Math 58 Test # 3 Fall 2014 Chapter 9, Part 1 Instructor: Smith-Subbarao

Size: px

Start display at page:

Download "Math 58 Test # 3 Fall 2014 Chapter 9, Part 1 Instructor: Smith-Subbarao"

Theresa Weaver
5 years ago
Views:

1 Math 58 Test # 3 Fall 2014 Chapter 9, Part 1 Instructor: Smith-Subbarao Solutions Name Score: If you are not sure about notation, please ask for help! (4 + 1 ) / x means is in numerator and x is in the denominator. (4 + 1) / (x + 2) means that is in the numerator and (x + 2) is in the denominator. If there is a mixed number, e.g., 3 1/2, there will be a space between the number and the fraction. Compare with 31/2 where then is no space, and it means 31 divided by 2. Directions: Show all work and circle/box your answers. Partial credit may be given, even if the answer is incorrect, if your work is clear attach additional scratch pages you wish to be considered. If you do not show your work, you may not get credit. Unless otherwise instructed, leave all answers as fraction; improper fractions are OK, but you will lose one point if you do not simplify your fractions. Scoring: Each problem was 5 points. I curved the final answer by adding 10 points to your score, then calculating the percent. Problem 7 befuddled everyone, so I eliminated it, giving a total of only 14 problems. If I gave you points on problem 7, I added that to your final % grade. NO: Telephones, Books, Notes; CALCULATORS ARE NOT ALLOWEED Suggestions: Choose the problems you understand best to work first. If you get stuck, write down what you do understand for partial credit and move on Show your work clearly

2 Check your solutions Evaluate your solutions for reasonableness

3 1. If the solution to mx = 10 is x = 1/2, what is m? substitute for x: m (1/2) = 10 Multiply both sides by 2: m = Evaluate the expression x 3 + y 4 + 3xy for x = -2 and y = -1. Substitute: - (-2) 3 + (-1) 4 + 3(-2)(-1) = Joe came home from school very excited. He has learned a new way to multiply by a two digit number: You take the larger number and make it into the number of tens plus the number of ones. Then you multiply each of those by the smaller number and add them together. He gives the example that 5 x 31 = 5 (30 + 1) = 5 x = = 155. a. What property(s) of arithmetic is he using in this method? The distributive property: a (b+c) = ab + ac b. Using Joe s method, multiply 6 x 21. Show all the steps for full credit. 6x21 = 6 (20 + 1) = = Evaluate: a. The product of a number and its multiplicative inverse. n x 1/n = 1 Product means times b. The quotient of a number and its additive inverse. a / (-a) = -1 quotient means divide

4 5. The longest interstate in the US is I-90, which connects Seattle to Boston. The second longest is I-80, which connects San Francisco to Teaneck NJ, is miles shorter than I-90. If the length of I-80 is m miles, express the length of I-90 in terms of an algebraic expression containing m. Length of I-80 is miles. This is shorter than I-90. To get I-90 have to add miles (m of them) I-90 = m miles 6. Solve for y: 7(2y + 1) = 18 y 19 y. Combine terms on the right hand side: 18y 19y = -y Distribute the 7: 14y + 7 = -y Add y to both sides 15y = 7 Divide both sides by y y = 7/15 7. There are five classrooms on one side of a school s science building. They are numbered with consecutive even integers. If the last room (the one with the highest number) on that side of the building is numbered x, write an expression for the sum of the five classroom numbers. (Hint: draw a picture of the classrooms and label them with their numbers to discover a pattern.) Let x be the number of the highest numbered room. Since they are all consecutive evens, what is the next smallest? Next is x-2, then x 4, x 6, x - 8 If we add them all together, we have x + x-2 + x-4 + x-6 + x-8. This is 5x ( ) = 5x 20 Since no one got this right, I made it a bonus question. You got 1 point for simply drawing the rooms and trying to label them. Another point if you made a reasonable attempt at an equation. No one got more than 2 points. Sorry. I didn t think it would be this hard. 8. Solve for n: -3n 1/3 = 8/3. Add 1/3 to both sides: -3n = 9/3 = 3 Divide both sides by -3: n = -1 You can clear the fraction first and get the same result: -9n 1 = 8, -9n = 9, n = -1

5 9. Simplify the following fractions. You do not need to write the solution as a mixed number. (Hint: Remember prime factorization.) a. 360/ = 2x2x2x3x3x5 72 = 2x2x2x3x3 360/72 = 5 b. 81/ = 3x3x3x3 549 = 3x3x61 81/549 = 9/ Combine: 8 wz + 6 wzk 3wz + 5wk 2 3zk + ½ wk 2. 5(wz) + 6wzk 3zk + (5 ½) wk 2 The only problem here was adding 5 and ½. You can leave it at 5 ½, 5.5 or 11/2. All are correct. 11. Solve for r: r 8.6 = Add 8.6 to both sides: r = = r = 0.5

6 12. Solve for x: 10 3x 6 9x = 7. Start by combining terms: -12x + 4 = 7 Subtract 4 from each side: -12x = 3 Divide each side by -12: x = -1/4 13. Evaluate: 1/3 (5 + 1/2) 1/9. This is not an equation: You can t multiply both sides by 3. If you do, you have to divide by 3 in the end!!! Start with the parentheses: 1/3 ( 11/2) 1/9 Multiply 1/3 by the parentheses to get 11/6 1/9 Common denominator is 18: 33/18 2/18 = 31/ Solve for c: c + 1/6 = 3/8 + 2c Subtract c fro both sides: 1/6 = c + 3/8 Subtract 3/8 from both sides: c = 3/8 1/6 Common denominator is 24: c = 4/24 9/24 c = -5/ Evaluate (1/3)(4 + 1/2) 5 3 Again, you cannot multiply to get rid of the fraction. This is an order of operations problems: First evaluate the parentheses: (1/3)(9/2) 5 3 Now, start the multiplication from left to right: 9/6 5 3 Since 9/2 = 3/2, we put that in = 3/2 5 3 Divide 3/2 by 5 and get: 3/10 3 Common denominator is 10 and we get: 3/10 30/10 = -27/10

Test 4 also includes review problems from earlier sections so study test reviews 1, 2, and 3 also.

MATD 0370 ELEMENTARY ALGEBRA REVIEW FOR TEST 4 (1.1-10.1, not including 8.2) Test 4 also includes review problems from earlier sections so study test reviews 1, 2, and 3 also. 1. Factor completely: a 2