Algebra II & Geometry
Quiz on Chapter 9 Review
Chapter 9 - Quadratic and Higher Degree Equations and Functions
Name___________________________________
Date: ________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the equation by completing the square.
1) x2 + 3x - 9 = 0
Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the
trinomial.
2) x2 + 8x + _______
Solve the equation by completing the square.
3) 9x2 + 18x + 8 = 0
Find two possible missing terms so that the expression is a perfect square trinomial.
4) x2 +
+ 49
Solve.
5) An isosceles right triangle has legs of equal length. If the hypotenuse is 8 inches long, find the length of each
leg.
1
Solve the equation by completing the square.
6) x2 + 16x + 47 = 0
Use the square root property to solve the equation.
7) x2 = 25
Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the
trinomial.
8) x2 + 1 x + _______
3
Find two possible missing terms so that the expression is a perfect square trinomial.
49
9) x2 +
+
4
Solve the equation by completing the square.
10) 8x2 + 1 = 5x
2
Solve.
11) Because of the increase in traffic between Springfield and Orangeville, a new road was built to connect the two
towns. The old road goes south x miles from Springfield to Freeport and then goes east x + 5 miles from
Freeport to Orangeville. The new road is 15 miles long and goes straight from Springfield to Orangeville. Find
the number of miles that a person saves by driving the new road over the old one.
Springfield
Freeport
Orangeville
Use the quadratic formula to solve the equation.
x2 + x + 21 = 0
12)
8
16
Use the discriminant to determine the number and type of solutions of the equation.
13) x2 - 5x - 5 = 0
Use the quadratic formula to solve the equation.
z2 = z + 7
14)
-2
9
-18
15) x2 + 22x + 121 = 0
3
16) x2 + 10x + 3 = 0
17) x(x + 2) = 2
Use the discriminant to determine the number and type of solutions of the equation.
18) x2 - 3x + 8 = 0
Solve.
19) The base of a triangle is 8 more than twice its height. If the area of the triangle is 22 square centimeters, find its
base and height.
20) The hypotenuse of an isosceles right triangle is 2 feet longer than either of its legs. Find the exact length of each
side.
21) x = 32 + 4
22) x =
x
6x + 40
4
23) x4 - 5x2 + 4 = 0
24)
2 = 1
x+9
x2
25)
8
= 2x - x
2
x-3
x-6
x - 9x + 18
26) (4x - 5)2 - 8(4x - 5) + 12 = 0
27) Shelly can cut a lawn with a riding mower in 2 hours less time than it takes William to cut the lawn with a push
mower. If they can cut the lawn in 4 hours working together find how long to the nearest tenth of an hour it
takes for William to cut the lawn alone.
28)
24x - 24 = x + 5
29) x2/3 - 6x1/3 + 8 = 0
5
30) Two pipes can be used to fill a pool. Working together, the two pipes can fill the pool in 5 hours. The larger pipe
can fill the pool in 3 hours less time than the smaller pipe can alone. Find the time to the nearest tenth of an
hour it takes for the smaller pipe working alone to fill the pool.
Solve the inequality. Graph the solution set and write the solution set in interval notation.
31) x2 - 4x + 3 > 0
32)
6
>0
3x - 7
33)
(x - 8)(x + 8) ≤ 0
x
34) (x + 6)(x + 4) > 0
6
Find all numbers that satisfy the following.
35) A number minus the product of 25 and its reciprocal is less than zero. Find the numbers.
Solve the inequality. Graph the solution set and write the solution set in interval notation.
x-8 <0
36)
x+6
37)
(x + 10)(x - 6) ≥ 0
x-1
38)
-5
>0
-5x - 7
39) x(x + 3)(x - 4) > 0
7
40) (x + 1)(x - 1) ≤ 0
8