ALGEBRA 2/ TRIGONOMETRY 41 Part I Answer all 27 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. For each question, write in the space provided the numeral preceding the word or epression that best completes the statement or answers the question. J. What is the measure, ill radians, of a central angle formed by cutting a circular pizza into lwelve t:ljllal wedge shaped pieces? (l)~ e) 2" (3)2" (4)~ 6 ~ 5 4 3 2. Whidl lju;l(jralic equation has roots that have a sum of -12 and a produl:l of 32" ( I ) ~ 121:+ 32=0 (3) 2 +12+32 =0 (2) 1-12-32=0 (4) 2 + 12-32=0 2 ~l. What is the eact value of the sec eif (5, 2) is on the terminal side ore in standard position? ( 1)_2 (2)5m (3)_m (4)m 3 2 29 2 5 -- IJ. Solve for : 8-, +4 = 16 3 (I) I (2) 2 (3){%} (4){~} 4 5. Solve: ~+1 < _1_ - 2-2 (1) ( < 1) or ( > 2) (3)(1 <<2) (2) ( < -1) or ( > 2) (4) (- 2 < < -1) 5 6. If the roots of a quadratic equation are real, rational, and unequal, /7 2-4ac could equal (1) - 9 (2) 9 (3) 3 (4) 0 6 7. If a fair coin is tossed 8 times, what is the probability it lands heads up at least 6 times? Round to the nearest percent if necessary. (1) 11% (2) 14% (3) 60% (4) 75% 7 8. Simplify (8 4 / F 2 (1)4 2 / V (2)4y2 V (3) ~648y6 (4)~5127y6 8 _ 9. What is the quotient when (2 + 5i) is divided by (1 - i)? 7+7i -3+7i ( 1) -2- (2) -3 (3)-2- (4)7 9
42 ALGEBRA 2 / TRIGONOMETRY 10. Art and his friends go out for dinner. They want to split 3 appetizers. If the restaurant offers 14 appetizers, how many different combinations could they choose? (1)2,184 (2)364 (3)42 (4)8 10 II. Which epression is found when J-80 4 is simplified? 2 (I) -4 15 (2) 16 2 i15 (3) 4 1 i15 (4) -16215 II 12. A container of liquid decreases continuously at a rate of 1.02% per day. If the weight of the liquid starts out at 50 grams, what will its weight, to the nearest tenth ofa gram, be at the end of 19 days? (1)0 (2)6.5 (3)41.2 (4)316.5 12 13. Which formula would give you the 15th term of the sequence -1 0, -5,0,5,...? n(a +a ) a (I-rn) (I) 12 n (2) II_r (3)a +(n-l)d (4)a r" - 1 13 l 1 8. 4 14. Evaluate: 2 + 12 ~ 2 + 3 _ 18 (I)(+3) (2) ( - 3) (3)(-3) (4) ( + 2) 2 15. What is the 7th term for the sequence that follows the recursive rule an + 1 = 20n - 3 and given that 01 = 20? (I) 37 (2) 1,091 (3) 547 (4) 11.5 15 16. If sin e= - f ' the values of e in the interval 0:0; e< 360 are (1)60 0 and 120 (3) 120 and 300 (2) 120 and 240 (4) 240 and 3000 17. What is the sum of the coefficients in the epansion of(a + b) 5? (I) 5 (2) 16 (3) 32 (4) 40 18. Perform the indicated operation and epress your answer in simplest form: 2m + 3196 (1)2.Ji20 (2)16m (3)16.j6 (4)5.j6 19. Solve this system ofequations: 2-4 - 4 = Y 2+y=4 (I) (4, - 2) (3) (-4, -4), (2, 8) (2) (4, -4), (-2, 8) (4) (4, -2), (-4, 8) 19 14 16 17 18 ALGEBRA 2 / TRIGONOMETRY 20. Find all values of 0 :0; e< 360 that satisfy the equation 4 = 5-2 tan e, to the nearest degree. (I) 27,153, 207,333 (3) 27, 207 (2) 27, 153,207 (4) 153, 333 1+1 21. Simplify: I - - I (2) (3) + I I (I)~ (4) _ I 21 -I - I 22. Find the eact value of cot 9 if e is in standard position and (-7, 2) is on the terminal side of e. (1)_315 (2) 715 (3)_l (4)_2 22 7 15 7 2 23. Which of the following eamples would require calculating a permutation? (I) Finding the arrangement of7 people wai ting in line at the bank (2) Choosing 3 candidates for a job in which 10 applied (3) Electing which 2 students in the group of 8 will give the project presentation (4) Choosing 3 ice cream toppings from a list of 12 23 24. Evaluate: 2 log3 (t) (I) 0.25 (2) -0.4 (3) - I (4) -4 24 25. What is the domain of the function f(s) = ~(4 - ) + 3? (I) ~ 4 (2):O;7 (3):O;4 (4)allreals 25 26. What is value of 9 and its reference angle, labeled a, that are sketched in this diagram? (I) 9 = 120, a= 60 (2) e=240, a = 30 (3) e= -120, a = 60 (4)9 = -120, a=30 26 27. Solve for : 2-4 + 2 = 0 (I) {2+2J2,2-2J2} (3) {2 + J2, 2 - J2} (2) {4 + J2, 4 - J2 } (4){ 2+2.Ji, 2-2 J2 ) 20 27 43
44 ALGEBRA 2/ TRIGONOM ETRY Part II Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only I credit. ALGEBRA 2 / TRIGONOMETRY 31. Sketch the graph of g() = I - 31. Name three ordered pairs that belong to the function g(). 45 9 28. find the partial sum of the following arithmetic series L 3k + 2? k =5 29. Jessie purchased enough mulch to cover her square garden that has an area of 864 square feet. Find the length of one side of the garden. Epress yo ur answer in simplest radical form. -2 3 32. Simplify: \ ~5. ;e 0, y;e 0 y 30. The lifetime of a light bulb is normally distributed with a mean life of 1000 hours and a standard deviation of 30 hours. find the probability that a randomly selected light bulb lasts longer than 1045 hours. 33. Evaluate: sin 200 cos 70 + cos 200 sin 70
46 ALGEBRA 2 / TRIGONOMETRY 34. A circle with a radius of 6 inches is inscribed in a square as shown below. If a dart is thrown inside the square, what is the probability that it lands inside the circle? Round to the nearest percent. ALGEBRA 2 / TRIGONOMETRY 47 Part III Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. 36. Solve for : log/ - 4) + log3( + 2) = 3 35. State the domain that is needed for Tan so that its inverse Arctan is a function. Determine the range ofarctan. +9 37. Find the inverse off() = - - and evaluate f -I(4). 38. In triangle ABC, mla = 40 and mlb = 56. The longest side of the triangle is 36 cm. Find the length of the shortest side to the nearest tenth ofa centimeter.
48 ALGEBRA 2 / TRIGONOMETRY Part IV Answer the question below. The correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. A correct numerical answer with no work shown wih receive only 1 credit. 39. Perform the indicated operations and epress the answer in simplest form. 2-5 2--12 2-8+16 -,--. +--- 2-9 5- -4