Baruch College MTH 00 Sample Final B Form 0809 PAGE MTH 00 SAMPLE FINAL B BARUCH COLLEGE DEPARTMENT OF MATHEMATICS SPRING 00 PART I (NO PARTIAL CREDIT, NO CALCULATORS ALLOWED). ON THE FINAL EXAM, THERE WILL BE 5 MULTIPLE CHOICE QUESTIONS ON THIS PART, WITH PROBLEMS SIMILAR TO OR SLIGHTLY DIFFERENT FROM ANY OF THE FOLLOWING:. For f() = and g ( ), find the composite function defined by (fog)().. b) 4 + 4 8 + 4 +. Solve: 4 0. 0 4,, b) 0,4 0,4, 0 4,, 0 4,. Solve for : log log ( 6). only b) = 9 only = and 9 = only and = 9 4. The graph below represents a shift of the graph of y ln. Which of the following is the best choice for the graph s equation? [Hint: Try sketching the graph of y ln on the same aes below, to help you see the shift.] y 4. y ln( 4) b) y ln( ) y ln( ) y ln( ) 4 ln 4 5. Solve for : log 5. only b) = only = only only = and =
Baruch College MTH 00 Sample Final B Form 0809 PAGE 6. Find the -intercepts and verte for f() = + 4 0. 6. -intercepts (, 0) and ( 5,0); verte (, 6) b) -intercepts (, 0) and (5,0); verte (, ) -intercepts (, 0) and ( 5,0); verte (, ) -intercepts (, 0) and ( 5,0); verte (, 6) -intercepts (,0) and ( 5,0); verte (, ) 7. Solve for : 7 7. b) 9. 8. Perform the operation and epress your answer in simplest comple form. 5i i 7i b) 6+7i-5i 7i 7i 7i 8. 9. What are the center and radius of y 6y? 9.,, r b),, r,, r,, r,, r 0. Given the circle y 69, what is the equation of the tangent line at the point (, -5)? 0. 5y 69 b) 5y 69 5y 69 5 y 69 5 y 69. Simplify 5 ( ab ) a b b) a b ab 0a b 0ab.. What is the minimum value of y 4 6?. b) 6 0 6
Baruch College MTH 00 Sample Final B Form 0809 PAGE. Find the domain of f ( ). is a real number and is a real number and is a real number and } } b) is a real number and } is a real number and } } 4. Given the function f() = + + 4. What can you say about the graph s -intercepts? The graph has NO -intercepts b) The graph has ONE RATIONAL -intercept The graph has TWO RATIONAL -intercepts The graph has TWO IRRATIONAL -intercepts Not enough information is provided 4. 5. Which equation best represents the graph below?. 5. y = + b) y = + y = + y = y = 6. Solve: 6. or b) or only only 6. only 6
Baruch College MTH 00 Sample Final B Form 0809 PAGE 4 7. Given the function f() = 6, find f - (). 7. / f - () = / 6 + 6 b) f ( ) f - () = ( + 6) 6 ( 6) f ( ) f - () = ( + 6) / 6 y 4 8. Solve the system of equations: y How many real solutions are there to the system? 8. no solution b) solution solutions solutions 4 solutions 9. Let f() = ( ) + 8. Find the verte and determine if it is a maimum or minimum. 9. (, 8) ma b) (, 8) min (, 8) ma (,8) min (, 8) ma 0. Solve for.. 0. 5 only b) 5 and only no solution only 0 only. Write as a single logarithm. Assume that all variables represent positive real numbers.. log log y log z log b) yz log yz log yz z log y 6log yz. Simplify 7 z 9 5 y (Assume that the variables do not have negative values.). 4 7 yz yz b) 8 4 y z yz 4 yz yz yz yz y z 7 4
Baruch College MTH 00 Sample Final B Form 0809 PAGE 5. Find the function f() that describes the line containing (,) and (5,5).. f ( ) 4 5 b) f ( ) 4 6 f ( ) 4 f()= - f ( ) 5 4 4. Solve: a a. 4. i 4 4 7 4 b) i 4 4 5, 4 4 i 4 5 5. Rationalize the denominator. 6 9 6 b) 6 6 6 5. 6 END OF PART I. PART II BEGINS ON NEXT PAGE.
Baruch College MTH 00 Sample Final B Form 0809 PAGE 6 PART II (CALCULATOR ALLOWED). THIS PART OF THE FINAL EXAM WILL HAVE 0 MULTIPLE CHOICE QUESTIONS. For problems #6 - #9, round your solution to the nearest HUNDREDTH and determine the digit in the TENTHS place of your solution. For eample, if your solution were =.57, then you would choose the answer 5, since 5 is the digit in the tenths place. 6. Solve the equation for :. Round your answer to the nearest HUNDREDTH. THE DIGIT IN THE TENTHS PLACE OF THE SOLUTION IS: 6. 0 b) 7 8 4 7. Solve the equation for : log ( ) log ( ) log. Round your answer to the nearest HUNDREDTH. THE DIGIT IN THE TENTHS PLACE OF THE SOLUTION IS: 7. 7 b) 4 6 0 5 8. Solve for to the nearest hundredth: e 6. THE DIGIT IN THE TENTHS PLACE OF THE SOLUTION IS: b) 6 4 9 8. 9. Solve for to the nearest hundredth: ln( 4) 7. THE DIGIT IN THE TENTHS PLACE OF THE SOLUTION IS: b) 8 4 5 9 9. 0. A virus is introduced to a population and spreads continuously at a rate of 6% per day. At first, people are infected. Determine how many people are infected after days. 0.6t Use the formula A( t) e, where t is the number of days since the virus was introduced. Round your answer to the nearest WHOLE NUMBER. 0. 6 b) 5 5 86. Evaluate: log 5 00. Round your answer to the nearest HUNDREDTH.. 5.00 b) 0.00.86 4.6.6
Baruch College MTH 00 Sample Final B Form 0809 PAGE 7. A ball is thrown up from a height of 5 feet at an initial velocity of 0 feet per second. Its height after t seconds is given by h ( t) 6t 0t 5. Determine the time it takes for the ball to hit the ground. Round your answer to the nearest HUNDREDTH..0 seconds. b) 6.00 seconds 0.94 seconds 0.50 seconds 5.0 seconds. Approimate the distance between the points (-, 9), (-7, -5) to the nearest tenth: 5. b) 6. 4. 7. 4.9. 4. An initial investment of $50 is made into an account that is compounded continuously. If after 6 years the amount in the account is $00, what is the interest rate to the nearest hundredth? 5.4% 4. b).8% 0.05%.0% 0.0% 5. Given a profit function P ( ) 6 66 8000, find the MAXIMUM PROFIT (round your answer to the nearest thousan. 5. 8000 b),000 000 4,000 5,000 END OF PART II. ANSWERS TO MTH 00 SAMPLE FINAL B (UPDATED SPRING 00). A. B. D 4. B 5. C 6. C 7. A 8. A 9. C 0. C. B. D. E 4. A 5. B 6. A 7. E 8. E 9. C 0. A. D. B. A 4. D 5. E 6. E 7. A 8. D 9. B 0. C. C. A. C 4. A 5. B