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ADAMS STATE UNIVERSITY EXTENDED STUDIES
MATH 097 – BASIC ALGEBRA SKILLS
Final Exam
I certify that the student named on this exam did not receive assistance and did not have unauthorized access to
books or notes. I have returned this exam to the instructor on ____________________ (date).
Proctor Name: ______________________________
Signature: _________________________________
Vocabulary: Fill in each blank with one of the words or phrases listed below.
equation
reciprocal
variable
x-intercept
y-intercept
slope
point-slope
slope-intercept
coefficient
term
distributive
function
domain
range
parallel
perpendicular
1. Two lines are ______________________ if the product of their slopes is –1.
2. A(n) ______________________ is a relation in which each first component in the ordered pairs
corresponds to exactly one second component.
3. A(n) _________________________ is a mathematical statement that two expressions are equal.
4. A(n) _______________________ is a symbol used to represent a number.
5. A(n) _______________________ is a point of the graph where the graph crosses the y-axis.
6. The ______________________ of a relation is the set of all second components of the ordered pairs
of the relation.
7. The _______________________ of a line measures the steepness or tilt of the line.
8. The _________________________ of a term is its numerical factor.
9. The equation y = mx + b is written in ______________________________________ form.
10. A _________________________ is a number or the product of a number and variables raised to
powers.
Adams State University – Extended Studies©
Instructor: Russell Randolph
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Name: ________________________________
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March 2016
ADAMS STATE UNIVERSITY EXTENDED STUDIES
MATH 097 – BASIC ALGEBRA SKILLS
Final Exam
Exercises
1. Simplify the expression, 20 – (8)(–2).
2. Simplify the expression,−
5
9
2
+ .
3
2
3
3. Simplify the expression,(− ) ( ).
9
4
4.
1
Given the set {−5.5, −4, −1, −0.3, 0, 3 , 3.3, 5, √26, 10} list the numbers that also belong to the set
of integers.
+ 3
for x = 4, y = 2 and z = –2.
5.
Evaluate
6.
Identify the property illustrated by the equation, 3(x + 9) = 3x + 27.
3
7. Simplify the expression, 4(a + 3) – 3(a – 5).
8. Solve the equation, 4 − 1 + = 11 + .
Adams State University – Extended Studies©
Instructor: Russell Randolph
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Name: ________________________________
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March 2016
ADAMS STATE UNIVERSITY EXTENDED STUDIES
MATH 097 – BASIC ALGEBRA SKILLS
Final Exam
9. Solve the equation, –2(n – 5) = 4n – 8.
10. Solve the equation,
4( −1)
5
= 2 + 3.
11. Find the value of c if a = 15 and b = 123 in the formula, b = 4a – 7c.
12. Solve the formula, =
1
3
ℎ for ℎ.
13. Solve the inequality and write the answer using solution set notation. Graph the solution set.
4x – 7 > 2x – 3
-4
-3
-2
-1
0
1
2
3
14. Find the slope of the line.
Adams State University – Extended Studies©
Instructor: Russell Randolph
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Name: ________________________________
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March 2016
4
ADAMS STATE UNIVERSITY EXTENDED STUDIES
MATH 097 – BASIC ALGEBRA SKILLS
Final Exam
15. Find the slope of the line passing through (1, 5) and (–4, –10).
16. Graph the equation, 2x – y = –7
17. Graph the equation y = –5
Adams State University – Extended Studies©
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March 2016
ADAMS STATE UNIVERSITY EXTENDED STUDIES
MATH 097 – BASIC ALGEBRA SKILLS
Final Exam
18. Graph the inequality 2x + 7y < 5.
1
19. Without graphing, determine whether the graphs of y = 6x – 3 and x + 6y = 6 are parallel lines,
perpendicular lines or neither. Show your work algebraically to support your answer.
20. Write an equation of the line with a slope of –5, through the point (0, 3). Write the equation in
standard form.
21. Write the equation of the line through the points (–2, 5) and (–4, 6). Write the equation in slopeintercept form.
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Instructor: Russell Randolph
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March 2016
ADAMS STATE UNIVERSITY EXTENDED STUDIES
MATH 097 – BASIC ALGEBRA SKILLS
Final Exam
22. Evaluate(6 )0 .
4 3
23. Simplify( 2 )
5
2
.
−4 −2
24. Simplify(
5
)
−2 5
.
4
25. Simplify( −1 2 ) . Write your answer using positive exponents only.
26. Write 0.000002874 in scientific notation.
27. Combine like terms by adding or subtracting the expression,
(2 6 + 4 − 3 3 + 6 2 + ) − (4 6 − 4 + 3 2 − 7 ).
28. Multiply (5a + 2)(6a – 1).
Adams State University – Extended Studies©
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March 2016
ADAMS STATE UNIVERSITY EXTENDED STUDIES
MATH 097 – BASIC ALGEBRA SKILLS
Final Exam
29. Multiply (4 + 2 )(4 − 2 ).
30. Divide ( 2 + 7 + 12) ÷ ( + 3).
31. Simplify( + 2)3 .
32. Find the domain and range of the relation, {(−2, −1), (1, 0), (3, −1), (4, 8)}. Also determine
whether the relation is a function.
Domain: ______________________________
Range: _______________________________
Is it a function? ________________________
33. Determine whether the graph is a function or not and justify your answer using the vocabulary from
this unit.
Adams State University – Extended Studies©
Instructor: Russell Randolph
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March 2016
ADAMS STATE UNIVERSITY EXTENDED STUDIES
MATH 097 – BASIC ALGEBRA SKILLS
Final Exam
34. Find the domain of the rational function, ( ) =
3+ 1
−2
.
35. A pebble is hurled upward from the top of a 225 foot tall cliff with an initial velocity of 60 feet per
second. Neglecting air resistance, the height, ℎ( ), of the pebble after t seconds is given by the
polynomial function, ℎ( ) = −16 2 + 60 + 220. Find the height of the pebble after 2 seconds.
+ 3 if ≤ 0
36. Graph {
−2 − 5 if > 0
37. Match the common function with its common graph.
a. ( ) =
b. ( ) = 2
c. ( ) = √
d. ( ) = | |
_______________
_______________
Adams State University – Extended Studies©
Instructor: Russell Randolph
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_______________
_______________
March 2016
ADAMS STATE UNIVERSITY EXTENDED STUDIES
MATH 097 – BASIC ALGEBRA SKILLS
Final Exam
38. Sketch the graph of the function, ( ) = ( − 2)2 + 4
39. Solve | + 5| ≥ 3 and graph the solution set on a number line. Be sure to label the units on your
number line.
40. Sketch the graph of the function, ( ) = −| + 1| − 3.
BONUS:
A local gasoline station recently increased the price of diesel by 15%. If diesel originally
cost $2.20 per gallon, find the mark-up and the new price.
Adams State University – Extended Studies©
Instructor: Russell Randolph
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Name: ________________________________
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March 2016
ADAMS STATE UNIVERSITY EXTENDED STUDIES
MATH 097 – BASIC ALGEBRA SKILLS
Final Exam
Adams State University – Extended Studies©
Instructor: Russell Randolph
Page 10 of 10
Name: ________________________________
Please Print
March 2016
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