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Name:
Questions 1 through 4 refer to the following:
Solve the given quadratic equation by taking a square root and express irrational roots in radical form:
1)
Show your work.
Answer: ____________________
2)
Show your work.
Answer: ____________________
3)
- 12 = 0
Show your work.
Answer: ____________________
4)
Show your work.
Answer: ____________________
Question 5 refers to the following:
Solve the given quadratic equation by completing the square and express the answers in radical form if
necessary:
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5)
- 15 = 0
Show your work.
Answer: _______________
Questions 6 through 13 refer to the following:
Solve the given equation, using factoring methods, for all values of the variable:
6)
- 18 = 0
Show your work.
Answer: __________
7)
- 3x - 1 = 0
Show your work.
Answer: __________
8)
- 40x + 80 = 0
Show your work.
Answer: __________
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9)
Show your work.
Answer: __________
10)
Show your work.
Answer: __________
11)
- 36x = 0
Show your work.
Answer: __________
12)
- 132x = 0
Show your work.
Answer: __________
13)
- 64 = 0
Show your work.
Answer: __________
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14) Find the solution set for
Show your work.
by factoring.
Answer: __________
Question 15 refers to the following:
Solve the given equation using the quadratic formula and express the answer in radical form if needed:
15)
Show your work.
Answer: _______________
16) Solve the equation below algebraically, and express the result in radical form:
-x
Show your work.
Answer: _______________
17) Find the roots of
Show your work.
-
to the nearest tenth.
Answer: _______________
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18) Part A
Find the values of x to the nearest hundredth:
Show your work.
Answer: _______________
Part B
Solve for x in radical form:
Show your work.
Answer: _______________
19) The lengths of the sides of a right triangle are consecutive even integers. Find the lengths of the three
sides of the triangle.
Show your work.
Answer: _______________
20) The length of the shorter leg of a right triangle is 8 less than the length of the hypotenuse. The length of
the longer leg is 1 less than the length of the hypotenuse. Find the lengths of all three sides of the triangle.
Show your work.
Answer: _______________
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21) If the square of a positive number is decreased by five times the number, the result is 14. Find the number.
Show your work.
Answer: _______________
22) If the square of a negative number is decreased by 18, the result is three times the number. Find the
number.
Show your work.
Answer: _______________
23) The sum of the squares of two consecutive odd integers is 202. Find the integers.
Show your work.
Answer: _______________
24) Find three consecutive positive integers such that the square of the third is 51 more than the sum of the
first and second.
Show your work.
Answer: _______________
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25) The side of one square is 2 centimeters longer than the side of a second square. If the sum of their areas is
100
, find the length of the side of each square.
Show your work.
Answer: _______________
26) The length of a rectangle is 5 more than the side of a square and the width of the rectangle is 1 more than
the side of the square. If the area of the rectangle is 96, find the length of the side of the square.
Show your work.
Answer: __________
27) A playground is 20 yards by 30 yards. If the city wants to double the area of the playground, by what
equal amount should both the length and width be increased?
Show your work.
Answer: __________ yd
28) The area of a (uniform width) sidewalk around a swimming pool is equal to the area of the pool. If the
pool is 8 meters by 12 meters, then how wide is the sidewalk?
Show your work.
Answer: __________ m
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29) A rectangular patio measuring 6 meters by 8 meters is to be increased in size to an area measuring 150
square meters. If both the width and the length are to be increased by the same amount, what is the
number of meters, to the nearest tenth, that the dimensions will be increased?
Show your work.
Answer: __________ m
30) Barb pulled the plug in her bathtub and it started to drain. The amount of water in the bathtub as it drains
is represented by the equation
- 8t + 120, where L represents the number of liters of water in
the bathtub and t represents the amount of time, in minutes, since the plug was pulled.
Part A
How many liters of water were in the bathtub when Barb pulled the plug?
Show your work or explain your reasoning.
Answer: __________ L
Part B
Determine, to the nearest tenth of a minute, the amount of time it takes for all the water in the bathtub to
drain.
Show your work.
Answer: __________ min
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