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Livingston High School Page 1
Algebra 1 Honors Final Exam
REVIEW June 2015
Name: Period: Your final examination will consist of 52 multiple-choice questions worth one point each
which will be completed on a Scantron form. The exam will include material from the
following units: Exponents, Polynomials, Factoring, Radicals, Quadratics, Compound
Inequalities, Absolute Value Equations and Inequalities
NOTE: School policy mandates a penalty for cheating on an exam to be a grade of
ZERO for that exam. The term cheating includes "intent to cheat." NO CELL
PHONES. All cell phones must be kept out of sight. If a cell phone is seen during
an exam, you will receive a grade of ZERO.
All calculators may be checked for inclusion of extraneous material. No papers
should be placed in calculators. No information should be written on the
front/back of calculators. The program portion of the graphing calculator will be
checked. Any information entered there can be considered intent of cheating.
Before the examination, clear your calculator of any formulas, notes or any such items, which
could be perceived as "useful" or providing unfair advantage. The best solution is to RESET
and clear the memory completely.
The following pages provide a comprehensive review of the materials to be studied for this
exam. We will take a few days of class time to review for this exam. Please feel free to stop
in on your own time for further assistance. Good Luck!
Mr. Ladolcetta and Ms. Riggi
ALGEBRA 1 HONORS JUNE 2015 Review for FINAL EXAM
Livingston High School Page 1
Exponents
TOPICS –
LAWS OF EXPONENTS, SCIENTIFIC NOTATION, EXPONENTIAL FUNCTIONS
PROBLEMS –
1. What is the value of 4 2c c
c
when c = 3?
a. 3 b. 24 c. 27 d. 216
2. In simplified form, 2 3 25x y xy is
a. 3 65x y b.
4 55x y c. 3 55x y d.
3 55x y
3. In simplified form, 2 5
5 2
3
18
a b
a b
is
a. 3
36
b
a b. 3 46a b c.
4
36
b
a d.
4
36
b
a
4. In simplified form, 2
2 5 3 03 2c d c d =
a. 8 76c d b. 7 512c d c. 8 512c d d. 126c d
5. In simplified form, 3 3 3 2v w v w is
a. w b. 5
6
w
v c. 6 5v w d.
w
v
6. In scientific notation, 28,700,000,000 is written as:
a. 72.87 10 b. 7287 10 c. 102.87 10 d. 2.87 910
ALGEBRA 1 HONORS JUNE 2015 Review for FINAL EXAM
Livingston High School Page 2
7. In decimal notation, 96.05 10 is
a. 0.000000000605 b. 0.00000000605 c. 0.00000605 d. 0.000000605
8. Find the value of: a. 2
32 b. 5
83
10
1010 c.
3 3
2
3 3
6
Simplify:
9. 3 2 53 7a b a b 10. 4 7
2
5 6
2
p p
p
11. 3
22cd 12. 2
4 53x y
13. 6
9
r
r 14.
5 8 4
7 5 4
15
25
v w z
v w z
15. 2
1 3
14
7
ab
a b
ALGEBRA 1 HONORS JUNE 2015 Review for FINAL EXAM
Livingston High School Page 3
16. Write each number in scientific notation:
a. 90,000,000 b. 0.00007 c. 305 d. 0.000406
17. Write each number in decimal notation:
a. 68 10 b. 1.05 710 c. 3.2 510 d. 2.06 910
18. Write in scientific notation:
20. Simplify 23
23
108
103.5
. Give your answer in scientific notation.
21. The equation of the asymptote of the function f(x) = 2
x is:
a. x = 0 b. y = 0 c. x = 2 d. y = 2
22. The function ( ) (
)
models:
a. linear growth b. linear decay c. exponential growth d. exponential decay
ALGEBRA 1 HONORS JUNE 2015 Review for FINAL EXAM
Livingston High School Page 4
Graph the following functions and state the domain, range and asymptote. Tell whether the function models
exponential growth or decay.
23. 24. ( ) ( )
Polynomials and Factoring
TOPICS –
POLYNOMIALS –degree of, standard form, monomial, binomial, trinomial
Name by degree- constant, linear, quadratic, cubic, quartic
Adding, subtracting, multiplying, dividing
FACTORING – gcf, differences of squares, trinomials, factoring by grouping
Solving equations by factoring, simplifying rational expressions by factoring
PROBLEMS –
1. The polynomial 3 2x - 2x +1 is a
a. monomial b. binomial c. trinomial
2. In standard form 4 2 37 2 8a a a is
a. 2 3 48 7 2a a a b. 4 3 22 7 8a a a c. 2 3 47 2 8a a a
ALGEBRA 1 HONORS JUNE 2015 Review for FINAL EXAM
Livingston High School Page 5
3. By degree, the polynomial 9 3x +1 is classified as
a. constant b. quadratic c. cubic d. quartic e. linear
4. By degree, the polynomial 2x - 8x + 2 is classified as
a. constant b. quadratic c. cubic d. quartic e. linear
5. Simplify: 4 2 4 3 23 7 9 5 2 1r r r r r r
a. 4 24 12 3 10r r r b. 4 24 2 8r r r
c. 4 3 24 5 5 8r r r r d. 4 3 24 5 9 8r r r r
6. Simplify: 5 3 2 3 22 3 3 5 7x x x x x
a. 5 3 23 4x x x b. 5 3 23 8 10x x x
c. 5 3 28 10x x x d. 5 3 22 4x x x
7. Multiply / simplify: 2 26 3 1y y
a. 4 218 6y y b.
49 6y y c. 418 1y d. 18
3 26y y
8. Multiply / simplify: 2
4 3p
a. 216 6 9p p b.
216 12 9p p c. 216 24 9p p d.
216 9p
9. Multiply / simplify: 5 3 2 2x x
a. 210 16 6x x b. 10x – x – 6 c. 210 4 6x x d. 215 4 4x x
ALGEBRA 1 HONORS JUNE 2015 Review for FINAL EXAM
Livingston High School Page 6
10. Multiply / simplify: 3 2 3 2x x
a. 29 4x b. 23 6 4x x c. 29 4x d. 29 2 4x x
11. What is the GCF of 4 23a b c and 2 3a b c
a. 2 33a b c b. 2 2a b c c. 4 33a b c d. 2 3a b c
12. Factor: 2 3 3 2 22 8 6a b a b a b
a. 2 22 4 3a b b ab b. 22 4 3ab ab ab a
c. 2 3 3 2 22 8 6a b a b a b d. 2 22 4 3a b b a
13. What are the solutions to the equation 2 5 6 0x x ?
a. –2 and 3 b. 2 and –3 c. –2 and –3 d. 2 and 3
14. Factor completely: 29 36 36x x
a. 9(x + 2)(x - 2) b. 3(x + 3)(3x + 4) c. 9(x – 4)(x + 1) d. 9 2
2x
15. Factor completely: 2 425 9a b
a. 16 2 2a b a b b. 2 2 225 1 3 1 3a b b
c. 2 25 3 5 3a b a b d. 2
25 3a b
ALGEBRA 1 HONORS JUNE 2015 Review for FINAL EXAM
Livingston High School Page 7
16. Factor completely: 26 12x x
a. 2 3 2 3x x b. 3 4 2 3x x
c. 3 4 2 3x x d. 6 1 2x x
17. Simplify: 3 2 3 2( 3 5 ) 4 9 12x x x x x
18. Simplify and put in standard form: 3 33 2 3 5 8x x x x
19. Simplify and put in standard form: 2 3 2 37 9 3 3 8 9y y y y
20. Find each product:
a. 23 5 6 1w w w b. 2 24 2 4 2a b a b
c. 2
2 3x d. 3 8 2 3x x
e. 5 12x x f. 23 2 4 8x x x
ALGEBRA 1 HONORS JUNE 2015 Review for FINAL EXAM
Livingston High School Page 8
21. Factor each completely:
a. 29 4r b. 2 7 18z z
c. 2 10 25m m d. 3 27 28 35a a a
e. 2 11 24y y f. 5 3 2 4 218 9 27a b a b a b
g. x4 – 81 h. 6x
2 – 19x – 20
i. x3 + 6x
2 – x – 6 j. 20x
3 – 26x
2 + 8x
ALGEBRA 1 HONORS JUNE 2015 Review for FINAL EXAM
Livingston High School Page 9
22. Solve each equation by factoring:
a. 2 4 3 0x x b. 2 25 0x
c. 2 8 15x x d. 2 8 20x x
e. 2x2 + x = 11(2x + 1) f. 7b
2 – 14b = 0
23. Evaluate: 24 3 5x x for x = -3
24. Find the missing value if: 28 _ 14 48x x x x
25. Simplify: 6 228 32
4
m m
m
26. Simplify: 2 5 2 7 3
3
42 49 14
7
r s r s rs
rs
ALGEBRA 1 HONORS JUNE 2015 Review for FINAL EXAM
Livingston High School Page 10
27. Multiply: 2834124 22 yzyyzy
28. Fill in the following table:
POLYNOMIAL DEGREE NAME BY # OF NAME BY
DEGREE TERMS # OF TERMS
50x2 – 3x + 2
12m + 8
-3.5
2y4 + y
3 + 3y + 1
29. Simplify each expression by factoring. State any restrictions.
A. a
a
5
105 B.
6
632
xx
x C.
25
51122
2
x
xx
ALGEBRA 1 HONORS JUNE 2015 Review for FINAL EXAM
Livingston High School Page 11
Radicals
TOPICS –
Simplifying Square Roots
Adding, Subtracting Square Roots
Multiplying and Dividing Square Roots (rationalizing the denominator)
PROBLEMS –
Simplify the following expressions.
1. 300 2. 2 162
3. 7873 4. 50192424
15. 4810125 6. 238
7. 1835 8. 7
5
9. 123
612
ALGEBRA 1 HONORS JUNE 2015 Review for FINAL EXAM
Livingston High School Page 12
Quadratics
TOPICS –
Quadratic Equations –Quadratic Formula, Discriminant,
Graphing Quadratic Equations in Vertex and Standard Forms
Word Problems
PROBLEMS –
1. Find the vertex and axis of symmetry of the graph of y = .5(x – 6)2 – 3.
2. The vertex of the graph of y = x
2 + 8x – 9 is:
A. (4, 39) B. (-4, -57) C. (-4, -25) D. (4, 0)
3. The # of real solutions to the equation 3x
2 – 2x + 1 is:
A. 0 B. 1 C. 2 D. 3
4. The # of real solutions to the equation 4x = 4x
2 + 1 is:
A. 0 B. 1 C. 2 D. 3
5. The discriminant of 6x
2+ 23x + 20 is:
A. 49 B. 7 C. -7 D. -49
ALGEBRA 1 HONORS JUNE 2015 Review for FINAL EXAM
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6. Solve the following equations using the quadratic formula. Round to nearest tenth if needed
A. 2y2 – 8y = 8 B. –x
2 – 3x - 10 = 0 D. x
2 – 15 x + 2 = 0
7. Graph the following functions clearly showing the vertex, axis of symmetry, and at least 4 other points.
Then state the domain and range.
A. f(x) = x2 + 2 B. y = x
2 – 6x + 5
ALGEBRA 1 HONORS JUNE 2015 Review for FINAL EXAM
Livingston High School Page 14
C. ( ) = ( + 5)2 + 7
8. To approximate the profit per day for her buisness, Mrs. Howe uses the formula p = -x2 + 50x – 350.
The profit, p, depends on the number of cases, x, of decorator napkins that are sold. How many cases of
napkins must she sell to break even (not lose money)? To make the maximum profit? Find the maximum
profit.
9. A boat fires an emergency flare that travels upward at an initial velocity of 25 meters per second. To
find the height in meters, h, of the flare at t seconds, use the function h = -5t2 + 25t. After how many seconds
will the flare be at its maximum height? What is its maximum height? When will it hit the ground?
ALGEBRA 1 HONORS JUNE 2015 Review for FINAL EXAM
Livingston High School Page 15
Compound Inequalities, Absolute Value Equations and Inequalities
TOPICS –
Solving and Graphing Compound Inequalities
Solving Absolute Value Equations
Solving Absolute Value Inequalities
PROBLEMS –
Solve the following equations.
1. 7x 2. 2 = 3 - i
3. 2.293
62
y 4. 1198
5
3 p
5. What compound sentence is graphed below?
A. 32 y B. 32 y C. 2y or 3y D. 32 y
ALGEBRA 1 HONORS JUNE 2015 Review for FINAL EXAM
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6. Solve and graph each of the following inequalities:
a. – b.
c. – d. 4m – 5 – (3m + 7) < 0
e. – f.
g. – ( – ) h. 2
x
< 14
7. Write an inequality describing each graph below:
a. b.
5 0 -2
-2 -1 5
o
ALGEBRA 1 HONORS JUNE 2015 Review for FINAL EXAM
Livingston High School Page 17
8. Graph each solution.
a. –1 < x < 4 b. x < 3 or x > 4
c. 0 y < 7.5 d. k < 12 or k ≤ 13
9. Solve and graph the following compound inequalities.
a. –5 x + 2 < 0 b. 10y > -2 or 2 + y -15 c. –4x < 8 or –3x 9
10. Solve and graph each of the following absolute value inequalities.
a. | | b. | |
c. 53
10
q d. 4005003
5
x
ALGEBRA 1 HONORS JUNE 2015 Review for FINAL EXAM
Livingston High School Page 18
11. Which of the following is a graph of the solution set of 1684 x ?
A.
B.
C.
D.
12. Which graph represents the solution of 963 x ?
A.
B.
C.
D.
**End of Review packet. Please be sure to study notes,
homework assignments and, previous assessments!