MAT 123 Final Exam. Part I (Type A) November 21, θ =

Transcription

1 MAT Final Eam Part I (Type A) November, 00 Student ID: Name: NOTICE. On your OPSCAN form you should write your last name, first name and Stony Brook ID only. Bubble in the circles correspondingly. DO NOT write anything in the BIRTHDATE and SPECIAL CODES bo. Instructions to fill in those boes will be given to you in part II.. Do not fold your OPSCAN sheet as the machine will not be able to read it.. Do not mark anything on the bottom of the OPSCAN where black markers are printed.. The answers you mark on this eam paper will NOT count! You should make sure you have bubbled in all your answers on the OPSCAN.. You will only be allowed to work with your calculator for the first 7 minutes. After that, you will receive part II, which is to be worked without any use of calculators. After receiving part II you may still work on part I, but without the use of the calculator.. For which of the following value(s) does sinθ = 0. hold I. III. θ = II. θ = θ = 6 I only I and III I, II and III I and II II and III. Given that cosθ : 9 sinθ = and < θ <, find

2 . Daniel put $0,000 in a bank where the interest rate is % per year compounded monthly. If he withdraws the money after 0 years, how much money would he gain (assume that he does not withdraw or deposit any money during that 0 years.) $.0 $8,06. $8,0.8 $8,.8 $8,07.. Find the -intercepts of the graph of the function f ( ) = + the correct answer below. - only -,-, only 0 only 0,, - only There are no -intercepts and choose 6. In a bacteria culture, initially there were N=000 bacteria. Half an hour later, the population grew to N=00. Assuming eponential growth, which of the following equations best describes the relation between number of bacteria N and time t (hours) N = 000e ln 0.(ln00) t N = 000e (ln00) t N = 000e (ln.) t N = 000e N = (00 000) e t 0.t 7. The half life of the radioactive element plutonium-9 is,000 years. If g of plutonium-9 are initially present, how many grams are present after 0,000 years 0g g 6g 8g. Which of the following equation has a slanted asymptote and does not have any vertical asymptote y = y = + y = y = What is the amplitude and the period of the graph of y = sin( ) + 6 Amplitude = 8, Period = Amplitude =, Period = Amplitude = 8, Period = Amplitude =, Period =

3 Θ Θ 9. The base lengths of above triangles are = in. and y= in. The angles are θ =/ rad and θ =0. What is the sum of the lengths of the two triangles hypotenuses Round to the nearest tenth. ( Figures not drawn to scale. Notice that the two angles have different units!) What is the (natural) domain of the + function f( ) = y [0,] (0,) [0,) (0,]. For the graph given below, indicate which of the graphs in figures or represents the correct inverse f ( ) Find the average rate of change of the function f () = + sin from = 0 to =

4 . A rectangle of sides a and b has total perimeter 8. How much is the area when b is times a 6 6 6/. The annual subscription for Moose Town Daily costs $0 and it has currently 0 subscribers. Recent analysis shows that for each dollar of subscription fee raised, the number of subscribers will drop by 9. What is the equation that correctly describes this analysis ( N is the number of subscribers and s is the annual subscription fee.) N = 60 0( s 9) N = 0 9( s 0) N = 0 90s N = 9 0s. What is the end behavior of the function f( ) = ( )( )( 00) and (falls left and falls right) and (rises left and falls right) and ( falls left and rises right) and (rises left and rises right) The graph has a horizontal asymptote so it becomes flat at both ends. 6. Select all odd function(s) from below. (An odd function is a function having a point symmetry at the origin.) I. ( + )( + ) II. + III. sin I only II and III I and III III only I, II and III 7. What is the horizontal asymptote of the function y = + 0 y = 0 = 0 = 0 y = 8. What is the y -intercept of the graph of cos y = ln a = and lnb =. What is log a b.

5 0. Solve the equation log = and choose the correct answer below. = or = only = only = only = only. Find the slope of the tangent line to y = + + at = Write ln( + ) + ln( + ) into a single logarithm. ln ( ) + ( + ) ln ( ) / ( + ) ln ( ) ln (( + ) ( ) ). Convert to radians: 8 8. What is the derivative of f ( ) =.. The inflection points of the function f( ) = + are: =, =, = only =, = 0, = only = 0, =, = only = 0, = only.

6 MAT Final Eam Part II (Type A) November, 00 Student ID: Name: IMPORTANT : You should fill in and bubble in the first column of the BIRTH DATE - DAY bo as follows. Please leave the second bo of DAY and the other boes - MO. YR. and SPECIAL CODES blank. Part I Type A Type A Type B Part II Type A Type B Type A DAY 0 IF YOU MARK THIS WRONG, ALL YOUR ANSWERS WILL BE GRADED INCORRECTLY. PLEASE TAKE CARE TO WRITE THE CORRECT SPECIAL CODE. Type B Type B 6. What is the value of sin 8. Which of the following has the same value as sec 6 cos csc 6 sin sec 6 7. If sinθ < 0 and secθ > 0 quadrant in which the angle θ lies. Quadrant I Quadrant III Quadrant II Quadrant IV, find the The terminal side of the angle lies on the coordinate ais. 9. Compute sin ( tan ) :

7 0. Which of the following is the graph of y = sin( ) Which of the following graphs represents the function f( ) = What is the equation of the slanted asymptote of y = + y = y = + + f( ) = + The function does not have a slanted asymptote.. Evaluate the epression log8 6 and choose the correct answer. 6 6

8 . Select correct equation(s) from below. I. ln + ln y = ln y log II. ( ) = log III. ln( + y) = ln + ln y I only I and II I, II and III I and III II and III 6. The graph of y = f( ) is shown below Which of the following is the graph of y = f ( ) Solve the following equation for : e 8e + 7=0 = = e,ln7 7 = ln e =, ln

9 7. Let f( ) = + 6. Find all critical point(s) of f ( ). =, = only =, = only = only = only. 9. What is the maimum value of f ( ) = in the interval [,] f ( ) = +. Select all correct statement(s) from below. I. The point (0,-) on the graph of f ( ) is the only point where the concavity changes from concave down to concave up. II. f ( ) has no local maimum or local minimum. III. f ( ) is an increasing function on any interval. (Note: local maimum/minimum is also called relative maimum/minimum in some books.) II and III I and III I, II and III I and II I only 0. In which interval(s) is the function f () = + + concave up/down Concave up: (, ), Concave down: (, ) Concave up: (, ), Concave down: (, ) Concave up: (, ) and (, ) Concave down: (,) Concave up: (, ), Concave down: (,).