Math 115 Chapter 4 Exam - Part 1 Spring Break 2011

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1 Spring 20 Name: Math 5 Chapter 4 Exam - Part Spring Break 20 Directions: i. On 8.5" x " paper, show all relavent work. No work, no credit. ii. On two 882-E SCANTRON forms, fill in all your answers. iii. This exam is due April 27, 20. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Identify the base and the exponent. ) (0x)5 Base: 0x, exponent: 5 Base: 25, exponent: 5 Base: 5, exponent: 0x D) Base: x, exponent: 5 2) -60 Base: 6, exponent: 0 Base: 0, exponent: -6 Base: 0, exponent: 6 D) Base: -6, exponent: 0 3) (-9y)7 Base: y, exponent: 7 Base: 7, exponent: -9y Base: -9, exponent: 7 D) Base: -9y, exponent: 7 4) y 9 Base:, exponent: 9 Base: y, exponent: 20 Base: 9, exponent: y D) Base: y, exponent: 9 Simplify. Assume that no denominator is zero and that 00 is not considered. 5) D) 492 6) (6x5)(2x3) 2x8 8x5 8x8 D) 2x5 7) 24k 3 6k 4k2 8 8k2 D) 4k 8) a 6 a4 a.5 a0.5 D) a2 GC -

2 9) -70x 5-0x3 7 7x5 7x D) 7x2 0) 32m 6p2 8m0p 4m4p2 4m 4 p 4p m4 D) 4mp Simplify the expression. ) D) 2 2) x0 0 x D) - 3) 4x0 4 0 D) 4x 4) D) 2 5) D) 2 6) 30 + (-0)0-7 2 D) 0 7) (-4)0 + (-4) D) -2 Simplify. 8) (55) D) 57 9) (-5a5)3 (-5)5a5 (-5)5a5 (-5)3a5 D) -5a5 2

3 20) (3r8)2 3r6 9r0 9r8 D) 9r6 Simplify. Assume that no denominator is zero and that 00 is not considered ) x 25 x 25x2 5 x2 D) 25 x2 22) a3 b4 2 a 4 b8 a 8 b6 a 6 b4 D) a 6 b8 23) x5y z3 5 x 0y5 z8 x 5y25 z5 x 25y5 z5 D) x 25y5 z3 24) a5 6-7b2 - a 7,649b8 a 7,649b8 a30 7,649b2 D) - a30 7,649b2 25) 4x6y4 8z8 2 6x 2y8 8z0 6x 2y8 64z6 6x 2y6 64z6 D) 6x 8y6 64z0 26) 2 4 5g 6 625g4 2 5g4 6 5g4 D) 6 5g Express using positive exponents. Then, if possible, simplify. 27) D) ) (-3 ) D) - 9 3

4 29) x-4 x4 x4 4x D) x-4 30) x-3 3x x3 x-3 D) x3 3) c c c3 27 c3 D) 27c3 32) 3 u -4 u 8-8 u4 u 4 8 D) 8u4 Express the following using negative exponents. 33) D) 53 34) (-)-7 D) 7 35) a a a- -a D) (-)-a Simplify. Do not use negative exponents in your answer. 36) D) 38 37) x x-4 x3 x3 x5 D) x5 4

5 38) y-6 y-2 y4 y8 y-8 D) y8 39) (a-3b-2)(a-2b-5) a5b7 a5b5 a 5 b7 D) b 7 a5 40) (x-4y-5)(x8y-9) x4 y4 y 4 x4 x4y4 D) x4y4 4) (y-8z-5)(y-3z-8) y5z3 yz3 z 3 y D) y3z 42) (x-8y0z4)(x-4y-4z8) x7y2z4 y6 x2z2 x4y6z2 D) y 6z2 x2 43) z -9 z-3 z-6 z2 z6 D) z6 44) y -3 y2 y5 y5 y- D) y 45) t 8 t t7 t8 t7 D) t 46) x x2 x2 x x2 D) x 5

6 5x-3 47) y-4z2 5 x3y4z2 y4 5x3z2 5y4 x3z2 D) 5x3 y4z2 48) 35x -6yz2 5x2y4z 7z x4y3 7 x8y3z 7z x8y3 D) 30z x8y3 49) (x-6) 3 x-3 x-3 x8 D) x8 50) (n8) -3 n24 n5 n24 D) n5 5) (mn)-7 n m7 m7n7 m n7 D) m7n7 52) (4t3) -3 64t9 64t9 t 9 64 D) 64 t9 53) (x-2y-4) -6 y 24 x2 x 2 y24 x2y24 D) x2y24 54) x x6 x x6 D) 25x6 55) 3 y4 4 y y6 8y6 D) 8y6 6

7 56) x5y5-5 wz6 wz30 x25y25 w 5z30 x25y25 x25y25w 5 z30 D) x 25y25 w5z30 57) 7x-4 0 4y-2z 0 7y2 4x4z D) 7y 2z 4x4 Convert to decimal notation. 58) D) 9,700 59) ,689, ,900 D) 46,890,000 60) ,400 D) ) ,73, D) Convert to scientific notation. 62) 6,300, D) ) D) ) D) ) D) ) D)

8 Perform the indicated operation. Write the answer in scientific notation. 67) D) ) D) ) D) Solve the problem. Express the answer in scientific notation to two decimals unless requested otherwise. 70) The national debt of a small country is $ 7,520,000,000 and the population is 2,589,000. What is the amount of debt per person? $ $ $ 2.90 D) $ ) A company produced 2,880,000 small appliances in one year and made a profit of $ 6,370,000. What was the profit on each appliance? $ 22.2 $ $ D) $ ) If the distance from the earth to the sun were 92,900,000 miles, how long would it take a rocket, traveling at miles per hour, to reach the sun? (Round to three places) hr hr hr D) hr 73) A light-year is the distance that light travels in one year. Find the number of miles in a light-year if light travels miles/second. (Round to one decimal place, and assume that there are 365 days in a year.) miles miles miles D) miles 74) A computer can do one calculation in seconds. How long would it take the computer to do a trillion (02) calculations? (Round to one decimal place.) sec.4 06 sec.4 02 sec D).4 05 sec 75) Assume that the volume of the earth is 5 04 cubic meters and the volume of a bacterium is cubic meters. If the earth could be filled with bacteria, how many would it contain? (Round to one decimal place.) bacteria bacteria bacteria D) bacteria 8

9 Provide an appropriate response. 76) Rank the numbers in order from smallest to largest , , , , < < < < < < < < < < < < D) < < < < ) Tell whether or not the number is given in scientific notation No Yes 78) Tell whether or not the number is given in scientific notation No Yes Identify the terms in the polynomial. 79) -5x5 + 7x3-3x2 + 8x -5x5, 7x3, -3x2, 8x -5x5, -7x3, -3x2, 8x -5, x5, 7, x3, 3, x2, 8, x D) 5x5, 7x3, 3x2, 8x 80) t5 + 3t4-8t3 + 4t2-6 t5, 3, t4, -8, t3, 4, t2, -6 t5, 3t4, -8t3, 4t2, -6 t5, 3t4, 8t3, 4t2, 6 D) t5, 3, t4, -8, t3, 4, t2 8) -n7-3n3 + 2n2 + 3n + 4 -, n7, -3, n3, 2, n2, 3, n, 4 -n7, 3n3, 2n2, 3n, 4 -, n7, -3n3, 2n2, 3n, 4 D) -n7, -3n3, 2n2, 3n, 4 82) 4y - 9y2-3y 4y, 9y2, -3y 4y, -9y2, -3y 4, y, -9, y2, -3, y D) 4y, -9y2, 3y Determine the coefficient and the degree of each term in the polynomial. 83) x7 + 3x Coefficients:, 3, degrees: 7,, 0 Coefficients:, 3 degrees: 7, Coefficients:, 3 degrees: 8, D) Coefficients:, 3 degrees: 7, 0 9

10 84) x6 + 3x4 - x - Coefficients:, 3, -, degrees: 6, 5,, 0 Coefficients:, 3, -, - degrees: 6, 4,, 0 Coefficients:, 3,, degrees: 6, 4,, 0 D) Coefficients:, 3, 0, - degrees: 6, 4,, Determine the leading term, leading coefficient, and the degree of the polynomial. 85) 4x2 + 4x - 2 4x2, 4, 4 x2, 4, 2 4x2, 4x, -2 D) 4x2, 4, 2 86) 7a2 + 5a5-5a 5a5, 5, 7a2, 5, 2 5a5, 5, 5 D) -5a, -5, 87) -x - 3x2-3x3-3x x5, -3, 5 -x, -, -3x5, -3, 3 D) 3x5, 3, 5 Identify the polynomial as a monomial, binomial, trinomial, or none of these. 88) x2 Trinomial Binomial None of these D) Monomial 89) -8x Trinomial Binomial None of these D) Monomial 90) 6s8 + 5s - 6 Binomial Monomial None of these D) Trinomial 9) 5y5 + -4y None of these Monomial Binomial D) Trinomial 92) 6z5 + 9z4-5z3 + 2 Trinomial Binomial None of these D) Monomial Combine like terms. Write the answer in descending order. 93) 7y7-8y5 + 8y5 + 6y7 3y7-6y5 26y7 3y7 D) 3y7 + 6y5 94) 7p6 + 9p3 + 2p6 + 5p3 8p6 + 28p3 9p6 + 4p3 9p6 + 4p3 D) 5p6 + 4p3 0

11 95) 4 x 6+ 9x x3-9 4 x x 6 + 5x3 + 7 x 6 + 5x3 + 7 x 5 + 5x2 + D) 7 x 6 + 3x ) 96.8x2-8.2x x x x x x2-5.2x x x + 05 D) 70.6x x Evaluate the polynomial. 97) 7x2-0x - 8 for x = D) 5 98) -6x3-5x2-2 for x = D) 56 99) -2x3-6x2 - x - 32 for x = D) 43 00) y2-5y + 3 for y = D) -3