math for SUBBU

here

All work must be shown to receive credit. Formulas can be found on the last page.

1. Use transformation tables to graph. Be sure to show any asymptotes.

Solve each equation in # 2-7, giving exact answers.

2. 3.

_________________ __________________

4. 5.

_________________ ___________________

6. 7.

_________________ ___________________

8. Evaluate without a calculator. Give exact answers.

__________________

9. Find the inverse, , of the function .

__________________

10. Simplify

__________________

11. Express as a sum or difference of logs. Express exponents as factors. Simplify
when possible.

_________________

12. Evaluate to 4 decimal places.

_________________

13. Estimate how long it will take for $5000 to grow to $8400 at an interest rate of 6%
compounded:
a) Semiannually b) continuously

__________________ ____________________
14. Find the effective rate if the annual interest rate is 4.5% and interest is compounded daily.

_________________
15. A construction worker wants to invest $60,000 in a pension plan. Estimate how long it will
take the worker’s $60,000 to grow to $80,000 if interest is 6.75% compounded
continuously? (SHOW YOUR COMPUTATION)

__________________
16. Carbon 14 has a half-life of 5730 years. How long will it take for 100 grams to decay to
40 grams?

_________________
17. A piece of metal is heated to 300⁰C and then placed in a cooling liquid of 50⁰C. After 4
minutes the piece of metal has cooled to 175⁰C. Estimate the temperature after 12
minutes.

__________________
18.As age increases so does the likelihood of coronary heart disease (CHD). The fraction of

people x years old with some CHD is estimated by.
a)
Evaluate and interpret the result.

________________________________________________________________________
b) At what age does this likelihood equal 50%?

____________________
19. The table shows the number of aircraft midair near collisions y,x years after 2000.

Year

2000

2001

2002

2003

x

Near Collisions, y

239

205

180

162

a) Find an exponential function that models this data. Round coefficients to two decimal places.

____________________
b) Estimate the number of near collisions in 2006

____________________
20. Find the exact values of the six trigonometric functions for the angle in standard position
having the point (3,-1) on its terminal ray. Rationalize denominators.

sin_______ cos_______ tan_______ cot_______ sec_______ csc_______

21. Use trigonometric identities to find the exact value for cos A given .

___________________
22. Find the exact length of the arc of a circle with radius 12 cm that is intercepted by a central
angle of 135⁰.

_________________
Evaluate the following, giving exact values. Be sure to show reference angle and quadrant as your work.

23. tan(135⁰) 24. sin 25. cos

______________ _______________ ______________

26. csc(315⁰) 27. cot 28. sec

______________ _______________ ______________
Use a calculator to evaluate the following, rounding to two decimal places.

29. cot 30. sec170
_______________ ______________
31. A company safety committee has recommended that a floodlight be mounted on a pole 39.82
feet tall that is 51.74 feet from the employee exit. In order to illuminate the exit what angle
of depression should the light be set at?

______________________
32. A ship leaves port on a bearing N 27⁰ E and travels 100 kilometers.The ship then turns 90⁰
toward the south and travels 140 kilometers. What is the new bearing?

______________________

33. Identify the amplitude, period, phase shift, and vertical shift for
amp:____________
per:_____________
p.s._____________
v.s._____________

34. Graph one cycle of using transformation tables. Label your axes.

35. Write an equation of the form y = Asin(Bx-C)]+D with period , phase shift , and
range [-2,4].

_____________________

51
4
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