Sample Questions
Sample Multiple Choice Question:
Pennsylvania
Keystone
Exams
A baseball team had $1,000 to spend on supplies. The team spent $185 on a new bat. New baseballs cost $4 each.
The inequality 185 + 4b ≤ 1,000 can be used to determine the number of new baseballs (b) that the team can
purchase. Which statement about the number of new baseballs that can be purchased is true?
A. The team can purchase 204 new baseballs.
B. The minimum number of new baseballs that can be purchased is 185.
C. The maximum number of new baseballs that can be purchased is 185.
D. The team can purchase 185 new baseballs, but this number is neither the
maximum nor the minimum.
Solution Explained:
If you solve the inequality that is given, 185 + 4b ≤ 1000, you can determine the maximum amount of baseballs that
the team can purchase and not exceed $1000.
185 + 4b ≤ 1000
4b ≤ 815
b ≤ 203.75
Consider how you should round that answer:
ROUND UP? If you let b = 204, then the team will exceed their budget:
185 + 4(204) = 1001
Do not round up.
ROUND DOWN? If you let b = 203, then the team will not exceed their budget:
185 + 4(203) = 997
Round down.
The maximum amount of baseballs the team can buy is 203. This means that they can buy 203 or LESS.
Read each answer choice:
A. The team can purchase 204 new baseballs.
No – The team would go over budget if they tried to purchase 204 baseballs.
B. The minimum number of new baseballs that can be purchased is 185.
No – The minimum number of new baseballs that can be purchased is 0 baseballs.
C. The maximum number of new baseballs that can be purchased is 185.
No – As determined above, the team can purchase a maximum of 203 baseballs.
D. The team can purchase 185 new baseballs, but this number is neither the
maximum nor the minimum.
Yes – The team can buy 185 baseballs, but it is not the minimum or maximum number of baseballs that
they can purchase.
All information regarding the content of the Keystone Exam was taken from www.pdesas.org.
Pennsylvania
Keystone
Exams
Sample Questions
Sample Constructed Response Question:
width = h + 4
Keng creates a painting on a rectangular canvas with a width that
is four inches longer than the height, as shown in the diagram.
height = h
A. Write a polynomial expression, in simplified form, that
represents the area of the canvas.
Painting
Area of a Rectangle = (height)(width)
A = hw
Formula.
A = (h)(h + 4)
Substitute h with h. Substitute w with h + 4.
2
A = h + 4h
Distribute to create a polynomial expression.
Answer to Part A: h2 + 4h
Keng adds a 3-inch-wide frame around all sides of his canvas.
B. Write a polynomial expression, in simplified form, that represents the total area of the canvas and the frame.
You must add 3 inches in every direction.
h + 10
The new width of the painting will be h + 10.
Find this by adding 6 to h + 4.
h+4
The new height of the painting will be h + 6.
Find this by adding 6 to h.
Area of a Rectangle = hw
A = hw
A = (h + 6)(h + 10)
A = h2 + 16h + 60
h+6
h
Formula.
Substitute w with h + 10 and h with h + 6.
Multiply the binomials to create a polynomial expression.
Answer to Part B: h2 + 16h + 60
Keng is unhappy with his 3-inch-wide frame, so he decides to put a frame with a different width around his canvas.
The total area of the canvas and the new frame is given by the polynomial h2 + 8h + 12, where h represents the height
of the canvas.
C. Determine the width of the new frame. Show all your work. Explain why you did each step.
Answer & Explanation to Part C: The width of the new frame is 1 inch. To answer this problem, I factored
h2 + 8h + 12 to (h + 6)(h + 2). h + 6 is the width of the frame and h + 2 is the height of the frame. Subtract away the
width (h + 4) and height (h) of the painting to find the amount the frame added to the painting:
h + 6 – (h + 4) = h + 6 – h – 4 = 2
h+2–h=2
2 inches have been added to each dimension, therefore 1 inch is added to each side of the frame.
All information regarding the content of the Keystone Exam was taken from www.pdesas.org.