Name: ________________________
Quadratic Applications – Practice Exam
1
When a textbook sells for $20, 70 copies are
purchased. Every time the price is increased by
$3, the number of people purchasing the book
decreases by 8. Which equation can be used to
determine the number of $3 increases needed to
make the total revenue from the books equal to
$1426?
Date: ___________
Algebra Common Core
Topic 15
Practice Exam
4
The length of the shortest side of a right triangle is
10 inches. The lengths of the other two sides are
represented by consecutive integers. Write an
equation that could be used to find the lengths of
the other sides of the triangle.
5
A printer wants to put 48 square inches of text into
a rectangle of a 9 inch by 12 inch sheet of paper.
She wants the text to be surrounded by a border of
constant width. Write an equation that could be
used to find the width of the border (x).
6
Steven has a rectangular patio that measures 9 feet
by 12 feet. He wants to increase the area by 25%
and plans to increase each dimension by equal
lengths, x. Write an equation that can be used to
determine x. [Write as a quadratic equation in
standard form.]
(1) (20 − 3𝑥)(70 − 8𝑥) = 1426
(2) (20 − 3𝑥)(70 + 8𝑥) = 1426
(3) (20 + 3𝑥)(70 + 8𝑥) = 1426
(4) (20 + 3𝑥)(70 − 8𝑥) = 1426
2
3
The length of a rectangular room is 5 less than
double the width, w, of the room. Write an
expression to represent the area of the room.
Samantha is going to fence a rectangular pasture
for her horse. The amount of fencing to be used is
32 feet. The fenced pasture will have an area of 63
square feet. Write an equation that can be used to
determine the length x of the pasture.
7
The square of a number decreased by 8 times the
number equals 9. Determine the two possible
values of the number.
9
8
Marsha and Billy have ages that are consecutive
odd integers. The product of their ages is 99. If
Marsha is the youngest, find both of their ages.
10
A landscaper is creating a rectangular flower bed
such that the width is half of the length. The area
of the flower bed is 40 square feet. Write and
solve an equation to determine the width of the
flower bed to the nearest tenth of a foot.
A rectangular field is 20 yards longer than it is
wide. Its area is 2400 square yards. Find the
dimensions of the field.
11
A contractor has 48 meters of fencing that he is
going to use as the perimeter of a rectangular
garden. The length of one side of the garden is
represented by x, and the area of the garden is 128
square meters. Determine, algebraically, the
dimensions of the garden in meters.
12
A garden measuring 12 meters by 16 meters is to
have a pedestrian pathway that is x meters wide
installed all the way around it, increasing the total
area to 285 square meters.
Write an equation that can be used to determine the
width, x, of the pathway.
Explain how this equation models the situation.
Use this equation to solve for the width of the
pathway.