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MATH 115 Precalculus Fall, 2016, V1.1 MATH 115 FINAL EXAMINATION This is an open-book exam. You may refer to your text and other course materials
MATH 115 Precalculus Fall, 2016, V1.1 MATH 115 FINAL EXAMINATION This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. You must complete the exam individually. Neither collaboration nor consultation with others is allowed. Record your answers and work on the separate answer sheet provided. There are 28 problems. Problems #1-6 are Multiple Choice. Problems #7-17 are Short Answer. (Work not required to be shown) Problems #18-28 are Short Answer with work required to be shown. MULTIPLE CHOICE 1. Solve | 9 - 7x | 12 and write interval notation for the solution set. A. \u0001, \u0001 3\u0001, \u0001 B. , 3 C. \u0001, \u0001 D. \u0001, \u0001 1. _______ 2. Which of the following polynomials has a graph which exhibits the end behavior of upward to the left and upward to the right? 2. _______ A. B. C. D. f (x) = 4x5 + x + 8 f (x) = -5x4 - 9x2 - 5 f (x) = 3x6 + 7x3 - x - 5 f (x) = -2x3 - 3x3 - x vvvv 3. Express in equivalent form: log (x + 2) + log 1 - 3 log z A. log + 3 3 B. log C. D. 3. _______ log Page 1 of 7 MATH 115 Precalculus 4. Determine the interval(s) on which the function is increasing. A. ( ,1) and ( 4, ) B. ( , C. ( 1.25, 3.25 ) D. ( 1/ 3, 3) Fall, 2016, V1.1 4. ______ 1/ 3) and (3, 4.75) and ( 4.75, ) 5. Which of the functions corresponds to the graph? 5. ______ A. f ( x ) = 1 + e x B. f ( x ) = 1 + e x C. f ( x ) = 1 e2 x D. f ( x ) = e2x Page 2 of 7 MATH 115 Precalculus Fall, 2016, V1.1 6. Which of the functions corresponds to the graph? 6. ______ A. f (x) = 2 sin x + 1 B. f (x) = sin(2x) + 1 C. f (x) = 2 cos x + 1 D. f (x) = 2 - cos x SHORT ANSWER: 7. Points (1, 6) and (3, -8) are endpoints of the diameter of a circle. (a) What is the exact length of the diameter? (Simplify as much as possible) Answer: ________ (b) What is the center of the circle? Answer: ____________ (c) What is the equation of the circle? Answer: ___________________________ 8. Find the value of the logarithm: log . Answer: ____________ 9. A salesperson earns a base salary of $1,540 per month and a commission of 7.6% on the amount of sales. If the salesperson has a paycheck of $4,819.40 for one month, what was the amount of sales for the month? Answer: _____________ Page 3 of 7 MATH 115 Precalculus Fall, 2016, V1.1 10. A bowl of soup at 180 F. is left in a room of constant temperature 70 F to cool. - 0.075 t After t minutes, the temperature T of the soup is given by T(t) = 70 + 110e Find the temperature of the soup 6 minutes after it is left to cool. (Round to the nearest degree.) Answer: ________ 1 11. Given the function = 4 , find a formula for the inverse function. 9 Answer: __________________ 12. (a) State the reference angle associated with 315. Answer: ________ (b) Convert 315 to radians. Leave the answer in terms of . Answer: ________ 13. Given y = 3 sin(4x - ), state the (a) period Answer: ________ (b) phase shift Answer: ________ (cos x)(2sin x - 1) = 0 in the interval [0, 360). 14. Solve the trigonometric equation Answer: _________________ 15. Find the exact value of arccos sin (b) Find the exact value of arcsin sin (a) Answer: ________ Answer: ________ 2 16. For the parabola given by (x + 5) = 8(y - 3), find the following: (a) direction parabola opens (to the left, right, up, or down) Answer: ___________ (b) vertex Answer: ___________ (c) focus Answer: ___________ Page 4 of 7 MATH 115 Precalculus 17. Let = Fall, 2016, V1.1 (a) State the domain. Answer: _________________ (b) State the vertical asymptote(s). Answer: _________________ (c) State the horizontal asymptote. Answer: _________________ (d) Which of the following represents the graph of = 5 ? 3 GRAPH A. GRAPH B. GRAPH C. GRAPH D. Answer: ______________ Page 5 of 7 MATH 115 Precalculus Fall, 2016, V1.1 SHORT ANSWER, with work required to be shown, as indicated. 18. Find the equation for a line which passes through the points (-3, 5) and (9, 2). Write the equation in slope-intercept form. Show work. 19. Find the exact solutions and simplify as much as possible: 8x2 = 6x + 1. Show work. 20. Let f (x) = 5x2 + 9 and g(x) = x - 3. (a) Find the composite function ( f o g )( x) and simplify. Show work. (b) Find ( f o g )(1) . Show work. 21. A projectile is launched from a platform 10 feet high with an initial velocity of 72 feet per second, The height h of the projectile at t seconds after launch is given by h = -16t2 + 72t + 10 feet. (a) How many seconds after launch does the projectile attain maximum height? (b) What is the maximum height? 22. Solve: + = 0. Show work. Show work. Show work. 23. Suppose that sin = 3/5 and that is a Quadrant II angle. (a) Find the exact value of cos . Show work. (b) Find the exact value of sin(2 ). Show work. 2 24. Prove the identity (sin x + cos x) 1 = sin 2x Page 6 of 7 MATH 115 Precalculus Fall, 2016, V1.1 25. From a point 48 feet from the base of a redwood tree, the angle of elevation to the top of the tree is 56.3. Find the height of the tree to the nearest foot. Show work. (sketch is not to scale) 26. For the triangle ABC, we are given that A = 46, B = 64, and c = 35.0. Find the length of side b, rounded to the nearest hundredth. Show work. = 2, -6 and = 9, 3. 27. Let (b) . Show work. Calculate the dot product (c) and . Round the result to the nearest degree. Show work. Determine the angle between 28. An ellipse has the equation + =1 (a) Is the major axis horizontal or vertical? (b) Find the exact values of the foci of the ellipse. Show work. Page 7 of 7
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