Exponential & Logarithmic Functions
Angles & The Unit Circle
Right Triangle Trigonometry
Trigonometric Functions
Probability & Statistics
100
The inverse of ln x
What is e^x ?
100
Convert to radians: 240 degrees
What is 4pi/3 ?
100
This is the formula for csc theta, where theta is an acute angle in a right triangle.
What is hypotenuse / opposite ?
100
Which trigonometric function is positive in the 3rd quadrant?
What is tangent (or cotangent)?
100
The most frequently occurring element in a data set.
What is the mode?
200
Solve for x: 2^(x+5) = 64

What is x = 1?

Solution:

2^(x+5) = 2^6

x+5 = 6

x = 1

200
Find the arc length formed by a central angle of 30 degrees in a circle with a radius of 6 cm.

What is pi cm? (Or what is 3.14 cm?)

Solution:

s = r(theta)

s= (6 cm) (30 deg)(pi rad/ 180 deg)

s = (6 cm)(pi/6)

s = pi cm

200
This is equivalent to sec(90 - theta)
What is csc theta ?
200
The formula for sec theta, in terms of x, y and/or r.
What is r/x ?
200
The value of x that will make the median of this data set {1, 2, 3, 4, 5, 6, 7, 2, x, 1} equal to 3.
What is x = 3?
300
Solve for x: log(3x+7) = 2

What is x = 31?

Solution:

3x+7 = 100

x = 31

300
Find an angle that is coterminal to 3pi/17

What is 37pi/17? (or -31pi/17)

Solution:

Add 2pi: 3pi/17 + 34pi/17 = 37pi/17

Subtract 2pi: 3pi/17 - 34pi/17 = -31pi/17

300

Solve for a: tan 22 = a/300

(the angle is in degrees)

What is 121.21 ?
300
An asymptote of the graph y = tan x
What is pi/2 ? (or -pi/2, or 3pi/2, -3pi/2, etc)
300
In a standard deck of 52 playing cards, the probability of choosing an Ace, given that the card is a club.
What is 1/13?
400
Solve for x: e^(2x) - 4e^x + 3 = 0

What is x = {0, ln3} ?

Solution:

((e^x) - 3)((e^x) - 1) = 0

e^x = 3 OR e^x = 1

x = ln3 OR x = ln1

{0, ln3}

400
Sin(pi/4)
What is sqrt(2)/2 ?
400
Find the length of the hypotenuse of right triangle ABC, if angle A = 37, angle B = 90 and side c = 10.

What is 12.52 ?

Solution:

cos 37 = 10/hypotenuse

hypotenuse = 10/cos 37

hypotenuse = 12.52

400
The general formula for finding the period of Asin(Bx-C)+D.
What is 2pi/B ?
400
The number of ways you can pick 3 out of 6 muffins.
What is 20 ?
500
In 2000, the population of Israel was 5 million. By 2050, the population is expected to grow to 10 million. Use the exponential growth model A = Aoe^kt, where t is the number of years after 2000, to model this population growth.

What is A = 5e^0.0139t ?

Solution:

10 = 5e^50k

2 = e^50k

ln2 = 50k

k = (ln2)/50 = 0.0139

500
Find the sin t if the cos t = sqrt(21)/5

What is 2/5?

Solution:

(sin t)^2 + (sqrt(21)/5)^2 = 1

(sin t)^2 = 1 - (21/25)

(sin t)^2 = 4/25

sin t = 2/5

500
What is the angle of elevation of the sun if a 125ft tower casts a 172ft shadow?

What is 36 degrees?

Solution

tan (theta) = 125/172

theta = (tan^-1)(0.7267)

theta = 36 degrees

500
cos((sin^-1)(9/41))
What is 40/41 ?
500
There are 20 muffins at a buffet, and 4 of them are chocolate. If your friend selects 5 muffins for you, this is the probability exactly 2 of the muffins will be chocolate.

What is 0.217 or 21.7%

Solution:

2 of 4 chocolate muffins: 4C2

3 of 16 non-chocolate: 16C3

5 of 20 total muffins: 20C5

prob=(4C2)(16C3)/(20C5) = 0.217

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