Show:
Volume and Surface Area
Probability and Combinatorics
Algebra II and Complex Numbers
DESMOS and Topology
Miscellaneous
100
The volume of a sphere with radius 3.

What is 36pi.

100

The probability of drawing any given card from a deck of 52.

What is 1/52.

100

The sum of (4+2i) and (2-i).

What is (6+i).

100

The zeros of the polynomial x4+4x3-10x+1, to two decimal places.

What are x = 0.10 and x = 1.32.

100
True or false: All rectangles are squares, but not all squares are rectangles.

False. 

200

The surface area of a globe with radius 6 meters.

What is 144pi meters.

200

The number of ways you can arrange six books on a shelf.

What is 6!, or 720.

200

The number of components of a complex number.

What is 2.

200

The shape given by the equation x2+y2 < 23 {x > 0}

What is a half circle.

200

Name a set of numbers that is a subset of the real numbers.

Example responses include: natural numbers, rational numbers, irrational numbers, whole numbers, integers, etc.

300

The surface area of a square base pyramid, where the base length is 'b', and the side length to its tip is 's'.

What is SA = b2 + 2bs.

300

There are 6 students in a class. How many distinct teams of three students could you make?

20.

300

The classification of the function f(x) = (x+1)1/2.

What is a 'radical function'.

300

The genus of a hollow sphere with two punctures.

What is 1.

300

Given A = {1, 2, 4, 5} and B = {2, 3, 5, 6}, find A U B.

A U B = {1, 2, 3, 4, 5, 6}.

400

The volume of an apple of radius 3 inches with its core, of radius 1 inch, removed.

What is 104pi/3 in3.

400
Two red marbles, three blue marbles, and seven yellow marbles are placed in a bag. What is the probability of picking the two red marbles out in a row?

1/66

400

The end behavior of the polynomial p(x) = -4x4+7x3+x+1.

What is p(x) to infinity for x to either positive and negative infinity.

400
The property that one object can be smoothly deformed into another.
What is topological equivalence.
400

Show, using a diagram, that A U B = A is only true when B ⊆ A.

Example solution illustrates that B ⊆ A has no elements of B outside of A, therefore A U B = A.

500

A cylindrical silo has an open top. Its height is thrice its diameter, and its interior has a surface area of 300m2. Find its radius and height.

Its radius is approximately 2.71 meters, and its height is approximately 16.26 meters.

500

The alphabet has 26 letters. How many different three-letter passwords can be made? (you can repeat letters)

17,576.

500

The quotient of (2+i) and (1+i).

What is (1.5-0.5i).

500

The genus of a sphere that has two non-intersecting tunnels.

What is 2.

500

True or False:  (A∩B) ∩ (A∩C) = A∩B∩C

(∩ means 'intersection')

True.