Test # 1 Review Math MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 Test # 1 Review Math 135 Name (Sections 1.3,.,3.7,..1,.3,11.1,11.,11.3,and 11.) _ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Factor out the greatest common factor. 1) 1m9 + 1m6 + m A) 3m(m7 + 7m + 8) B) No common factor C) m(1m7 + 1m + ) D) 3(m9 + 7m6 + 8m) 1) ) ( + 5)6 + 3( + 5)8 A) 7( + 5)6 B) 7( + 5) C) ( + 5)6(3 + 79) D) ( + 5)6( ) ) Factor completel. 3) A) ( + 1)( - 7) B) Prime C) ( + 9)( - 8) D) ( + 8)( - 9) 3) ) A) Prime B) 5( - )( + 3) C) 5( + )( - 3) D) (5 + 10)( - 3) ) 5) u - uv - 8v A) Prime B) (u - 6v)(u + v) C) (u + 6v)(u - 8v) D) (u - 6v)(u + 8v) 5) 6) 9-36 A) (7 + 6)(7-6) B) (7 + 6) C) (7-6) D) Prime 6) 7) 81 + A) (9 + ) B) Prime C) (9 - ) D) (9 + )(9 - ) 7) 8) A) ( + 9)( - 9) B) ( + 9) C) Prime D) ( - 9) 8) 9) A) (10-7)( ) B) (10 + 7)( ) C) (1000-7)( ) D) (10-7)( ) 9) 10) 16c A) (6c + 5)(36c - 30c + 5) B) (6c + 5)(36c + 5) C) (6c - 5)(36c + 30c + 5) D) (16c + 5)(c - 30c + 5) 10) Find the slope of the line, if it is defined. 11) Through (-, ) and (-3, -) A) - B) C) Undefined D) -1 11) 1

2 Find the slope and the -intercept of the line. 1) - 3 = -15 A) m = 3 ; b = 5 B) m = 3 ; b = 5 1) C) m = - 3 ; b = -3 D) m = - 3 ; b = -15 Choose one of the four lines graphed which most closel resembles the graph of the given equation. 13) = A) B) ) C) D)

3 Find the - and -intercepts for the equation. Then graph the equation. 1) - 36 = ) A) (0, -1), (, 0) B) (0, -1), (6, 0) Decide whether the pair of lines is parallel, perpendicular, or neither. 15) 3-8 = = -0 A) Perpendicular B) Neither C) Parallel 15) Find an equation of the the line satisfing the given conditions. 16) Through (, 3); m = ) A) = 55 B) = -55 C) = -55 D) 7-9 = 55 Write an equation in standard form for a line passing through the pair of points. 17) (-, ) and (5, -8) A) + 13 = -1 B) = -1 C) = 6 D) - 7 = 6 17) Find an equation of the the line satisfing the given conditions. 18) Through (-3, -1); parallel to - 7 = 53 A) + 7 = 10 B) - 7 = 10 C) -7-6 = -1 D) -3-7 = 53 18) 19) Through (9, ); perpendicular to 3 + = 31 A) - 3 = 1 B) + 3 = 1 C) 3 - = 1 D) - 3 = 1 19) 3

4 Solve the problem. 0) Let C() = be the cost to manufacture items. Find the average cost per item to produce 50 items. A) $88 B) $8 C) $113 D) $9 0) Graph the rational function ) f() = ) A) B) C) D)

5 Give the equation of the vertical asmptote(s) of the rational function. 3 ) g() = + 7 A) = -7 B) = -7 C) = 0 D) = ) g() = A) = -3, = 1, = 0 B) = -5 C) = 3, = -1 D) = -3, = 1 ) 3) ) F() = A) = - B) None C) = D) = 3, = -3 ) Give the equation of the horizontal asmptote of the rational function. 3 5) g() = + 8 5) A) = -8 B) = 0 C) = 3 8 D) = 3 6) f() = ) A) = B) = 0 C) = 3 D) = Solve the problem ) If the average cost per unit C() to produce units of plwood is given b C() =, what is + 0 the unit cost for 0 units? Round our answer to the nearest cent. A) $10.00 B) $0.75 C) $-5.00 D) $ ) An oil refiner can produce gasoline, heating oil, or a combination of the two. The product echange function for gasoline,, and heating oil,, in thousands of gallons per week is: 7) 8) = 7, B sketching the quadrant I portion of the graph of this function, estimate the maimum quantit of each product that can be produced per week. A) gasoline: 1,500,000 gal; heating oil: 500,000 gal B) gasoline: 1,000,000 gal; heating oil: 3,000,000 gal C) gasoline: 3000 gal; heating oil: 1000 gal D) gasoline: 3,000,000 gal; heating oil: 1,000,000 gal 5

6 Classif the function as a linear, quadratic, or eponential. 9) f() = 5 + A) Quadratic B) Eponential C) Linear 9) 30) f() = A) Eponential B) Quadratic C) Linear 30) 31) f() = 3- A) Linear B) Quadratic C) Eponential 31) Without graphing, describe the shape of the graph of the function and complete the ordered pairs (0, ) and (1, ). 3) f() = -(6) 3) A) The graph lies above the -ais, falls from left to right, with the negative -ais as a horizontal asmptote; (0, 1) and (1, ). B) The graph lies above the -ais, falls from right to left, with the negative -ais as a horizontal asmptote; (0, ) and (1, 6). C) The graph lies below the -ais, falls from right to left, with the negative -ais as a horizontal asmptote; (0, ) and (1, 6). D) The graph lies below the -ais, falls from left to right, with the negative -ais as a horizontal asmptote; (0, -1) and (1, ). Graph the function. 33) f() = 33) A) B)

7 C) D) ) f() = 1 3 3) A) B)

8 C) D) ) f() = 5-35) A) B)

9 C) D) Solve the equation. 1 36) 5- = 65 A) 1 15 B) - C) D) 1 36) 37) 59-3 = 15 A) -9 B) 7 C) D) -5 37) Solve the problem. 38) The amount of particulate matter left in solution during a filtering process is given b the equation P() = 700()-0.6n, where n is the number of filtering steps. Find the amounts left for n = 0 and n = 5. (Round to the nearest whole number.) A) 700, 5600 B) 700, C) 100, 88 D) 700, 88 38) 39) The deca of 8 mg of an isotope is given b A(t)= 8e-0.05t, where t is time in ears. Find the amount left after 8 ears. A) 6 B) 61 C) 31 D) 7 39) Convert to eponential form. 0) log 1 6 = -3 0) A) 3 = 1 6 B) -3 = 1 6 C) 1 3 = D) 6 = 3 6 Write in logarithmic form. 1) - 1 = 16 A) - = log1/ 16 B) - = log C) 1 16 = log - D) = log ) 9

10 Decide whether the limit eists. If it eists, find its value. ) lim f() ) A) 3 B) 0 C) D) Does not eist 3) lim f() 1 3) A) 0 B) 1 C) D) Does not eist ) lim f() 0 ) A) 0 B) - C) Does not eist D) -1 Use a calculator to estimate the limit. 5) lim A) Does not eist B) 0 C) 5 D) 10 5) 6) lim A) 0 B) C) Does not eist D) 6) 7) lim A) Does not eist B) -1 C) 0 D) 1 7) Use the limit properties to find the following limit. 8) If lim -1 f() = and lim -1 g() = 1, find lim -1 f() + g(). 6g() 8) A) 3 1 B) 9 10 C) - 5 D) -1 10

11 Use the properties of limits to evaluate the limit if it eists. lim + 6 9) 6 ( - 6) A) B) Does not eist C) 6 D) 0 9) Solve the problem. 50) A compan training program determines that, on average, a new emploee can do P(s) pieces of 8 + s work per da after s das of on-the-job training, where P(s) = s + 8. Find lim s 10 P(s). A) 9 B) 65 C) Does not eist D) 5 50) Find the average rate of change for the function over the given interval. 51) = + 3 between = 3 and = 8 A) 35 B) 1 C) 88 5 D) 11 51) 5) = - 1 between = 1 and = 5 5) A) 1 B) -8 C) - D) Solve the problem. 53) Compute the instantaneous rate of change of the function at at = a. f() = +, a =. A) 8 B) 10 C) 1 D) -8 5) For a motorccle traveling at speed v (in mph) when the brakes are applied, the distance d (in feet) required to stop the motorccle ma be approimated b the formula d = 0.05 v + v. Find the instantaneous rate of change of distance with respect to velocit when the speed is 0 mph. A) 10 mph B) 1 mph C) 5 mph D) mph 53) 5) Find the equation of the tangent line to the curve when has the given value. 55) f() = + 5 ; = A) = B) = C) = D) = ) 11

12 Find the point from those given that has the given propert. 56) The point where the slope of the tangent is greatest 56) A) (0,0) B) (-,-) C) (,6) 57) The point where the slope of the tangent is least 10 57) A) (0,0) B) (-,-) C) (,6) Find fʹ() for the function, then find fʹ() for the given. 58) f() = 5 + 9, fʹ() A) fʹ() = 5; fʹ() = 5 B) fʹ() = 5; fʹ() = 10 C) fʹ() = 5; fʹ() = 5 D) fʹ() = 5; fʹ() = 10 58) 59) g() = 3 -, gʹ(3) A) gʹ() = 6 - ; gʹ(3) = 1 B) gʹ() = 3 - ; gʹ(3) = 5 C) gʹ() = 3; gʹ(3) = 9 D) gʹ() = 6; gʹ(3) = 18 59) Solve the problem. 60) The total cost to produce handcrafted wagons is C() = Find the marginal cost when = 5. A) 1 B) 35 C) 3 D) 35 60) Find the derivative. 61) f() = A) - 6 B) - 6 C) 8-6 D) ) 1

13 6) = A) B) C) D) ) 63) f() = 97/ A) / B) /5-10 C) 63 5 / D) 63 5 / ) 6) = - 6) A) ʹ = 1 - B) ʹ = + C) ʹ = 1 + D) ʹ = 1 + Find the following. 65) fʹ(16) if f() = 3/ - 51/ A) B) 91 C) D) ) Solve the problem. 66) Let C() be the cost function and R() the revenue function. Compute the marginal cost, marginal revenue, and the marginal profit functions. C() = ,000 R() = 350 A) Cʹ() = Rʹ() = 350 Pʹ() = B) Cʹ() = Rʹ() = 350 Pʹ() = C) Cʹ() = Rʹ() = 350 Pʹ() = ) Find the value of the epression. 67) log ) A) 0 B) -1 C) 7 D) 1 68) ln e A) -1 B) 0 C) e D) 1 68) Evaluate the logarithm. 69) log 8 A).3598 B).3579 C) 5.93 D) ) 13

14 Write the epression as the logarithm of a single number or epression with a coefficient of 1. Assume all variables represent positive numbers. 70) log 9 + log 63 - log 7 70) A) log 81 B) log 13 C) log 6 D) log 9 71) ln(8 + 3) + ln( + 6) A) ln (9 + 9) B) ln (8 + 3) ( + 6) 71) C) ln ( ) D) ln ( ) Write the epression as a sum and/or a difference of logarithms with all variables to the first degree. 7) log 6rs6 A) log 6 + log r + 6 log s B) log 8 + log r + 6 log s C) 1log r + 6 log s D) log 1r + log 6s 7) Graph the function. 73) = log 3 73) A) B)

15 C) D) ) = log ( - 3) 7) A) B)

16 C) D) Solve the problem. 75) The population growth of an animal species is described b F(t) = log3 (t + 1) where t is measured in months. Find the population of this species in an area 0 month(s) after the species is introduced. A) 590 B) 065 C) 1160 D) ) 16

17 Answer Ke Testname: TEST # 1 REVIEW MATH 135 1) A ) D 3) D ) C 5) C 6) A 7) B 8) B 9) D 10) A 11) A 1) A 13) B 1) A 15) A 16) A 17) C 18) B 19) D 0) B 1) D ) A 3) D ) B 5) B 6) C 7) A 8) D 9) C 30) B 31) C 3) D 33) C 3) C 35) A 36) C 37) C 38) D 39) A 0) B 1) B ) B 3) D ) B 5) C 6) D 7) A 8) A 9) B 50) A 17

18 Answer Ke Testname: TEST # 1 REVIEW MATH ) B 5) A 53) B 5) C 55) D 56) C 57) B 58) A 59) A 60) A 61) D 6) C 63) D 6) D 65) A 66) C 67) B 68) D 69) B 70) A 71) C 7) A 73) D 7) B 75) C 18