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Algebra 3/Trigonometry Final Exam Review A. Solve for x: 1 1. log 25 x 2 2. log 8 1 x 32 3. log 3 x log 3 (2x 51) log 4 256 4. log243 3 81 x 5. 12 log12 2 x 2 6. 4(log 81 x)2 3(log 81 x) 1 0 1 7. log x 3 8 8. 9. log 25 log 3 log 2 x 0 10. log x log(2x 3) 2 6 2x 1 216 2x 1 11. 16log2 3 12. 23x 2 32x 1 (simplify as far as possible WITHOUT a calculator) B. Given f(x) 2x 9 , g(x) 1. f 1 (x) 1 x3 2x 3 , h(x) , m(x) and n(x) x 3 find 2 x x 1 x5 2. m1 (x) 3. g 1 (x) 4. n 1 (x) 5. g f 6. g n 7. m h 8. f(g(n(4)) 9. m(h(g(2)) C. Coordinate Geometry 1. Write the following in standard form and graph the following completely a) x2 6x y 2 4y 3 b) 2x 2 4x y 3 c) 9x 2 4y 2 36 d) 4x2 16x 9y 2 18y 29 e) 2y 2 x 2y 1 3. Write the equation of the hyperbola that has foci at (4, 5) and (-4, 5) and has slopes of asymptotes of 2 4. Write the equation of the conic that has as major axis endpoints (-13, 7) and (-1, 7) and minor axis endpoints (-7, 10) and (-7, 4). 5. Find the equation of the conic that has width points (12, 3) and (12, 1) and opens left. 6. Find the equation of the conic that has major axis endpoints (2,0) and (4,0) and a focus at (0,0). D. Trigonometry 1. Find each of the following: 11 a) sin 6 3 b) sin 4 c) tan (315) d) sec (210) e) cos (150) 9 f) cot 4 g) sec -1 (-2) h) cos-1 (-1) i) cot -1 1 j) cos tan 1 2 + sin -1 3 2. If cos x = - 3 k) tan cot-1 3 tan 1 6 3 and tan x 0 , find the values of the other five trig functions. 4 3. Graph the following functions completely. a) f(x) 4cos(2x ) 1 b) f(x) 2 tan 3x 3 2 c) f(x) 3sin x 2 3 x d) f(x) cot 1 4 e) f(x) 4csc(2x ) 1 f) f(x) 4. Prove the identity 1 3 sec x 2 4 2 cos3 x sin 3 x sec x sin x 1 2sin 2 x tan x 1 2 5. If sin , in quadrant 2 and sec 4, in quadrant 1 find the following. 5 a) sin2 c) cos 2 b) cos( ) , sin( ) and quadrant of ( ) d) tan( ) e) cot 2 6. Solve the following for 0 x 2 a) sin2x tanx 0 c) 4(sec 3x)2 16 b) 6 2cos2 x 9sin x d) cos2 x sin x cos x sin2 x Directions: Set up an equation and isolate the unknown completely. Do NOT use a calculator. 7. A triangular parcel of land is bordered on one side by 115 meters of hedges, and the other by flower beds with lengths of 76 meters and 92 meters. At what angle do the flower beds meet? 8. A triangular parcel of land is bordered on one side by hedges and the other by flower beds with lengths of 76 meters and 92 meters. If the flower beds meet at an angle of 47.0, find the length of the hedge border. Answers: A. 1. 1 5 9. 8 2. - 5 3 10. 300 199 3. 3 2 4. 11. 34 4 15 5. 2 12. 6. 3, 1 81 7. 1 2 8. 3 7 log12 log 8 9 B. 1. x9 2 7. x 18 3x 2 2. x3 1x 8. 7 3. 1 x 9. - 4. x 2 +3 5. 1 (2x 9)2 6. 1 x 3 73 11 C. 1. a. (x 3)2 +(y+2)2 =16 2 1 1 3 e) y x 2 2 2 5. y 2 2 1 2 x 12 2 1 b. (x 1)2 (y-5) 2 x 2 (y 5)2 3. 1 16 64 5 5 6. (x 3)2 y 2 1 1 8 c. x2 y 2 1 4 9 d. (x 2)2 (y 1)2 1 9 4 (x 7)2 (y 7)2 4. 1 36 9 D. 1. a) g) 1 2 b) 2 3 2 2 h) c) 1 i) 6 d) j) 2 3 3 2 10 2 5 15 e) 3 2 k) f) 1 17 9 3 7 7 4 7 4 cot tan csc 7 3 7 3 3. a) Start: - , End: ; graph in class b) Asympt: - , , ; graph in class 6 6 2 2 2 8 2 ; graph in class d) Asympt: 0, 4, 8; graph in class , End: c) Start: 3 3 3 5 ; graph in class f) Asympt: - , , e) Asympt: - , 0, ; graph in class 4 4 4 2 2 4. (proof) 2. sin 7 4 sec 5- 21 32 21+25 15 10 21 2 15 2 - 3 35 4 21 e) d) c) , QIII , b) 2 39 4 20 20 25 2 4 5 7 8 10 11 13 14 16 17 5 3 5 7 , , , , , c) , , , , , , 6. a) 0, , , , , ,2 b) , 9 9 9 9 9 9 9 9 9 9 9 9 6 6 4 4 4 4 3 5 d) 0, , , , , 4 4 2 2 5. a) 1152 762 922 7. cos 1 2(76)(92) 8. 762 922 2(76)(92)cos47 9. x= 35sin23 sin63