The GOATs jeopardy

trigonometry

100

Find the exact value of sin30°

1/2

200

Solve for x on the interval [0,2pi):

     2 cos x = 1

pi/3, 5pi/3

300

A right triangle has a hypotenuse of 13 and one leg of 5. Find the sine of the angle opposite leg of length 5. 

5/13

sequenceandseries

100

Find the tenth term of the arithmetic sequence:

3, 7, 11, 15...

39

200

Find the sum of the first 20 terms of the arithmetic sequence:

5, 8, 11, 14...

670

300

Determine whether the geometric series converges or diverges: 

2/3+ 4/9+8/27+16/81+...

2

polar,vector,parametric

100

Convert the polar coordinate:

(4,60°)

(2, 2 sqrt3)

200

Find the magnitude of the vector:

(6,8)

10

300

A particle is described parametrically by x=t²+1, y=2t-3.  Find the coordinates when t=4

(17,5)

limits

100

Evaluate: 

lim(x->3) (2x+5)

11

200

Evaluate:

lim(x->0) [(x²-4)/(x-2)]

4

300

Evaluate:

lim(x->0) [sin(x)/x]

1

derivative

100

Find the derivative of: 

f(x)=4x³

12x²

200

Find the derivative of: 

f(x)=3x² -5x+7

6x-5

300

Find the equation of the tangent line to

y=x²+1

at x=2

y=4x-3