Math 120, 122
Practice Test #3
This test is designed to help you prepare for the test you will take in the learning center. The types of problems is similar to
the test you will be taking (but there will be fewer of them - 25 on the actual test you take) and the answers are provided.
When you are ready to take the test in the learning center consider the following:
1. Check with the learning center for their hours and allow yourself enough time to take the test. There is not time
limit, but you must finish the test in one sitting. You may not start, turn it in, and then come back later to finish.
2. When you arrive at the learning center to take the test, please sign in on the computer, and then ask for the test that
you want at the front desk. Be prepared to show your ID. You will also be asked to sign in on the test folder. The
person at the desk will record the time the test is taken out and the time that it is returned.
3. When you turn in the test you should also turn in the HW set that goes with that test. If you forget you may turn it
in later in the learning center or my box in 18 - 109.
4. You may use a calculator, but no notes or books are allowed.
Use the square root property to solve the equation.
1) x2 = 169
13) x2 + 3x - 9 = 0
14) x2 + 12x = -13
2) x2 - 12 = 0
15) x2 + x + 3 = 0
3) x2 = 88
Solve.
4) 4x2 = 28
16) An isosceles right triangle has legs of equal
length. If the hypotenuse is 16 inches long,
find the length of each leg.
5) x2 + 121 = 0
17) The distance, s(t), in feet traveled by a freely
falling object is given by the function
s(t) = 16t2, where t is time in seconds. Use this
6) (x + 2)2 = 11
7) (9 - 13x)2 = 26
formula to find the time it would take for an
object to fall to the ground from a cliff that is
1600 feet high.
8) (x - 6)2 = -4
Add the proper constant to each binomial so that the
resulting trinomial is a perfect square trinomial. Then
factor the trinomial.
9) x2 + 18x + _______
Use the quadratic formula to solve the equation.
18) x2 + 7x + 6 = 0
19) 5x2 - 3x - 8 = 0
10) x2 - 8x + _______
20) 2x2 + 12x = - 5
Find two possible missing terms so that the expression is a
perfect square trinomial.
11) x2 + _____ + 100
21) 7x2 + 5x + 8 = 0
22)
Solve the equation by completing the square.
12) x2 + 4x - 21 = 0
x2
11
+x+
=0
18
3
23) x(x - 8) = 3
1
Solve the inequality. Graph the solution set and write the
solution set in interval notation.
24) (x + 7)(x - 1) = -4
39) (x + 4)(x + 1) > 0
Solve.
25) A ball is thrown upward with an initial
velocity of 28 meters per second from a cliff
that is 70 meters high. The height of the ball is
given by the quadratic equation
h = -4.9t2 + 28t + 70 where h is in meters and t
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
40) (x + 1)(x - 5) ≤ 0
is the time in seconds since the ball was
thrown. Find the time it takes the ball to hit the
ground. Round your answer to the nearest
tenth of a second.
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
41) x2 + 10x + 21 > 0
Use the discriminant to determine the number and type of
solutions of the equation.
26) x2 + 7x + 6 = 0
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
27) 3 - 4x2 = -6x - 5
42) x2 - 3x - 18 < 0
28) x2 + 4x + 6 = 0
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
29) x2 + 12x + 36 = 0
Sketch the graph of the quadratic function. Give the vertex
and axis of symmetry.
43) f(x) = x2 + 2
Solve.
30) The diagonal of a rectangular storage room is
11 yards long. If its length is 2 times its width,
find the dimensions of the room.
y
10
31) x =
6x + 40
5
32)
33)
34)
18x - 45 = x + 2
-10
4
2
=
x2 x + 5
-5
5
-5
9
x
11
+
=
x - 1 x + 1 x2 - 1
-10
35) x4 - 625 = 0
36) x4 - 17x2 + 16 = 0
37) (4x - 4)2 - 2(4x - 4) - 3 = 0
38) x3 - 8x + x2 - 8 = 0
2
10
x
44) f(x) = (x - 1)2
51) f(x) = x2 + x - 2
y
Sketch the graph of the quadratic function by finding the
vertex, intercepts, and determining if the graph opens
upward or downward.
52) f(x) = x2 - 2x -8
10
5
y
-10
-5
5
10
10
x
-5
5
-10
-10
-5
5
10
x
5
10
x
-5
45) f(x) = (x + 4)2 - 1
y
-10
10
5
53) f(x) = -x2 - 4x + 5
y
-10
-5
5
10
10
x
-5
5
-10
-10
46) f(x) = -x2 - 2
-5
y
-10
10
5
-10
-5
-5
Solve.
5
10
54) The cost in millions of dollars for a company to
manufacture x thousand automobiles is given
by the function C(x) = 5x2 - 20x + 36. Find the
x
-5
number of automobiles that must be produced
to minimize the cost.
-10
55) The profit that the vendor makes per day by
selling x pretzels is given by the function
P(x) = -0.002x2 + 1.4x - 250. Find the number
Write the function in the form y = a(x - h)2 + k.
47) f(x) = -x2 + 10x - 8
of pretzels that must be sold to maximize
profit.
48) f(x) = x2 + x + 6
Find the vertex of the graph of the quadratic function.
49) f(x) = -x2 + 2x - 8
50) f(x) = 2x2 + 4x - 9
3
Answer Key
Testname: MATH 120 PRACTICE TEST #3 F05
1)
2)
3)
4)
5)
6)
-13, 13
-2 3, 2 3
-2 22, 2 22
- 7, 7
-11i, 11i
-2 - 11, -2 +
38) -1, - 2 2, 2 2
39) (-«, -4) U (-1, «)
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
11
40) [-1, 5]
9 - 26 9 + 26
7)
,
13
13
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
8) 6 - 2i, 6 + 2i
9) x2 + 18x + 81 = (x + 9)2
41) (-«, -7) U (-3, «)
10) x2 - 8x + 16 = (x - 4)2
11) -20x, 20x
12) 3, -7
-3 - 3 5 -3 + 3 5
13)
,
2
2
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
42) (-3, 6)
14) -6 - 23, -6 + 23
-1 - i 11 -1 + i 11
15)
,
2
2
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
43) vertex (0, 2); axis x = 0
16) 8 2 in.
17) 10 seconds
18) - 1, - 6
8
19) , -1
5
20)
-6 - 26 -6 + 26
,
2
2
21)
-5 - i 199 -5 + i 199
,
14
14
y
10
5
-10
-5
5
10
x
5
10
x
-5
22)
23)
24)
25)
26)
27)
28)
29)
-9 - 15, -9 + 15
4 - 19, 4 + 19
-3 - 19, -3 + 19
7.6 seconds
two real solutions
two real solutions
two complex but not real solutions
one real solution
11 5
22 5
30)
yards by
yards
5
5
-10
44) vertex (1, 0); axis x = 1
y
10
5
-10
31)
32)
33)
34)
35)
36)
10
7
1 - 11, 1 + 11
-4 - 3 2, -4 + 3 2
-5, 5, -5i, 5i
-1, 1, -4, 4
3 7
37) ,
4 4
-5
-5
-10
4
Answer Key
Testname: MATH 120 PRACTICE TEST #3 F05
45) vertex (-4, -1); axis x = -4
53)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-10
-10
54) 2 thousand automobiles
55) 350 pretzels
y
10
5
-5
5
10
x
5
10
x
-5
-10
47) y = -(x - 5)2 + 17
1 2 23
48) y = x +
+
2
4
49) (1, -7)
50) (-1, -11)
1
9
51) - , 2
4
52)
y
10
5
-10
5
-5
46) vertex (0, -2); axis x = 0
-10
-5
-5
-5
-10
5
10
x