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A final examination for a mathematical models course, covering topics such as calculus, logarithms, trigonometry, vectors, and complex numbers. It includes multiple choice and numerical questions, as well as problems to be solved using various mathematical methods.
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Mathematical Models 1 201- December 2008 Final Examination
Instructor: Bob DeJean
Calculate, giving your answer to the right number of significant digits: (2.31 x 10 4 ) (5.062 x 10 -1^ ) =
Write 178° in radians.
Which is bigger: 2 radians or 113°?
Calculate: log 7001 =
ln 86.31 =
log (-23) =
e 2 =
Is there any place where this graph is not continuous?
Many years ago Toronto had 25 cycle electric current, that is the frequency was 25 Hz. My Dad says it was so slow you could see the lights flicker. What was the period of this current?
What was its angular velocity?
For y = 7x^6 – 6x^5 + 4321 find y’ =
and y” =
and even y’” =
Pat and Tiffany are standing about 10 m from their campfire. To block some of the light, they hold up a sleeping bag. The sleeping bag is a rectangle, about 1.2 m by 2.1 meters. About what solid angle of firelight are they blocking?
Alex had an aluminum cylinder, diameter 3 cm, 15 cm long. He put one end in a grinder, making that end a cone 4 cm high. The thing looks a bit like a freshly sharpened pencil. What is its volume?
Find the magnitude and direction of the vector (^8 ,^5 )
Add: ( 3 , 15 )+ (− 8 , 6 )=
Write using simple logs
^ =
5 ln 6 x
Write using one log log 20 + ½ log x =
Solve: ln x + ln(x + 2) = 4.143 134 8
Find these limits:
( − ) = →
x x x
2 4
lim
x
x x lim (^) ln
lim^322 (^2) x
x x x
Calculate (4 + 3j) – (11 – 3j) =
(2 + 5j) (3 + j) =
j
j 2
Write in rectangular form: 7 / 30° =
Calculate:
Solve for angle x: 3sin x = 2
Find the derivative: y = 32x – 2x^3
x
y^ x
3 7
y = 7 x − 6
Find the derivatives y = 16 cos (½ x)
y = 3x tan x
Find the equation of the line tangent to
x
y x at the point (1, ½).
Sketch the graph of y = 6 sin( 8x + π/2) Vertical Shift = Amplitude = Phase Shift = Period =
Use the limit definition to find the derivative of y = 3x^2 Show your steps.
1 + 17j (19 + 22j) / 5 6.0621 + 3.5j 8 / 50° 64 / -18°
5 /15°, 5 / 105°, 5 /195°, 5 /285° 300 + 1885j
41.81° +/- 360°n and 138.19° +/- 360°n 32 – 6x 2 6 / √x (x 2 + 8x – 4) / (x + 4)^2 105x 2 (x^3 + 2)^6 3.5 / √(7x – 6)
