MATH 100
PRACTICE
FINAL EXAM
Lecture Version
Name:
ID Number:
Instructor:
Section:
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appropriate spaces with a No. 2 pencil. Use the spaces marked “Year” under Birth Date to code
the version of the exam you are taking.
The exam has 50 multiple choice questions. Select the one best answer for each problem.
Use a No. 2 pencil to mark your answers on the answer sheet. Be sure to clearly mark your
answer with a heavy mark. Should you change an answer, be sure to erase your original answer
completely.
The test booklet has a limited amount of space with each problem. If the space is not
sufficient to show your work, use the back of the previous page. Label your work. Mark your
answer in the exam booklet and on the answer sheet. Answer all questions. There is no penalty
for guessing.
Good Luck!
1.
Solve the linear equation
1
10
5
1
a)
c)
2.
3.
4.
3
1._____
20
3
b)
17
d)
1
Decide whether the equation is an identity, a conditional equation, or a
contradiction.
2 3
4
6
5
a) identity
b) conditional equation
c) contradiction
d) none of these
The formula for the perimeter of a rectangle is given by
2
2 ,
where is the length and is the width. Assume the perimeter of a
rectangular plot of land is 480 ft. The length is twice the width. Find
the length of the rectangular plot of land.
a) 80 ft
b) 120 ft
c) 160 ft
d) 240 ft
A car dealership uses the linear model
1100
25000 to
predict the depreciation of car values as time progresses. If is how
old the vehicle is in years and is the current value of the vehicle,
what will the value of the vehicle be 5 years after purchase?
a) $18,400
b) $19,500
c) $22,700
d) $23,900
2._____
3._____
4._____
5.
6.
7.
8.
9.
Find the following sum.
7 3
5._____
2
5
2
3
a) 20
14
32
b) 19
2
c) 28
14
28
d) 19
14
2
29
6._____
Find the following product.
1 3
2
5
a)
3
5
17
5
b)
c)
3
7
13
5
d)
4
7
17
5
Factor out the greatest common factor from the following polynomial.
3
21
a)
3
c)
3
21
b) 3
21
7
d) 3
7
Factor the following polynomial by grouping.
15
6
10
4
8._____
a)
3
2 5
2
b)
3
2 5
2
c)
3
2 5
2
d)
3
2 5
2
Factor the following trinomial.
6
7._____
9._____
11
10
a)
3
2 2
5
b)
c)
3
2 2
5
d)
3
2 2
5
6 11
10
10.
11.
12.
Factor the following polynomial.
25
40
5
4 5
4
b)
c)
5
4 5
4
d)
5
4 5
40 25
Write the following complex number in standard form
24 √ 126
3
a)
8
c)
8
14
√126
b)
8
√14
d)
8
√14
4
16
11._____
.
.
12._____
Find the numerator of the quotient. Write the answer in standard form
.
5 3
2 7
13._____
Find the sum or difference. Write the answer in standard form
3 5
5 11
9 6
12
c) 17
a)
b) 7
12
11
c) 16
14.
16
a)
a) 7
13.
10._____
41
30
10
d) 17
10
b) 31
21
d) 11
41
Solve the following quadratic equation by the zero-factor property.
14
3
a)
2
b)
c)
2,
d)
2,
2,2
14._____
15.
16.
Solve the following quadratic equation by the square root property.
9
2
1
a)
1
b)
c)
1,2
d) No solutions
3,
c)
17.
18.
2
Solve the following quadratic equation by completing the square
9
12
3 0
a)
b)
6√7
d)
15._____
16._____
1, 1
√
17._____
, where
The Pythagorean Theorem for a right triangle is
and are the legs of the triangle and is its hypotenuse. The shorter
leg is 10 inches less than the other leg, and the hypotenuse is 10 inches
longer than that other leg. What is the length of the hypotenuse?
a) 30 inches
b) 40 inches
c) 50 inches
d) 60 inches
Bob wants to plant a 7 foot by 10 foot garden with a uniform border of
petunias around the outside and still have 28 square feet to plant
tomatoes and roses in the middle. How wide should the border of
petunias be?
a) 1.5 ft
b) 2 ft
c) 3 ft
d) 3.25 ft
18._____
19.
The height of a cannon ball, in feet, shot from a pirate ship is given by 19._____
2.84
20, where is given in seconds.
the equation
0.03
After how many seconds does the cannon ball splash into the water?
a)
6.58 sec
c) 47.33 sec
20.
21.
22.
b) 101.25 sec
d) 87.21 sec
Find and simplify the product of the following rational expression.
3
2 3
∙
4
3
a)
b)
c)
d)
Perform the following addition or subtraction.
2
4
3 5
2
a)
b)
c)
d)
Perform the indicated operations. Write each answer using only
positive exponents. Assume all variables represent positive real
numbers.
9 / /
/
a) 9
b) 9
c) 9
d)
20._____
21._____
22._____
23.
Solve the following rational equation.
2
1
3 2
1 2
a)
3
26.
27.
3
3
d) No solutions
Solve the following radical equation.
√3
25.
8
7
b)
c)
24.
23._____
24._____
13
1
a)
3
b)
4
c)
3,4
d) No solutions.
Solve the following inequality. Write the solution set in interval
notation.
2
1 3
2
a)
∞, 3
b)
c)
∞, 3
d)
25._____
3, ∞
3, ∞
Solve the following inequality. Write the solution set in interval
notation.
5 3
3
2
4
a)
1,
b)
1,
c)
1,
d)
1,
Solve the following quadratic inequality. Write the solution set in
interval notation.
2
35 0
a)
5,7
b)
∞, 5 ∪ 7, ∞
c)
5,7
d)
∞, 5 ∪ 7, ∞
26._____
27._____
28.
29.
30.
Solve the following rational inequality. Write the solution set in
interval notation.
9
0
6
a)
9,6
b)
9,6
c)
∞, 9 ∪ 6, ∞
d)
∞, 9 ∪ 6, ∞
Solve the following absolute value equation.
|2
11| 7
2
b)
c)
2, 9
d) No solutions.
9
30._____
Solve the following absolute value inequality.
|5
3|
1
c)
31.
29._____
a)
a) No solutions.
∞,
∪
,∞
28._____
b)
,
d)
∞, ∞
Given the following center-radius form of the equation for a circle,
find the center of the circle.
2
16
3
a)
3,2
b)
3,2
c)
3, 2
d)
3, 2
31._____
32.
Consider the following graph of the point A.
32._____
Which quadrant does A lie in?
a) Quadrant I
b) Quadrant II
c) Quadrant III
d) Quadrant IV
33.
Decide whether the following relation defines a function.
0,1 , 1,2 , 1,0 , 2, 3 , 3, 2
33._____
a) Yes, this is a function.
b) No, this is not a function.
34.
Give the domain and range of the following relation.
√
a) Domain is
1
∞, ∞ and Range is
b) Domain is 1, ∞ and Range is 0, ∞
c) Domain is 1, ∞ and Range is 0, ∞
d) Domain is 1, ∞ and Range is 0, ∞
∞, ∞
34._____
35.
36.
7, find
3 .
35._____
a)
34
b) 20
c)
16
d) 2
Determine the intervals of the domain for which the following function 36._____
is decreasing.
a)
c)
37.
3
For the function
4, 2 ∪
1,0.5
0.5,4
b)
2, 1
d)
2,2.5
Which of the following pairs of points has slope 2/9 ?
37._____
a)
1,3 and 2, 7
b)
1,2 and 3, 7
c)
2,3 and
d)
3,1 and
7,1
7,2
38.
Given the following graph of a linear function, what is the slope?
a) 3/5
c)
39.
b) 5/3
3/5
d)
5/3
3,7 with
39._____
Write the equation in slope-intercept form for a line passing through
the point 3,2 that is parallel to 4
7.
40._____
Write the equation of the line passing through the point
slope zero.
3
a)
c)
40.
38._____
a)
c)
7
4
3
b)
d)
14
b)
d)
7
4
10
41.
The following table lists data collected during a recent experiment. In
this case, represents age (in years) and represents the given
diameter (in inches).
1
5.73
3
6.44
5
7.01
7
7.67
9
8.23
11
9.11
41._____
13
9.85
Use the linear regression feature on your graphing calculator to find a
line of best fit for this data. Use the equation you found to predict the
diameter given an age of 6 years.
42.
a) 7.38 inches
b) 1.91 inches
c) 1.06 inches
d) 7.04 inches
1 .
For the following piecewise-defined function, find
1
5
2
1 2
a)
c) 3
3
if
if
if
2
2
1
b)
d) 6
1
1
42._____
43.
The following is a graph of
Which is the graph of
2
.
43._____
2?
a)
b)
c)
d)
44.
45.
46.
Suppose that the point 1,4 is on the graph of
. Find a point
on the graph when is translated left 3 units and reflected across the
x-axis.
a)
1, 4
b)
c)
2,4
d)
| |
b)
c)
√
d)
3
Let
1 and
2
c)
41
3
46._____
2 .
47._____
7
1
4
2
1/8
d) 5/7
For the function
c)
/
b)
c) 7/5
3
3 .
14
2
0
3
5
3/4
a)
1
d)
Use the following table to evaluate
a)
45._____
b) 39
1
0
2
8
48.
2, 4
7. Find
a) 27
47.
4, 4
Decide which of the following functions is even.
a)
44._____
4
3
4, find and simplify
b)
3
d)
3
3
48._____
4
49.
3
1
5
8
a)
5
3
8
1
3
49._____
1
5
3
8
b)
c) 5
50.
1 .
∘
Use the following table to evaluate
1
d) 8
2
Let
1 and
a)
8
6
c)
8
5
4
4
3
3. Find
b)
2
d)
32
∘
.
4
50._____
2
48
17
Geometry Formulas
Square
Rectangle
4
Perimeter:
Area:
Triangle
2
Perimeter:
Area:
2
Perimeter:
Area:
s
s
s
W
L
s
Parallelogram
2
Perimeter:
Area:
a
2
c
h
b
Trapezoid
Circle
Perimeter:
Area:
Diameter:
2
Circumference:
Area:
2
b
b
r
a
h
a
c
h
d
B
Cube
Rectangular Solid
Volume:
Surface Area:
Volume:
Surface Area:
6
Sphere
2
2
2
Volume:
Surface Area:
H
e
4
r
W
e
L
e
Cone
Right Circular Cylinder
Right Pyramid
Volume:
Volume:
Surface Area:
Volume:
area of the base
Surface Area:
√
(excludes the base)
h
2
2
(includes top and bottom)
h
r
h
r
Answer Key:
1. D
2. C
3. C
4. B
5. D
6. A
7. B
8. A
9. C
10. B
11. D
12. D
13. A
14. C
15. C
16. D
17. C
18. A
19. B
20. B
21. D
22. A
23. B
24. B
25. B
26. C
27. A
28. B
29. C
30. D
31. C
32. B
33. A
34. D
35. B
36. C
37. C
38. A
39. D
40. A
41. A
42. C
43. C
44. D
45. A
46. B
47. A
48. D
49. B
50. D