fall 2008 /3 1/3 x = 1/5 + 2/5 x 6 18. Simplify the following polynomial problems. a) 2(x + 3) 5x + 9(x 3) + 2 b) (3x2 + 2x 0.8) (0.1x2 + 5x 0.09) 19. Evaluate the following using: b) (½ x 2/5) + (3/5 x 9) x = 3, y = -2 and z = ½ If the problem involves fractions the final answer must be in fractions for full credit. a) x2 y b) x + (y z)2 20. Find the LCD for 2x2y3z & 3x3yz2 21. Build the higher term for the following: 22. Find the GCF of the terms and then factor the polynomial, rewriting as a product of the GCF and a polynomial. 15x2y3z 18xy2z2 + 24x3y c) 2 3x2y3 x + y z2 = ________ 18x3y3 Note: There are 3 questions I have not asked on this test that I will expect you to know on the in-class portion of the final. Study for these: a) Adding & Subtracting Real Numbers (with Fractions & Decimals too) b) Sets of numbers: Real #’s, Integers, Rational #’s, Whole #’s & Natural #’s c) Properties of the real numbers Y. Butterworth Take Home Final – Fall 2008 7