R S T. PreCalculus AB Final Exam SHOW YOUR WORK May 20, Name: 1. Find the area of this triangle. 2. Find the area of this trapezoid.

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1 1. Find the area of this triangle. 138 ft 6 18 ft. Find the area of this trapezoid. 10 ft 8 ft ft 3. Find the area of this trapezoid. 10 ft 8 ft 59 1 ft [A] 88 ft [B] 176 ft [C] 75.3 ft [D] 8.9 ft. Graph the solution to the sstem of inequalities: R S T ( )

2 Graph the solution to the sstem of inequalities: ( ) ( ) R S T 6. Sketch the sstem of inequalities. R + 1 S T [A] [B] [C] [D] 7. Solve: log ( + ) log = 5 5 Solve for : 8. log ( ) + log ( 1) = log 16 log ( 3) = 1

3 10. Solve: log ( + 17) log = 3 3 [A] 17 8 [B] 17 5 [C] none of these [D] 5 17 Simplif: log log 3 6 log log 3 8 [A] 3 [B] 1 [C] 9 [D] Graph: 13. log 1. log3 [A] [B] [C] [D]

4 15. Solve for : = Solve for : 16 3 = 3 [A] 3, 6 [B] 5, 9 [C] 5, 9 [D] 3, 6 Use Cramer's rule to solve for : R S T R S T 3 3 = 10 3 = 5 = = 5 [A] 3 [B] [C] 6 [D] Find three cube roots of 33 cis 135 and epress them in polar coordinates. 0. Find the four fourth roots of 81 and epress them in rectangular coordinates. Give eact answers. 1. Write the four fourth roots of 81 cis 180 in rectangular coordinates. Give eact answers.. Find three cube roots of 6 cis 5 and epress them in polar coordinates. [A] cis 15, cis 135, cis 55 [B] cis 15, 1.33 cis 75, cis 55 [C] 1.33 cis 15, cis 135, 1.33 cis 135 [D] 1.33 cis 15, 1.33 cis 75, 1.33 cis Solve cot 3 csc = 0 given that 0 < Solve cot + 3 csc = 0 given that 0 < 360. [A] 0, 60, 180, 300 [B] 10, 330 [C] 135, 315 [D] 60, 10, 0, 300

5 5. Develop the identit for tan(a B) b using the identities for sin(a B) and cos(a B). 6. Show: sec csc cos sec csc + cos = csc sec + csc 7. Which of the following is equal to? 1 + tan [A] cos [B] 1 [C] sec [D] csc 8. Find the number of grams of iodine-131 remaining after 16 das if 3 grams of the isotope were initiall present. The half-life of iodine-131 is 81 das. 9. The amount of a substance initiall present in an eperiment was 80 grams, and after 100 hours onl 0 grams remained. Assuming eponential deca, write the eponential equation describing the amount of substance present as a function of time and determine the half life of the substance. Sketch the graph. 30. Under the onslaught of the College Algebra second period class, a pile of homework problems decreased eponentiall. It decreased from 1300 to 800 problems in onl 5 minutes. How long would it take until onl 300 problems remained? 31. The sound of an approaching storm was increasing eponentiall. Onl 0 minutes after it began it was alread twice as loud. How man times louder will it be after three hours? 3. The half-life of P 33 (phosphorus) is approimatel 5 das and its deca is approimated b t the model Qt () Qe 0 where t is time in das, Q(t) is the quantit at time t, and Q 0 is the initial quantit. What percentage of a given amount remains after 3 das? [A].3% [B] 50% [C] 0.% [D] 1.% 33. Develop the identit for tan A b using the identities for sin A and cos A.

6 3. Which of the following possible identities is true? [A] csc + cot = cot [C] cos + sin = cot [B] cos + sin = cot [D] csc + cot = cot 35. Solve tan = 3 given that 0 <. 36. Show: sin + sin + cos = 1 + sin cos 37. Solve cos + 3 cos + 1 = 0 given that 0 <. [A] 5,,, [B] 0 [C] 5, [D],, A card is drawn from a standard deck of 5 cards. Find the probabilit that the card is either a four or a face card. 39. An urn contains 7 white balls and 9 black balls. Four of the white balls and one of the black balls are rough. What is the probabilit of drawing a ball that is either rough or white? 0. A card is drawn from a standard deck of 5 cards. Find the probabilit that the card is either a five or a diamond. [A] Graph: F I cschg K J 5 [B] 7 13 [C] 13 [D] 15 6

7 . Write the equation of the trigonometric function: c h b g b g 3. Write as a single logarithm: log 16 log 3log + log. Epand as the sum of individual logarithms, each of whose argument is linear: log z 5. Epand as the sum of individual logarithms, each of whose argument is linear: log 7 b 6 z 3 6. Epand as the sum of individual logarithms, each of whose argument is linear: ( 5) log 5 7. Use a calculator to compute: Write as a single logarithm: log 5 5 log 3 log 5 + log 5 [A] log b 5g 5 b g [B] log c h b g b g b 5g c 5h b 5g [C] log [D] log b 5g

8 9. The graph of = 7 is translated +5 units horizontall and units verticall. What is the general form of the equation of the translated graph? 50. The graph of = is translated +6 units horizontall and + units verticall. What is the general form of the equation of the translated graph? [A] 6 = 0 [B] = 0 [C] = 0 [D] 6 = The general form of the equation of an ellipse is = 0. Write the equation in standard form and give the coordinates of the center, the length of the major ais, and the length of the minor ais. Then graph the ellipse. 5. Graph: = 0 [A] [B] [C] [D] Find the sum of the infinite geometric series

9 5. A rubber ball dropped on a hard surface takes a sequence of bounces, each one 3 as high as the preceding one. If this ball is dropped from a height of 1 feet, how far will it have traveled when it hits the surface the fifth time? 55. Find the sum of the geometric series: [A] [B] [C] [D] Find the seventh term in the epansion of c h Find the sith term in the epansion of c h 10. [A] [B] [C] [D]

PRACTICE FINAL EXAM. 3. Solve: 3x 8 < 7. Write your answer using interval notation. Graph your solution on the number line.

PRACTICE FINAL EXAM. 3. Solve: 3x 8 < 7. Write your answer using interval notation. Graph your solution on the number line. MAC 1105 PRACTICE FINAL EXAM College Algebra *Note: this eam is provided as practice onl. It was based on a book previousl used for this course. You should not onl stud these problems in preparing for