Math Club Jeopardy

Algebra

100

3x + 5 = 14

Solve for x.

x = 3

200

2x(x - 5)(3x + 4)

Simplify.

6x³ - 22x² - 40x

300

Solve the system of equations.

2x + y = 12

x - y = 6

x = 6, y = 0

400

3x² + 5x - 2

Factor.

(3x - 1)(x + 2)

500

x² - 5x - 6 = 0

Solve for x.

x = 6, x = -1

Trigonometry

100

sin(x) / cos(x)

Simplify.

tan(x)

200

In a right triangle, if the opposite side is 7, the adjacent side is 5, and the hypotenuse is 13, what is the cosine of the angle?

5/13

300

Simplify: sin(2x)/2sin(x)

cos(x)

400

sin(pi/6)+tan(pi/2)+cot(pi/3)+cos(2pi)

undefined

because tan(pi/2) is undefined

500

3sin²(x)-2sin(x)-1=0

pi/2

Statistics

100

Find the average of: 

0, 1, 1, 2, 3, 5, 8, 13, 21, 34

8.8

200

What's the probability of flipping a coin and getting head 8 times in a row?

1/256

300

A bag of skittles contains:

10 yellow skittles

6 orange skittles

5 green skittles

7 red skittles

2 purple skittles.

What's the probability of picking a red or green skittle?

12/30 or 2/5 

400

One hundred people line up to board a plane. Each of them has a boarding pass with an assigned seat. However, the first person lost their boarding pass and chose a random seat. After that, each passenger sits in their assigned seat if it's unoccupied. Otherwise, they sit in an unoccupied seat at random. What is the probability that the last person to board gets to sit in their assigned seat?

1/2

500

A cookie jar contains 10 cookies of 3 types. There are 5 chocolate chip cookies, 3 oatmeal raisin cookies, and 2 sugar cookies. Sparsh reaches into the jar and chooses a cookie at random and then, without replacing the first cookie, reaches into the jar again and chooses another cookie at random. What is the probability that both of the cookies Sparsh chooses are the same type?

28/90

Calculus

100

derive: x

1

200

Integrate: x*x²+1

(x⁴/4)+x+c

300

derive: x³ln(x)

3x²ln(x)+x²

400

Integrate: (x²)/(x³+1)²

-1/3(x³+1) + c

500

Integrate: tan(x)/(sec³(x)+1)^1/2

(-2/3)tanh^-1(sec³(x)+1)^1/2

DE/LA

100

3xy = dy/dx

Solve in terms of y

y = Ce^{(3/2)x^2}

200

What is the 6th axiom of a Vector Space?

Existence of an additive inverse vector in V.

(For all u values which exist in V, there exists a -u in V such that u + (-u) = 0 where -u is the inverse of u.)

300

Use Cramer's Rule to solve the following system of equations.

-3x + 7y = 18

5x + 4y = -13

x = -3.47

y = 1.08

400

Use a Matrix to solve the system of equations by simplifying to Row-Echelon Form.

R₁ + R₂ + R₃ = E/I_o

R₁ + (1/2)R₂ + R₃ = E/I_a

R₁ + R₂ = E/I_b

R₁ = E/I_b - 2E/I_o + 2E/I_a

R₂ = 2E/I_o - 2E/I_a

R₃ = E/I_o - E/I_b

500

Solve the following differential equation:

y'' = y' + x²

y = -(1/3)x³ - x² -2x + C₁e^x + C₂