MATHEMATICS-^
Name: __________________________________________ Period: _________________ Date: ___________________
Final Review
DIRECTIONS: Read each question and choose the correct
answer. Mark the space for the answer you have chosen on your
answer sheet. Please show all your work.
(2)
36. Simplify
2 x 4  7 x 3  3x 2
. Assume the denominator cannot
2 x 2  3x  2
equal zero.
31. Simplify the following expression. Put your answer in simplest
form.
t
A.
B.
C.
D.
2t 3t

3 4
7t
12
11t
12
13t
12
17t
12
32. A rectangle has a length of x inches and a width 2 inches less
than the length. If the dimensions were doubled, what would be the
area of the new rectangle in terms of x?
A.
2x  4
B.
4x  8
C.
D.
A.
B.
C.
D.
37. How many times does the graph of the quadratic function
f x   x 2  1 intersect the x-axis?
A.
B.
C.
D.
A.
1
2
B.
1
C.
3
2
D.
2
3
2
1
0
38. Which relation below is a function?
4 x2  8x
4 x4  8x2
33. Brad is swimming 3 miles upstream. The trip takes 6 hours. He
swims back downstream to his original starting point in 2 hours.
How fast, in miles per hour, is the current traveling?
x3  3x 2
x2
3
x  3x 2
x2
3
x  3x 2
x2
3
x  3x 2
x2
x y
0 1
A.
1 2
2 3
3 4
x y
0 1
B.
1 2
0 3
34. What is the range of the function y  3 x  2 for the domain
2 4
4  x  8?
10  x  22
12  x  22
10  x  20
12  x  20
x y
0 1
A.
B.
C.
D.
C.
C.
 1 7
1 7
D.
22 7
2
3
3 4
1 2
35. What are the roots of x  x  3 ?
2
1  5
A.
B.
1
1
x y
0 1
D.
1 2
2 3
2 4
39. The area of the trapezoid below can be found by the formula
x4
x2  4
x4
x2  4
x4
x2  4
x4
x2  4
B.
C.
The area of this trapezoid is 16 square inches. If
b1  h
and
b2  h  6 , what is the length of h in inches?
D.
11
13
15
17

Q  1,2, 2,3, 3,4, 4,5, x, y 
w 2w
w 
2
3
B.
C.
D.
w
6
5w
6
7w
6
11w
6
4,6
5,6
6,7
6,8
A.
B.
C.
D.
f x = x2+5x+6
46. Which graph describes the equation
8
4
2
-10
-5
41. Which of the following relations is a function?
A.
x6
C.
D.
y  x2  5x  6 ?
6
-15
B.

45. Which ordered pair x, y could not be substituted in the
relation below so that the relation is a function?
40. Simplify the following expression. Put your answer in simplest
form.
A.
2
cannot equal zero.
A.
A.
B.
C.
D.
x
2

. Assume that the denominator
x 4 x2
44. Simplify
1
A  hb1  b2  .
2
x  6y
y6
y2  6x
5
10
15
5
10
15
5
10
15
5
10
15
-2
-4
f x = - x2+5x+6 
-6
8
A.
-8
6
-10
4
-12
2
-15
-10
-5
-2
42. How many more hours would it take a car traveling at an
average rate of 30 miles per hour to cover a distance of 90 miles,
than it would for a car traveling at a rate of 60 miles per hour?
A.
1.5
B.
2.5
C.
3
D.
4
-4
f x =  x2-5x +6
B.
-6
8
-8
6
-10
4
2
-12
-15
-10
-5
-2
43. What is 6 x  x  1 in factored form?
A.
3x  1 2 x  1
2
B.
C.
D.



3x  12x 1
3x 12x  1
3x 12x 1
-4
f x = - x2-5x+6 
-6
C.
8
-8
6
-10
4
-12
2
-15
-10
-5
-2
-4
D.
-6
-8
-10
-12
47. The following ordered pairs,
a function?
x, y  define the relation Q. Is Q
Q  1,2, 2,3, 3,4, 4,5
A.
B.
C.
D.
Yes, because there is exactly one y value for every x value.
Yes, because there is exactly one x value for every y value.
No, because there is more than one x value for some y values.
No, because there is more than one y value for every x value.
48. Simplify
A.
B.
C.
D.
4x
2

 13x  3  4 x  1 , where x  
x3
x 3
x  3 , with a  1 remainder.
x  3 , with a  1 remainder.
1
4
53. Simplify
A.
B.
C.
D.
2x
2

1
 3x  3  2 x  1 , where x   .
2
x2
x2
x  2 , with  1 remainder.
x  2 , with  1 remainder.
54. Which of the following shows
written in factored form?
A.
2x 1 b 1
B.
C.
D.
2x 1b 1  2x 1

 
2x 1b
2x 1b  1
2x 1b  2
49. What is the domain of the function
x5
2x  7
all real numbers except  5 .
7
all real numbers except .
2
7
all real numbers except  .
2
f x  
A.
B.
C.
D.
55. The graph of which of the following equations has x-intercepts
of 5 and  5 ?
y 5  x
A.
y  x 2  2 , for
all x  0 , y is a function of x because
A.
x cannot be negative.
B.
the graph of the equation is a line.
C.
each value of y has a unique value of x.
D.
each value of y has a unique value of y.
51. Which of the following shows
written in factored form?
A.
x2 y2
C.
D.
x  2 y 1  x  2
  
x  2 y  2
 x  2 y
x  2 y 1
52. An equation in the form ax  bx  c  0 is solved by the
quadratic formula. The solution to the equation is shown below.
2
x
2   24
2
What are the values of a, b, and c in the quadratic equation?
a  1, b  2, c  7
A.
B.
C.
D.
y 5  x
C.
y  25  x 2
D.
x  25  y 2
all real numbers except 3.
50. In the relation defined by the equation
B.
B.
a  1, b  2, c  7
a  1, b  2, c  7
a  1, b  2, c  7
56. What number should be added to both sides of the equation
below if you were going to solve the equation by completing the
square?
1
x2  x  2
3
1
A.
36
1
B.
6
1
C.
3
1
D.
2
57. Simplify:
2 x 4  5x3  2 x 2
. Assume the denominator
2 x 2  3x  2
cannot equal zero.
A.
B.
C.
D.
x3  2 x 2
x2
3
x  2x2
x2
3
x  2x2
x2
3
x  2x2
x2
58. How many times does the graph of the quadratic function
y  x 2  4 x  4 intersect the x-axis?
A.
B.
C.
D.
3
2
1
0
59. If the sum of x and y is 50 and x is 10 more than two times y,
which of the following systems of equations could be used to solve
for x and y?
A.
B.
C.
D.
x  y  50
x  2 y  10
x  y  50
x  2 y  10
x  y  50
x  2 y  10
x  y  50
x  2 y  10
60. The area of the trapezoid below can be found by the formula
A
1
hb1  b2  .
2
The area of this trapezoid is 20 square inches. If
b2  h  6 , what is the length of h in inches?
A.
B.
C.
D.
11
14
17
20
b1  h and
61. On the grid provided, sketch the solution set to the system of inequalities shown below.
3x  5 y  15

 x y  6
11
10
9
8
7
6
5
4
3
2
1
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10

Does the solution set contain the point
1,2 ? Verify your work algebraically.
6
7
8
9
10
11

How would the solution set from the system of inequalities above change if the system were as follows?
3x  5 y  15

 x y  6

Explain your answer or, if you choose to draw a graph, use the grid provided below.
11
10
9
8
7
6
5
4
3
2
1
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
1
2
3
4
5
6
7
8
9
10
11