Precalculus Final Exam Review 2014 2015 You Must Show Work .

PrecalculusFinal Exam Review2014 – 2015You must show work to receive credit! This review covers the major topics in the material that will be tested on the finalexam. It is not necessarily all inclusive and additional study and problem solvingpractice may be required to fully prepare for the final exam. Place answers in the blanks, when provided. Use additional paper, if necessary. Calculators may be used; however, the final exam will have non-calculator portions.Therefore, prudence suggests you prepare with and without a calculator so you canhandle any contingency.Name:Period:Due Date:The answers on this paper are my own. I did not receive nor give aid on this exam. I have complied with all aspects of theLCHS Honor Code.Student signature DateAdv Alg/Precalculus Final Exam

True-False1.Arithmetic sequences have a common ratio.2.The graph of a rational function can never cross a vertical asymptote.3.If interest is compounded continuously, use A Pent .4.1 The graph of y a x will always go through the points (0, 1), (1, a), and 1, .a 5.The function f ( x) 5x3 17 is a one-to-one function.6.The graph of the function f ( x) 7.7.5, 5, 2.5, 0, . is an example of an arithmetic sequence.8.ln e x9.log xlog y4 x3 x 2 5has an oblique asymptote.6 x3 5 x 2 8 x 10xlog xlog y10. The triangle described by a 10, b 14,and A 50 , has 2 solutions.11. The range of a function is the same as the domain of the function’s inverse.12. radians 36013. All reference angles must be between 0 and 9014. The Ambiguous Case for solving a triangle is when given angle-angle-side (AAS).15. Given side-angle-side (SAS) of a triangle, use the Law of Cosines to solve it.16. If interest is compounded continuously, use AP1rnnt17. The unit circle has a radius of 2.18. The natural base is 10.19. The common log (log) is the inverse of the natural log (ln).20. y21. ln e xlog x has a vertical asymptote at x0.xAdv Alg/Precalculus Final Exam2.

Multiple Choice22. Solve for x: 25 x 53 x 12a. 1b.23. Evaluate (81) 12c. 1,12d. no solution14b. –3a. 3c.13b.1 5 log 2 3x 7 log 2 y 4d. 1324. Express in expanded form: log 2 4 3x 5 y 7a. 4 3 log 2 5 log 2 x 7 log 2 y c.1 log 2 3 5 log 2 x 7 log 2 y 4d. 1 log 2 3 5 log 2 x log 2 y 425. Solve the equation: x 5 x 1b. –1a. 4c. 4, –1d. no solution26. Express the logarithmic equation as an exponential equation and solve: log 5x1 1 b. 125, x 3 5 1a. 125 , x 35xc. x 5 27. Solve1 x1251, x 3125d. 5 x 1, x 3125ex 3ex 2a. ln 3b. ln 3ec. ln32d. ln2328. The vertex of y x 2 2 x 5 is:a. (–1, 4)b. (1, –4)c. (1, 4)d. (–1, –4)c. exponentiald. logarithmic29. Which type of function cannot have an asymptote?a. polynomialAdv Alg/Precalculus Final Examb. rational3

30. Determine a polynomial of lowest degree with real coefficients that has 2i and 3 as roots.a. x 2 x 6b. x 2 x 6c. x 3 3x 2 4 x 12d. x 3 3x 2 4 x 1231. Determine any points of discontinuity for f ( x) a. 032. Solve e2 xb. 34e xx( x 5)( x 3)( x 5)c. 3, 5d. 0, 3, 5c. ln 0, ln 4d. ln 4c. 3,796,260d. 632,710c. 540xd. 12150 for x.a. 0, 4b. 4 157 33. Evaluate the expression 3 a.157!154!b. 15434. The 5th term in the expansion of (4 x 3)5 .a. 2160x 2b. 1620x35. Expand the expression ( x 9)5 using the Binomial Theorem.a. x5 45x4 1620 x3 14,580 x2 32,805x 9c. x5 45x4 810 x3 7290 x2 32,805x 59,049b. x5 45x4 810 x3 7290 x2 32,805x 9d. x5 45x4 1620 x3 14,580 x2 32,805x 59,04936. The triangle described by A 35 , a 6 , and b 12 has solutions.a. 0b. 1c. 2d. infinite37. The size P of a small herbivore population at time t (in years) obeys the function P(t ) 700e0.18t ifthey have enough food and the predator population stays constant. After how many years will thepopulation reach 2800?a. 16.91 yrsAdv Alg/Precalculus Final Examb. 7.7 yrsc. 42.5 yrs4d. 13.25 yrs

38. The half-life of a radioactive element is 130 days, but your sample will not be useful to you after80% of the radioactive nuclei originally present have disintegrated. About how many days can youuse the sample?a. 302b. 287c. 297d. 312x2 2x 339. Let f ( x) and g ( x) , the domain of g ( f ( x)) isx 1xa., x 0, 1, 2b. 2 40. The sum of the first 10 terms of the sequence 3 3 a. 1.767b. 3.93141. The domain of f ( x) , x 3,1c., x 0,1d.N 1.c. 8.844d. 4092c. x 1d. x 11is.x 1a. all real numbers2b. x 142. The inverse of f ( x) ( x 2)3 3 is f 1 ( x) a.3x 3 2b.3x 3 2c.3x 5d.3x 3 243. Let f ( x) 2 x 3 and g ( x) x 2 2 x 3 , g ( f ( x)) a. 2 x2 4 x 9b. 4 x2 8x 18c. 4 x2 8x 6d. 4 x2 4 x 644. A corner of McCormick Park occupies a triangular area that faces twostreets that meet at an angle measuring 85 . The sides of the area facingthe streets are each 60 feet in length (see diagram). The park’s60 ftlandscaper wants to plant begonias around the edges of the triangulararea. Find the perimeter of the triangular area to the nearest foot.85 60 fta. 125 ftb. 240 ftc. 180 ftd. 201 ft45. Find the domain of f ( x) log( x 5)a. x 0Adv Alg/Precalculus Final Examb. x 5c. x 55d. all real numbers

46. Identify the x and y –intercepts, if any, of the equation y a.x int : 1b.y int : None 5 47. Evaluate: 5 n 1 2 x int : Nonec.y int : 3x int : d.y int : 3b. 103c. 3 48. The sum of the infinite geometric sequence an 4 4 71649. Solve log 25 2 x 34x int : 1y int : 4n 1a. 5a. 1 4x 1b.167310d. not possiblen 1isc. 4d. not possiblec. 625d. 2503for x.2a. 125b. 62.5Free Response. Calculators may be used. Show all your work. Not all problems require acalculator. Round answers to three decimal places unless otherwise directed.50. If you invest 1000 an account that pays 7.5% interest compounded quarterly, how much will youhave in the account after 15 years? How much would you have if the same account was continuouslycompounded?51. Determine whether x 1 is a linear factor of 4 x 2 2 x 9Adv Alg/Precalculus Final Exam6yes or no

52. Express x 3 x 2 6 x as a product of linear factors.53. Determine any intercepts or asymptotes for g ( x) x 5.x 12x-intercept: (,)horizontal asymptote: y y-intercept: (,)vertical asymptote: x 13 2 85 54. Simplify x y z 55. Solve log 8 2 x 32 5 1 18 x y z . Use positive exponents. 5for x.356. Write as the sum and/or difference of logs. Express powers as factors. z ( x y ) 13ln y2 57. Express as a single logarithm and simplify.1log 3252log( x 1)3log( x 1)58. Identify all real zeros of f ( x) 2 x 4 x 3 3 .59. Solvex 5 x 2 x 3 4 x for x. (Hint: Graph it.)Adv Alg/Precalculus Final Exam7x

60. Solve 3 sin x x where 0 x 2 . Use radian mode and round to three decimal places.6x 61. If 2000 is invested in an account that compounds interest quarterly at 7.5%, what will be theaccount balance in 8 years?Balance:62. Solve 6log x7.332 for x.x 63. Solve 324 x163 xx 34for x.64. Find the coefficient of the x 6 term of the expansion of ( x 3)8 .coefficient 65. Find the 7th term of the expansion of (2 x 1)10 .7th term 66. Assume that the half-life of Carbon-14 is 5600 years.age Find the age (to the nearest year) of a wooden axe in which theamount of Carbon-14 is 30% of what it originally had.67. Find the amount owed at the end of 8 years if 5000 is loaned at a rate of 5% compounded monthly.amount Adv Alg/Precalculus Final Exam8

68. The formulaD 8e 0.6hcan be used to find the number of milligrams D of a certain drug that is in a patient's bloodstream hhours after the drug has been administered. The drug is to be administered again when the amount inthe bloodstream reaches 4 milligrams. What is the time between injections?time 69. Express as a single logarithm and simplify. x 2 4 x 32 x 2 3x 28 2ln ln ln x 16 x 64 ,x 7x 7 a 070. Write as the sum and/or difference of logs. Express powers as factors.5 ( x 6)( x 5) 2ln , x 54 ( x 8) 71. In ABC , A 47 , B 56 , and c 14, find b. (2 pts)72. How many years will it take for your investment to triple in value if it is placed in an account thatpays 12% interest and is compounded continuously?t 73. A culture of bacteria obeys the law of uninhibited growth. If 500 bacteria are present initially andthere are 800 after 1 hour, how many will be present after 5 hours?Adv Alg/Precalculus Final Exam9

74. Determine if the sequence is arithmetic, geometric, or neither. If arithmetic or geometric, write theexplicit rule.a. 1, 4, 9, 16, 25, b. –3, 6, –12, 24, –48, c. 10, 16, 22, 28, 34, 75. A triangle has side lengths of 12 feet, 18 feet, and 22 feet. What is the area of the triangle?f(x)676. Given the graph of f(x) is shown. Give all values whichfappear to satisfy the following conditions.Use interval notation where appropriate.a. domain of f ( x) :6–6b. range of f ( x) :c. all zeros of f ( x) :d. y-intercept of f ( x) :–6e. if f ( x) 2 , then x f. interval(s) over which f ( x) is constantg. interval(s) over which f ( x) is increasingh. interval(s) over which f ( x) is decreasingi. Give a justification for calling the relation graphed above a function.k. Is the inverse of f ( x) also a function? Justify your answer.Adv Alg/Precalculus Final Exam10x

Advanced Algebra/Precalculus Final Exam Review Formula SheetName:Law of Sines & CosinesExponential Growthabc sin A sin B sin CN (t ) N 0 e kta2Exponential Decayb2c22bc cos A b2 c 2 a 2 A cos 2bc A(t ) A0 e kt 1Arithmetic Sequences and SeriesExplicit:an a1 (n 1)dSum:Sn Area of Triangles:Area1bc sin A2Heron’s Formula:Areawhere ss( sGeometric Sequences and Seriesa)( s(ab2b)( sc)Explicit:c)Sum:Compound Interest Formula: r A P 1 n n 2a1 (n 1)d 2nSn a1 an 2an a1r n 11 rn,r 0, 11 r aa1r k 1 1 , r 1 1 rk 1Sn a1ntBinomial Theorem n n j j a x n j Continuous Interest FormulaA Pe rtAdv Alg/Precalculus Final Exam11

Adv Alg/Precalculus Final Exam Precalculus Final Exam Review 2014 – 2015 You must show work to receive credit! This review covers the major topics in the material that will be tested on the final exam. It is not necessarily all inclusive and additional study and problem solving practice may be required to fully prepare for the final exam.File Size: 303KBPage Count: 11