Math Final Exam Instructor: Ken Schultz April 28, 2006

Transcription

1 Name Math Final Exam Instructr: Ken Schultz April 8, 006 Exam Guidelines D nt pen this exam until are instructed t begin. Fllw all instructins explicitly. Befre yu begin wrking, make sure yur test has Multiple Chice Questins. The test will end exactly 50 minutes after it begins. Failing t write yur name in the specified area n this test r the scantrn will result in a lss f 5 pints per ffense. Abslutely NO ntes r bks may be used n this exam. There are 110 pints available n the exam. Yur final grade will be taken ut f 100. When yu are finished with yur exam, please turn it in at the frnt f the rm and quietly exit the rm. A frmula yu might find helpful: Yu + Cheat = Fail Gd Luck!

2 1. Which f the fllwing is NOT ne f the Laws f Csines fr any triangle ABC? a. a = b + c bccs A b. c = a + b accsc c. b = a + c accs B d. a = c + b cbcs A e. Each f the abve is part f the Law f Csines.. Yu are tld 5 i is a zer t a plynmial P with real cefficients, which f the fllwing is als a zer f P? a. 5 i b. 5 + i c. i + 5 d. i 5 e. Nt enugh infrmatin is given. 3. The value f a building lt n Gallian Island is jintly prprtinal t its area and the quantity f water prduced by a well n the prperty. A 00ft by 300ft lt has a well prducing 10 gallns f water per minute, and is valued at $48,000. What is the value f a 400ft by 400ft lt if the well n the lt prduces 4 gallns f water per minute? a. $47,400 b. $56,300 c. $44,600 d. $51,00 e. Nne f the Abve / Nt enugh infrmatin 4. Fr triangle ABC where A = 4, a = 70, and b = 1 what is the measure f B? (Rund t the nearest degree) a. 35 b. 1 c. 117 d. 70 e. N slutin / Nne f the Abve. (yu get sin(b) = 1.66 which is impssible)

3 5. Which f the fllwing is true fr any triangle ABC accrding t The Law f Sines? Asin A sin B a. = B A B C b. = sin C sin B sin C sin A c. = C A d. All f the Abve. (Nte: Sides dented by lwercase letters) 6. What is the mdulus f the fllwing cmplex number: z = 4 3 4i a. 8 b. 3 c. 1 d. 11π 6 7. Which f the fllwing is equivalent t ( x + y) a. sin xsin y + cs x cs y b. sin x cs y cs xsin y c. sin x cs y + cs xsin y d. sin xsin y cs x cs y sin? 8. Which f the fllwing is equivalent t ( x y) a. sin xsin y + cs x cs y b. sin x cs y cs xsin y c. sin x cs y + cs xsin y d. sin xsin y cs x cs y cx? 9. Which f the fllwing is nt ne f the Pythagrean Identities? a. sin x + cs x = 1 b. tan x + 1 = sec x c. sin x = 1 cs x d. 1 + ct x = sec x 3

4 10. What is the argument f the fllwing cmplex number: z = 5 + 5i. π a. π b. 3 π c. 6 d. π π e. Nne f the abve (answer is ) A triangular field has sides f lengths, 36, and 44 yards. Find the largest angle. Rund t the nearest whle number. a. 96 b. 9 c. 54 d State whether r nt the infrmatin given generates 0, 1, r triangles. a = 8, b = 15, A = 110 a. 0 b. 1 c. 13. An interesting applicatin f the Law f Csines is Hern s Frmula which is used t find the area f a triangle. Hern s Frmula is as fllws A = s( s a)( s b)( s c) where s is the semi-perimeter f the triangle (i.e. half f the perimeter). Knwing this, we knw a businessman wishes t buy a triangular lt in a busy dwntwn lcatin. He knws the lt has sides f length 15, 80, and 315 feet. What is the area f the lt? Rund t the nearest ft. a. 17,45 feet. b. 76,99 feet. c. 19,417 feet. d. 14,8 feet. 4

5 14. Find the indicated pwer: ( 1+ i) 0 0 a. 1+ i i b. 3 c. 4 64i d. Nt enugh infrmatin. e. Nne f the abve. ( -104 ) 15. Write the fllwing as a single trignmetric equatin: sin 18cs 7 cs18sin 7 a. sin 55 b. cs 55 c. sin 9 d. cs 9 (sin(-9)) 16. State whether the fllwing infrmatin generate 0, 1, r triangles. 0 b = 5, c = 30, B = 5 a. 0 b. 1 c. 17. tan x is equivalent t which f the fllwing? a. tan x 1 tan x b. tan x 1+ tan x c. 1+ tan x tan x d. 1 tan x tan x 5

6 The CN Twner in Trnt, Canada, is the tallest freestanding structure in the wrld. A wman n the bservatin deck, 1150 feet abve the grund, wants t determine the distance between tw landmarks n the grund belw. She bserves that the angle frmed by the lines f sight t these tw landmarks is 43º. She als bserves that the angle between the vertical and the line f sight t landmark A is 54º and the angle between the vertical and line f site t landmark B is 6º. Answer the next 3 questins using this infrmatin. Rund t the nearest ft. Landmark B Landmark A 18. What is the distance between the lady n the deck and Landmark A? a. 184 feet b feet c. 104 feet d. 141 feet e. Nne f the Abve 19. What is the distance between the lady n the deck and Landmark B? a. 130 feet b feet c. 450 feet d feet e. Nne f the Abve 0. What is the distance between Landmark A and Landmark B? a feet b feet c feet d. Nt Enugh Infrmatin e. Nne f the Abve 6

7 1. I have a drawer that cntains 176 red scks, 3 blue scks, 41 ht-pink scks and 19 black scks. I am in a hurry because my alarm didn t g ff because the pwer is ut because f sme stupid thunderstrm. What is the least number f scks I need t take with me t guarantee I have a matching pair? a. 177 b. 33 c. 130 d. 4 (The answer is 5). What is this shape: a. Circle b. Triangle c. Square d. Red e. Fishstick 7

8 This page left blank and is t be used fr scratch paper. D nt remve frm yu test. 8

9 This page left blank and is t be used fr scratch paper. D nt remve frm yu test. 9