Math Jeopardy

Algebra

100

3x-5=16

x=7

200

x^2-7x+10=0

x=?

x=5 or 2

300

What is x in 2x^2-5x+3=0 if one root is 1/2

x=2

400

f(x)=2x^2−3x+4 and g(x)=x^2+x−5, find f(g(1)).

31

500

2x+3y=11   4x-y=5

Solve

x=13/7 y=17/7

Geometry

100

Find the area of a triangle with a base of 6 units and a height of 4 units.

12

200

The area of a circle is 81π square units. What is the circumference of the circle?

18pi

300

In a regular polygon with n sides, the radius of the circumscribed circle is 6. If the perimeter of the polygon is 48 units, what is the value of n?(s=2Rsin(pi/n))

8

400

In a right triangle 𝐴𝐵𝐶, the right angle is at C. The length of side AB is 20 units, the length of side AC is 16 units, and the length of side BC is x. Additionally, there is a circle inscribed in the triangle that is tangent to all three sides. Find the radius of the inscribed circle.

4

500

A circle with center O has two tangents, PA and PB, drawn from an external point P. If the distance between P and the center O is 13 units, and the radius of the circle is 5 units, what is the length of the segment AB?

24

Calculus

100

Find the derivative of the function f(x)=3x2−5x+4

6x-5

200

Evaluate the integral:∫(4x^3−2x^2+5x−1) dx

x^4−2x^3/3+5x^2/2−x+C.

300

Find the critical points of the function f(x)=x^3−6x^2+9x+1, and determine if they are local minima, maxima, or points of inflection

x=1-local maximum

x=3-local minimum

400

Solve the following differential equation: dy/dx=3x^2+2x ,y(0)=5

y=x^3+x^2+5

500

Evaluate the following improper integral:

∫1∞ 1/x^2dx

1

Precalculus

100

Simplify the expression 3x^2−5x+2/x−1

3x-2

200

Find the sum of the roots of the quadratic equation 2x^2−4x+6=0

2

300

Find the value of sin⁡θ if cos⁡θ=3/5 and θ is in the second quadrant.

4/5

400

Solve the system of equations: 3x+2y=7,4x−y=1

x=9/11 y=25/11

500

Find the amplitude and period of the function f(x)=3sin⁡(2x−pi/4)

A=3 Period = pi

Logic/Reasoning

100

If all humans are mortal, and Socrates is a human, what can we conclude about Socrates?

Socrates is mortal.

200

A clock shows the time as 3:15. How many degrees are between the hour and minute hands?

7.5 degrees

300

A man is 10 times as old as his son. In 10 years, he will be 5 times as old as his son. How old are they now?

Son=8 Man=80

400

You have a basket with 5 red apples and 3 green apples. Without looking, what is the minimum number of apples you need to pick to guarantee at least one green apple?

6 apple

500

What is the next number in the sequence: 2, 5, 10, 17, 26, ___?

37