27 2 x 1 = Solve the equation. Check your solution. 5. Solve the equation. Check your solution. 7. Solve the equation. Check your solution.

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1 Algebra 3-4 Name: 2 nd Semester Exam Review Period: Answer each of the following questions. Some questions may require additional paper in order to show your work. These questions are intended to be a review of what you MAY see on the final exam. The final exam may include additional questions that are not listed on this review. Be sure to review any notes, homework and other items from class as well. Chapter 7 1. State whether the function represents exponential growth or decay.! y = 2 5 $ # & " 4 % x 2. Solve the equations. Check your solution x 1 = 3 3. Solve the equation. Check your solution. 6 x = 36 x 1 4. Solve the equation. Check your solution. log 8 b = 2 5. Solve the equation. Check your solution. log x 7 =1 6. Solve the equation. Check your solution. log 2 ( x 2 9) = 4 7. Solve the equation. Check your solution. log 6 x + log 6 (x 5) = 2 8. Solve the equation. Check your solution. 2 log 3 x log 3 (x 2) = 2

2 9. Solve the equation. Round to 4 decimal places. 2 x = Solve the equation. Round to 4 decimal places. 4 x 2 = Evaluate. e ln5 12. Evaluate. lne 3x 13. Solve the equation. Round to 4 decimal places if needed. 25e x = Solve the equation. Round to 4 decimal places if needed. ln(x + 2) = Evaluate with a calculator. Round to 4 decimal places if needed. log Evaluate without using a calculator. Round to 4 decimal places if needed. log 2 16 Chapter Find the LCM of the set of polynomials. x 2 3x 4, x Find the LCM of the set of polynomials. 18a 3 bc 2, 24b 2 c Simplify. x 2 5x + 4 2x 8 ( 3x 2 3x) 20. Simplify. x 2 +19x +84 2x 2 4x 4 x 2 + 9x +14

3 21. Simplify. 9u 2 28v 27u2 8v Simplify. x 2 4 2x 1 4x 2 1 x Simplify. x 2 1 2x 2 x 1 x 2 4 2x 2 3x Simplify. 6y 2 6 8y 2 +8y 3y 3 4y 2 + 4y 25. Simplify. 5 a 2 b 7a 5b Simplify. 7 y y 27. Determine the equations of any vertical asymptotes and the values of x for any holes in the graph of the rational function. f (x) = 4 x 2 + 2x Determine the equations of any vertical asymptotes and the values of x for any holes in the graph of the rational function. 29. If y varies directly as x and y = 15 when x = 3, find y when x = 12. f (x) = x + 3 x 2 + 7x +12

4 30. If y varies inversely as x and y = 16 when x = 5, find y when x = If y varies jointly as x and z, and y = 80 when x = 5 and z = 8, find y when x = 16 and z = 2. Chapter Find the next four terms of the arithmetic sequence. 40, 35, 30,. 33. Find the indicated term of the arithmetic sequence. = 4, d = 5, n = Write an equation for the nth term of the arithmetic sequence. 3, 5, 7, 9, Find the arithmetic means of the sequence. 2,,,, Find S n for the arithmetic series described = 90, a n = 4, n = Find the sum of the arithmetic series Find the sum of the arithmetic series. 5 k=1 (40 2k) 39. Find the first three terms of the arithmetic series described. = 25, a n =15, S n = Find the first 5 terms of the geometric sequence described. = 4, r = Find the indicated term of the geometric sequence. = 8, r = 2, n = 8

5 42. Write an equation for the nth term for the geometric sequence. 20, 40,80, Find the geometric means in the sequence. 1,,., Write the arithmetic series in summation notation Write the arithmetic series in summation notation. ( 20)+ ( 25)+ ( 30) ( 65) 46. Find the sum of each finite series. 5 n=2 (5n + 3) 47. Find the sum of the geometric series. 3 n=0 2(5) n 48. Find the sum of the infinite geometric series, if it exists. 49. Find the sum of the infinite geometric series, if it exists. = 2, r = Chapter Identify the conic section by writing the equation in standard form and sketching the graph. If it is a parabola, give the vertex, focus and directrix. If it is a circle, give the center and the radius. 51. Identify the conic section by writing the equation in standard form and sketching the graph. If it is a parabola, give the vertex, focus and directrix. If it is a circle, give the center and the radius. x 2 + y 2 8x 4y +19 = 0 x 2 8x y +19 = 0

6 52. Identify the conic section by writing the equation in standard form and sketching the graph. If it is a parabola, give the vertex, focus and directrix. If it is a circle, give the center and the radius. y 2 2x 4y = Identify the conic section by writing the equation in standard form and sketching the graph. If it is a parabola, give the vertex, focus and directrix. If it is a circle, give the center and the radius. x 2 + y 2 4x 6y 3 = 0

7 Chapter Your brother is ordering 5 pizzas for the family. There are 18 different kinds of pizza. How many different ways could he order 5 different kinds of pizzas? 55. A box contains 8 blueberry muffins, 6 banana muffins, and 4 pumpkin muffins. You pick one muffin from the box at random. Find each theoretical probability. a. P (banana) b. P(not pumpkin) c. P (banana or pumpkin) 56. J and K are independent events. P(J) = 1 4 and P ( K ) = 2. Find P (J and K) Use the following data set to answer the questions a. Find the mean, variance and standard deviation. b. Within how many standard deviations of the mean do all of the data values fall? 58. Find the probability of x successes in n trials for the given probability of success p on each trial. a. x = 4, n = 9, p = A set of data has a normal distribution with a mean of 36 and a standard deviation of 4. What percent of the data are within the interval from 32 to 40?

8 Chapter Rewrite the radian measure in degrees. 17π Rewrite the degree measure in radians. 135! 62. Find one angle with positive measure and one angle with negative measure coterminal. 50! 63. Find the exact value of the trigonometric function. cos225! 64. Find the exact value of the trigonometric function. " sin 5π % $ ' # 3 & 65. Solve ΔABC when angle C = 90!. Round measures of sides to the nearest tenth and measures of angles to the nearest degree. B = 42!, c = Determine whether the triangle should be solved by beginning with the Law of Sines or Law of Cosines. Then solve each triangle. C = 25!, a =12, b = Determine whether the triangle should be solved by beginning with the Law of Sines or the Law of Cosines. Then solve each triangle. a = 8, A = 49!, B = 58!