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Probability
Exponential & Log Functions
Rational Expressions & Equations
Rational Functions
Trigonometry
100
A family has three children.  Find the probability that all three children are boys.

1/8

100

A bank account is opened with a deposit of $5000.  It will earn 4% annual interest, compounded monthly, and will remain in the account for 10 years.  *Which equation is best for this situation?*

A=P(1+ r/n) ^ nt

100

List the restrictions:  (x+2) / (x-1)(x+5)

x /= 1, x/=-5

100

Where--and how--is the function discontinuous?

y = (x-1) / (x^2+4x-5)

x=-5 is a vertical asymptote 

x=1 is a hole

100

Sketch the angle 4pi/3

(See the white board)

200

A bag of candy has 6 red, 7 orange, and 7 yellow candies.  You reach into the bag and grab a candy, eat it, then grab another.  What's the probability you get two red candies?

6/20 * 5/19 = 30/380

200

Write an equation to model the following:  A starting sample of 25 bacteria increases by 75% every 10 minutes.  

A = 25 (1.75) ^ x/10

200

Simplify:  (x^2 - 16)/(x^2 + 3x - 4)

(x-4) / (x-1)

200

Find the inverse of g(x)= x^2 - 6

y = +- sqrt (x+6)

200

A ladder leans against a building, and makes an angle of 70 degrees with the ground.  If the ladder is 20 feet long, how high up the side of the building will it reach?

18.8 feet

300
A researcher needs 7 people to take a survey.  If there are 10 people willing to take the survey, in how many ways can 7 people be selected for the survey?

10 C 7 = 120

300

Graph the parent AND the transformed function:  

g(x) = -2^x  + 4 

(see whiteboard)

300

C varies directly with V, and C=24 when V=3.  Find the constant and write a specific equation to model this situation.  

C = 8V

300

Does f(x) have a horizontal or oblique asymptote and what is its equation?  f(x) = (x^2+2x-8) / (x-3)

oblique:  y = x + 5

300
Give one positive and one negative angle coterminal with 3pi/2

answers include: 630 degrees, -90 degrees

400

On a wheel with 12 evenly spaced sections, numbered 1-12, what's the probability of getting an even OR a multiple of 3 in one spin?

(6 + 4 - 2) / 12 = 8/12 

400
Solve for x:  ln (x-1) - ln 3 = 4

x = 164.79

400

Solve: 1/(x-4) + 3/(x-2) = 5/(x-2)

x = 6

400
Graph g(x) by graphing its parent, the new asymptotes, and the transformed function: 


g(x) = 1/(x-2)  - 5

(See white board)

400

Change 144 degrees to radians

4pi/5

500

A total of 10 people like watermelon and a total of 15 people like soda.  There are 9 people who like both and 5 people (including Mrs. Williams!) who like neither.  What's the probability that someone who likes soda also likes watermelon?

Probability = 9/15

500

Solve for x:

3 * 5^(4x) = 9

x = .171

500

Add:  (x+2)/(x-4) + 2/x

(x^2 + 4x - 8) / x*(x-4)

500

Without using technology, graph: 

f(x) = (x-3) / (x^2+3x-4)

(See white board)

500

Find the cotangent of 5pi/3

- (sqrt 3)/3