Final Review

Exponential & Logs

100

Make a table of values and graph f(x)= 2^x+4 -5

See Mrs. Stutzman

200

Solve 7^x=27

Round to three decimal places

1.694

300

Given log_a2=.693 and log_a3=2.183

a.  Find log_a6 

b.  Find log_a3/2

a.  2.876

b.  1.49

400

Following the birth of a child, a grandparent wants to make an initial investment that will grow to $70,000 for the child's education at age 18.  Interest is compounded continuously at 4.3%.  What should the initial investment be?

$32,281.53

500

Solve logx=1-log(x-9)

x=10

Trig

100

Given that cscx=9/8 and that the terminal side is in QII, find the cosx.

-square root 17/9

200

A 150-foot supporting cable is tied to the top of a cell phone tower then secured to a point on the ground.  If the angle of elevation from the point on the ground to the top of the tower is 35 degrees, find the height of the tower.  Round to the nearest tenth.

86 ft

300

Given that tanx=-5/12 and that the terminal side is in QIV, find cos(pi/2-x)

-5/13

400

Find an equivalent expression sin(x-pi/2)

-cosx

500

A fire is spotted from the top of a 125-foot tall fire tower.  If the angle of depression to the fire is 19 degrees, how far is the fire from the base of the tower.  Round to the nearest tenth.

363 ft

More Trig

100

Factor and simplify (2cos²x-5cosx-3)/(cosx-3) 

2cosx+1

200

a.  Find the exact value of sin^-1(-.5)

b.  Find the exact value of cos^-1(0)

a.  -pi/6

b.  pi/2

300

Simplify

(cosx-sinx)²

1-2sinxcosx or 1-sin2x

400

Prove the identity

tanxsin²x/1+cosx=tanx-sinx

Show Stutz

500

Prove the identity

sinx/1-cosx +sinx/1+cosx=2cscx

See Stutz

Triangles & Polar

100

In triangle ABC, angle A=47, angle B=52 and AC=13.  Solve the triangle.  Round to the nearest tenth.

Angle C=81

AB=16.3

BC=12.1

200

Find the standard notation a+bi

4(cos(pi/6) +isin(pi/6)

2root3+2i

300

Find the polar coordinates

(-2, -2)

(2root2, 5pi/4)

400

Given triangle JKL with JK=18, KL=16, and JL=12, solve the triangle.   Find angle J, K, then L.  Round all answers to the nearest tenth.

J=60.6

K=40.8

L=78.6

500

A boat leaves the dock and sails in a direction of 60 degrees.  Once reaching its destination on the opposite shore, it sails in a direction of 283 degrees and docks 123 km north of its original starting position.  What is the total distance the boat has traveled?  Round to the nearest tenth.

331.9 km

Misc

100

Indicate whether the following equation is an ellipse or hyperbola.

3x²+36y²-15x+227y+40=0

E

200

Graph the solution set of the system.

x²+y²<25

3x-4y>0

See Stutz

300

Solve the equation for the interval [0,2pi)

2cos²x-cosx-1=0

0, 2pi/3, 4pi/3

400

How long would it take an investment to triple at an APR of 3.7%, compounded continuously? Round to three decimal places.

29.692 years

500

Find a rectangular equation equivalent to the given parametric equations on the interval [0,2pi)

x=8sint, y=8cost

x²+y²=64