Pre-Calculus Problems of the Week
POW #1:
Build a sugar cube pyramid as follows: First make a 5x5x1 bottom layer. Then, center a 4x4x1
layer on the first layer, center a 3x3x1 layer on the second layer, and center a 2x2x1 layer on
the third layer. The fifth layer is a single 1x1x1 cube. Express the volume of this pyramid as a
percentage of the volume of a 5x5x5 cube.
Due: Wednesday, August 26
POW #2
The digits 1, 2, 3, 4, 5 can be arranged to form more than one hundred different five digit
numbers. If these five-digit numbers are arranged from least to greatest, in what position is
42513?
Due: Wednesday, September 2
POW #3
A jar contains 50 red gumballs and 30 blue gumballs. Seven balls are randomly selected from
the box without replacement. What is the probability of selecting a red gumball followed by a
blue gumball, then a red gumball followed by a blue gumball, then a red gumball followed by a
blue gumball, then followed by another red gumball? Please round your answer to the nearest
thousandths.
Due: Wednesday, September 9
POW #4
Suppose that the surface of the earth is smooth and spherical and that the distance around the
equator is 25,500 miles. A steel band is made to fit tightly around the earth at the equator,
then the band is cut and a piece of band 21 feet long is inserted. To the nearest inch, what will
be the gap, all the way around, between the band and the earth’s surface? (Use 3.14 as an
approximate value of pi)
Due: Wednesday, September 16
POW #5
Determine the values of a and b so that f is continuous.
𝑥2 + 𝑎
𝑓(𝑥) = { 𝑏𝑥 + 𝑎
√−𝑏 − 𝑥
𝑖𝑓
𝑖𝑓
𝑥≥3
−3 < 𝑥 < 3
𝑖𝑓
𝑥 ≤ −3
Due: Wednesday, September 23
POW #6
Sam's father gave him 49 dog biscuits to give to their three dogs – Alice, Joe, and Mickey. Sam must
divide the biscuits according to the size of the dogs. Joe needs to get twice as much as Alice and Mickey
needs to get twice as much as Joe. How many biscuits should Sam give each dog?
Due: Wednesday, October 14
POW #7
There are four separate pieces of chain, with three links in each. It costs 2¢ to open a link and 3¢ to close
a link. Use all 12 links to make a closed bracelet at a total cost of 15¢.
Due: Wednesday, October 21
POW #8
Find the area of the shaded square:
Hint: Work with just the lower triangle. Which
length do you need to know to solve the problem?
Due: Wednesday, November 4th
POW #9
What proportion of all three-digit positive integers have 7 as a digit?
Due: Wednesday, November 11th
POW #10
The large triangle is a right isosceles triangle with hypotenuse of
length 24. Inside is an equilateral triangle with a vertex on the
midpoint of the hypotenuse. If the length of each side of the
equilateral triangle is k(√3 − 1), find k.
Due: Wednesday, December 9th