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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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!