Calculus Jeopardy!

Math Memories

100

What is the ratio of the sides in a 30 60 90 triangle? 

1:2: square root of 3

200

What is the commutative property? 

a + b = b + a 

a x b = b x a 

(either answer is acceptable)

300

Two secants that intersect on the edge of a circle create an arc on the opposite side of that circle. 

What is the relationship between the arc and the angle created by those two secants?

the angle is half the arc

400

Name the 5 ways to prove two triangles are congruent

SSS, SAS, AAS, ASA and HL

500

Double points! Whichever team can name the most digits of pi wins the points 

3.141592653589793238462643383279 50288419716939937510

Can You Substitute?

100

Integrate: (6x²+4x)e^{(2x^3+2x^2+11)}

e^{(2x^3 + 2x^2 + 11)} + C

200

Integrate: sin(x+7) from 0 to 1 

-cos(8) + cos(7)

300

Integrate: (4x)(2x²+3)dx 

from 1 to 2 

48

400

Integrate: 

sin(2x)/(cos(2x) + 3) 

from 0 to pi

0

500

Integrate: 2x(cos(x² - 3)) 

from 2 to 3

sin(6) - sin(1)

Rules and Regulations

100

Derive: 

(3x² - 7x)(cos(x))

(6x - 7)(cos(x)) - (3x² - 7x)(sin(x))

200

Derive: 

(x - 5)/(x + 1) 

6/(x + 1)²

300

Derive:

e^{sin((x^2+7)/3)}

1/3(e^{sin((x^2+7)/3)}cos((x²+7x)/3)(2x+7))

400

Derive:

 12cos(sin(x²))

-24xsin(sin(x²))cos(x²)

500

Derive:  

(2x³ + 5)(sin(x))/x

(6x³(sin(x)) + x(2x³ + 5)cos(x) - (2x³ + 5)sin(x))/x²

That's a Solid Rotation!

100

What is the volume of the solid created when y = 3x + 2 is rotated around the x axis in the interval 0<x<1? 

13pi

200

what is the volume generated by rotating -(x - 2)² + 1 around the x axis?

- Calculator Allowed

16pi/15

300

what is the volume of the solid generated by rotating the area bound by x = 5, x = 7, y = 7 and y = 3 around the y axis?

96pi

400

What is the volume of the solid generated when the area between the y axis, the x axis and function x² + y²=4 in the first quadrant is rotated around the x axis?

16pi/3

500

Find the volume of the solid generated when the area between graphs y = x² + 3 and y = x + 3 is rotated around the x axis. (In terms of pi)

- Calculator allowed

17pi/15

Trivial Numbers

100

How much is a bakers dozen?

13

200

What letter only appears after 1,000,000 numbers when spelled out?

the letter M 

300

How many sides does a tetradecahedron have?

14

400

How long is the average English word (to the nearest whole number)?

5 letters

500

What are the odds of rolling a double 6 and then a double 5 on two die?

1/1296