Math 100 Eam 3 Review (Chapters 5-6) Name The problems included in this review involve the important concepts covered in chapters 5 and 6. You will comlete this review in two rounds: (1) In the individual round, ou will work at home and enter answers in Learning Cataltics. (2) In the team round, ou will work with our team and decide on the best answers. If our group gets stuck on a problem, let our instructor know. Be prepared to discuss an problems ou encounter in this process. Write the epression using eponents. 4 4 4 4 4 4 1) 3 3 3 3 3 3 Answer: 4 3 6 1) Identif the base and the eponent for the eponential epression. 2) 105 A) Base: 5, eponent: 10 B) Base:, eponent: 5 C) Base: 10, eponent: 5 D) Base: 5, eponent: Answer: B 2) Evaluate. 3) (-6)2 3) Answer: 36 Use the product rule, if possible, to simplif the epression. Write the answer in eponential form. 4) (-55)(42)(-26) 4) Answer: 4013 5) 74 48 A) 2832 B) 1112 C) 2812 D) The product rule does not appl. Answer: D Use the power rules for eponents to simplif. Write the answer in eponential form. 6) (-26) 4 A) - 224 B) - 210 C) 210 D) 224 Answer: D 5) 6)
7) z 8 Answer: (z 0) 7) 8 z8 Solve the problem. 8) Find an epression that represents the area of the figure.(leave π in the answer.) 8) 4t5 Answer: 16πt10 Provide an appropriate response. 9) Eplain how (-6)5 and -65 are different. 9) Answer: In the first, -6 is raised to the 5 power. In the second, 6 is raised to the 5 power, then the negative is applied. 10) Eplain how (-7)7 and -77 are different. 10) Answer: In the first, the power applies to both. In the second, the power onl applies to the. 11) Is it correct to simplif 53 35 as 1515? 11) Answer: No; the value of the epression is 30,375. Simplif b writing the epression with positive eponents. Assume that all variables represent nonzero real numbers. 12) (3 26) -3 (9-1) 2 (6) -5 12) A) 15 336 B) 6 26 15 C) 3 26 15 D) 33616 If the number in the statement is written in scientific notation, write it without eponents. If it is written without eponents, write it in scientific notation. 13) The population of a small countr is 5,646,000. 13) A) 5.646 104 B) 5.646 105 C) 5.646 10-5 D) 5.646 106 Answer: D 14) A computer can do one calculation in 1.4 10-7 seconds. A) 0.00000014 B) 14,000,000 C) 0.000014 D) 0.000000014 Answer: A 14)
Find the value of the polnomial. 15) 23 + 62 - - 26 when = -3 15) Answer: -23 Perform the indicated operation. 16) -(53 + - 5) + (73 + 22) - (82-3 -1) 16) Answer: 23-62 + 2 + 6 Graph the equation b completing the table of values. 17) = ( + 2)2-4 10-3 -2 5-1 0-10 -5 5 10 17) -5-10 Answer: -2 0-1 1 0 4 1 9 216 10 5-10 -5 5 10-5 -10 Find the product. 18) (3p - 1)(9p2 + 3p + 1) 18) Answer: 27p3-1 Find the product. Use the FOIL method. 19) (4 + 3)( + 9) 19) Answer: 42 + 39 + 27 20) Multipl. (4-6)(4 + 6) 20) Answer: 162-36
Solve the problem. 21) Find a polnomial that represents the area of the shaded region. 21) 3 + 8 12 + 2 Answer: 32 + 8 + 16 Find the product. 22) ( 2 + 9)2 22) Answer: 4 2 + 36 + 81 2 Perform the division. Write the answer with positive eponents. 23) 14 4 + 283 + 492 73 23) A) 9 + 4 B) 2 + 4 C) 2 + 4 + 7 D) 2 + 283 + 7 Perform the division. 24) (4-16) ( + 2) 24) Answer: 3-22 + 4-8 Solve the problem. 25) If a submarine goes 4k3 + 21 k2 + 7k - 45 miles in 4k + 9 hours, what is its rate of speed? A) k2-3k + 5 miles/hr B) k3 + 3k2-5k miles/hr C) k2 + 3k - 5 miles/hr D) k2 + 15 k - 5 miles/hr 25) ESSAY. Write our answer in the space provided or on a separate sheet of paper. Provide an appropriate response. 26) Eplain the error in the following: 2 + 2-15 = ( - 5)( + 3) Answer: The factorization ields a middle term of -2 rather than 2: 2 + 2-15 = ( + 5)( - 3)
Solve the equation. 27) 2 - = 56 27) Answer: {-7, 8} 28) m(2m - 13) = -15 28) Answer: 3 2, 5 29) ( - 7)2 + 2 = ( + 1)2 29) Answer: {4, 12} Solve the problem. 30) A triangle has a base of length + 2 and a height of + 8 and has an area of 36 square units. Find the base and height. (A = 1 2 bh) 30) Answer: base = 6 units; height = 12 units 31) Find three consecutive odd integers such that the sum of all three is 36 less than the product of the smaller two. Answer: 7, 9, 11 Solve the problem. Round to the nearest tenth, if necessar. 32) If an object is thrown upward with an initial velocit of 128 ft/sec, its height after t sec is given b h = 128t - 16t2. Find the maimum height attained b the object. (The object will attain maimum height eactl at the halfwa point in terms of the time t, where t = 0 is at the beginning of the objectʹs flight, and the final time is when the object hits the ground.) Answer: 256 ft 31) 32) Factor b grouping. 33) 152 + 20-9 - 12 A) (5 + 3)(3-4) B) (15-3)( + 4) C) (5-3)(3 + 4) D) (15 + 3)( - 4) Factor completel. 34) 42-20 + 25 A) (2 + 5)2 B) (2-5)(2 + 5) C) (2-5)2 D) Prime 35) 2162-360 + 150 A) (36-30)(6-5) B) 6(362-60 + 25) C) 6(6-5)2 D) 6(6 + 5)(6-5) 33) 34) 35)
Factor the polnomial completel. 36) 375k3m - 24m4 A) (15km - 6m2)(25k2 + 4m2) B) 3m(5k + 2m2)(25k2-10km + 4km2) C) 3m(5k - 2m)(25k2 + 10km + 4m2) D) 3m(125k - 2m)(k2 + 10km + 4m2) 36) 37) t3 + 64 37) Answer: (t + 4)(t2-4t + 16) ESSAY. Write our answer in the space provided or on a separate sheet of paper. 38) You want to bu a used car, but ou donʹt have an mone saved, and ouʹre just breaking even ever month. You do some research and find that the model ou want costs, on average, about $10,000. But our research also reveals that, due to added mileage and age, the car ou want loses value at a rate of about $100 per month. You want the car so bad that ou decide to quit drinking premium coffee ($120 per month), stop eating premium donuts ($80 per month), quit watching premium TV ($100 per month), and cancel our unlimited talk, tet and data plan ($100 per month). How long will it take ou to save enough to bu the car? What will the price of the car be at that time? (a) Let = value of the car months from now. Write an equation epressing in terms of. (b) Let = mone saved after months of saving. Write an equation epressing in terms of. (c) Graph the equations from parts (a) and (b) on the aes below. Label our aes and the lines ou graph appropriatel. 11000 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 (d) From our graph, what would ou estimate the solution to be? What does it mean? (e) Solve the sstem of equations from (a) and (b) b an algebraic method. Does our answer agree with our graph?
Answer: (a) = -100 + 10,000 (b) = 400 (c) 12000 11000 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 (d) The point of intersection apears to be (20, 8000), which means that ou will have enough to bu the car in 20 months, and it will cost about $8,000. (e) (20, 8000); Yes, it does agree with the graph.
Answer Ke Testname: EXAM 3 REVIEW (CH 5 6) SP 2016 4 6 1) 3 2) B 3) 36 4) 4013 5) D 6) D 7) 8 z8 8) 16πt10 9) In the first, -6 is raised to the 5 power. In the second, 6 is raised to the 5 power, then the negative is applied. 10) In the first, the power applies to both. In the second, the power onl applies to the. 11) No; the value of the epression is 30,375. 12) C 13) D 14) A 15) -23 16) 23-62 + 2 + 6 17) -2 0 10-1 1 0 4 5 1 9 216-10 -5 5 10-5 -10 18) 27p3-1 19) 42 + 39 + 27 20) 162-36 21) 32 + 8 + 16 22) 4 2 + 36 + 81 2 23) C 24) 3-22 + 4-8 25) C 26) The factorization ields a middle term of -2 rather than 2: 2 + 2-15 = ( + 5)( - 3) 27) {-7, 8} 3 28) 2, 5 29) {4, 12} 30) base = 6 units; height = 12 units 31) 7, 9, 11 32) 256 ft
Answer Ke Testname: EXAM 3 REVIEW (CH 5 6) SP 2016 33) C 34) C 35) C 36) C 37) (t + 4)(t2-4t + 16) 38) (a) = -100 + 10,000 (b) = 400 (c) 12000 11000 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25