Math Challenge! Jeopardy

Trigonometry

100

What are the three trigonometric functions and their inverses?

Sine, cosine, tangent. Inverses (in order) are cosecant, secant, and cotangent.

200

What is the sine of the angle in a right triangle with an "opposite" of 7 meters and a "hypotenuse" of 13 meters?

7/13

300

What is the angle in a right triangle with an "adjacent" side measuring 3 inches and a "hypotenuse" measuring 4 inches?

41.4 degrees.

400

A right triangle has angle values of 90, 55, and 35 degrees. Suppose the hypotenuse has a value of 6 centimeters. What are the other two side lengths?

4.9 cm and 3.44 cm

500

You are setting up a tent and have driven three stakes into the ground, two of which form a right angle with the third. If the distance between the stake "touching" the right angle and the two other stakes are 3 meters and 4 meters respectively, what is the length of the hypotenuse and the value of the other two angles?

Hypotenuse: 5 meters

Angles: 53.13 and 36.87 degrees

Algebra (standard)

100

Solve for x.

0=6x+3

x=-1/2

200

Solve for x.

7=35x+9

x=-2/35

300

Factor the following polynomial.

y=x²+6x+9

y=(x+3)(x+3)

400

Solve for x.

y=x²+13x+30

x=-3 and x=-10

500

Factor and solve for x.

y=3x³-6x²+9x

y=3x(x-3)(x-3)

x=0, x=3, x=3

Algebra (Boolean)

100

What are the 6 logic gates we discussed on Tuesday?

NOT, OR, AND, NOR, NAND, and XOR

200

You feed an input of 1 and 0 into an AND logic gate. What is the output?

0

300

Suppose you have an AND gate (inputs A and B) parallel to an OR gate (inputs C and D), with an AND output receiving an output from the first two gates.

If A=B=C=D=1, what is the final output?

1

400

x'=NOT x

Simplify the following: A'BC' + ABC'

BC'

500

Simplify the Following.

x'y'z + x'y'z' + xyz + x'y'z

x'y' + xyz 

Complex Numbers

100

/() = square root

Express /(-5) in terms of i.

5i

200

Simplify (1+2i)(3+i)

1+7i

300

Simplify i^200

(i^2)^100 = 1

400

What are the 3 forms of complex numbers called?

Cartesian, Polar, and Exponential

500

Convert 1+i to polar form.

/(2)(cos45 + isin45)

WildCard

100

Who invented math?

No one!

200

How many thermal calories are in one food calorie?

1,000

300

What are the 3 steps in an induction proof? 

1). Prove the base case

2). Prove the formula is true for an arbitrary integer k

3). Prove the formula is true for k+1 relative to k

400

What civilization knew about trigonometry 3,700 years ago?

The Babylonians

500

What two individuals are said to have invented calculus?

Isaac Newton and Gottfried Leibnitz