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Algebra II Honors Spring 2009 Semester Review 1 Name ________________________________________ Date ________ Read and answer all questions accordingly. All work and problems must be done on your own paper and work must be shown. No work = No Exemption = NO EXCEPTIONS. Chapter 8 - Polynomials Solve each polynomial by any method of factoring. State all multiplicity roots. 1. x( x 2 6 x 5) 0 2. x 4 6 x 2 27 0 3. List ALL POSSIBLE rational zeros for f ( x) 2 x3 4 x 2 10 x 9 . 4. The volume of a rectangular solid is 675 cubic centimeters. The width is 4 centimeters less than the height, and the length is 6 centimeters more than the height. V = lwh Write in the alternative form. 1. 161/ 4 2 2. 160.5 1 4 3. a b x 1 1 4. log81 3 4 Condense and Simplify. 5. log 4 128 log 4 8 Solve. 6. log 2 12.8 log 2 5 7. 4e x e4 x 8. 3x 1 729 x /2 9. ln x 1 6 10. log 2.5 3.125 log 2.5 x log 2.5 15.625 2 11. e7 x 6.9 12. log x log( x 9) 1 13. ln e 2 5. Write the polynomial with the roots of 1, 4, and –5. Tell whether the function shows growth or decay. Then graph. 6. f ( x) 0.4 x 6 7. f ( x) 1.2 5 14. Use the formula A Pe rt . If $5300 is deposited in an account at the bank and earns 7% annual interest, compounded continuously, what is the amount in the account, rounded to the nearest dollar, after 9 years? x Chapter 8 - Rational Expressions 1. If y varies directly as x, and y=15 when x=10, find y when x=14. 2. If y is directly proportional to the square of x, and y=12 when x=14, find y when x=6. 3. If c is inversely proportional to d, and c=2 when d=3.6, find c when d=4.5. Chapter 5 - Logarithms 4. Suppose r varies jointly as t and n and inversely as the square of v. When t=3, n=18, and v=5, then r=3.78. Find r when t=4, n=12, and v=4. Algebra II Honors Spring 2009 Semester Review 2 x2 x 6 5. Simplify f ( x) 2 . Identify any x-values for which the x 4x 3 expression is undefined. 6. Sketch the graph of f ( x) x 1 and label all x2 asymptotes. of f ( x ) 8. Label all asymptotes, f ( x) x2 1 . x2 Multiply or divide. Assume that all expressions are defined. 3x 3 . Then graph. x2 Solve each equation. 15. 2 7. Label all asymptotes and holes of x2 f ( x) 2 . x 4 x 9 x 5 2 9. 2 x 10 x 81 14. Identify the zeros and asymptotes 3 10 x 1 16. x x 5 x 1 3 x 1 Chapter 9 – Compositions of Functions If f(x) = x3 and g(x) = 2x2 + 7, solve the following: 1. f(x) – g(x) 2. g(x) • f(x) 3. f(g(x)) 4. g(f(x)) Chapter 11-Conics 1. The transmission of a radio signal can be received at the locations (1, 10) and (–11, 6) . Write an equation for the range of the signal if a line between the locations represents a diameter of the range. 3x3 9 x 2 2x 6 10. 2 2 x 16 x 8 x 16 2. Find the center, vertices, co-vertices, and foci of the ellipse with equation, 49( x 4)2 16( y 2) 2 =784 . Then graph. Add or subtract. Identify any x-values which the expression is defined. 11. 5 x x 5 2 x 10 12. 5x 9 x 6 x7 x3 13. Lorraine averaged 62 words per minute when typing the first 3 pages of a 6-page report. Her average typing speed for the last 3 pages was 45 words per minute. To the nearest word per minute, what was Lorraine’s average typing speed for the entire report? 3. A shelter for a patch of young strawberry plants is constructed in the form of an ellipse. If the shelter is 4.5 feet high at its highest point and the patch is 19 feet wide, write an equation for the ellipse. 4. Find the center, vertices, co-vertices, foci, and asymptotes of the x2 y 2 1 . Then graph. hyperbola with equation: 25 144 Algebra II Honors Spring 2009 Semester Review 5. Find the center, vertices, co-vertices, foci, and asymptotes of the hyperbola with equation: x 2 4 2 y 5 12 2 1 . Then graph. 3 Chapter 15 - Probability 1. A mall employee is dressing a mannequin. There are 6 pairs of shoes, 4 types of jeans, and 8 sweaters. Using 1 of each, how many ways can the mannequin be dressed? 6. Write the equation of the hyperbola with vertices (0, 7) and (0, -7) and conjugate axis length is 28. 2. How many ways can you award first, second, and third place to 8 contestants? 7. Find the vertex, value of p, axis of symmetry, focus, and directrix of the 3. How many ways can a group of 3 students be chosen from a class of 30? 1 parabola with equation: y + 4 = (x – 2)2. Then graph. 24 4. The table shows the results of tossing 2 coins. Find the HH HT TH TT experimental probability of tossing 2 tails. 8. Find the equation of the parabola with vertex at (-3,1), and focus (-1,1). 9. Find an equation of the ellipse with vertices at (-2,2) and (4,2), and covertices at (1,4) and (1,0). Each letter of the alphabet is written on a card. The cards are placed into a bag. Determine the indicated probability. 10. Write the equation of the circle in standard form. Identify the center and radius. x 2 y 2 4 x 6 y 9 0 11. Find the equation of the hyperbola with vertices (2,2) and (2,8), and foci (2,0) and (2,10). 12. Find the equation whose center is (1, –3), length of transverse axis is 7 units long on the x-axis. Length of the conjugate axis is 4 units. 5. The letter D is drawn, replaced in the bag, and then the letter J is drawn. 6. Three vowels are drawn without replacement. A card is drawn from a bag containing the 9 cards shown. Find each probability. 13. Find the equation whose vertices are (6, –6) and (0, –6) and focus at 3 13, 6 14. What is the discriminant and type of conic section of x2 + 4y2 − 6x − 7y = 0? 7. Selecting a C or even number 3 8. Selecting odd number or multiple of Algebra II Honors Spring 2009 Semester Review 4 9. The probability distribution for the number of absent students on any given day for a certain class is given. Find the expected number of absent students. Solve. 10. 8 P3 11. 8 P8 12. 8 C6 Evaluate each inverse trigonometric function. Give your answer in both radians and degrees. 2 2 Chapter 13-Trigonometry Find the values of the six trigonometric functions for θ. 1. Use the unit circle to find the exact value of each trigonometric function. 12. cos 210° 13. tan 11π/6 14. csc 315 15. cos 1 2. 16. sin 1 3 2 17. A limestone cave is 6.2 mi south and 1.4 mi east of the entrance of a national park. To the nearest degree, in what direction should a group at the entrance head in order to reach the cave? 3. Katy is flying on 150 ft of string. The string makes an angle of 62° with the horizontal. If Katy holds the end of the string 5 feet above the ground, how height is the kite? Round to the nearest foot. Use figure on the right to solve the question below 18. Use the given measurements to solve # DEF. Round to the nearest tenth. Draw an angle with the given measure in standard position. 4. 100° 5. –210° P is a point on the terminal side of θ in standard position. Find the exact value of the six trigonometric functions of θ. 6. P (–32, 24) 7. P (-3, -7) Convert each measure from degrees to radians or from radians to degrees. 8. 310° 9. –36° 10. 2π/9 11. –5π/6 19. An artist is designing a wallpaper pattern based on triangles. Solve all measurements if a = 28, b = 13, and m A = 102°. Round to the nearest tenth. 20. Solve LMN for its missing sides and angles. Round to the nearest tenth. 21. List 3 ways you will do to help you study for the final exam.