Algebra 2 ---- 1st Semester Final Exam Review

Algebra 2 ---- 1st Semester Final Exam Review

1st Semester Final Exam Review Chapter 1

Multiple Choice Identify the choice that best completes the statement or answers the question.

To which sets of numbers does the number belong?

____ ____ ____

1. a. irrational numbers, real numbers b. integers, rational numbers, real numbers c. rational numbers, irrational numbers d. whole numbers, integers, rational numbers, real numbers

2. ?17 a. integers, rational numbers, real numbers b. whole numbers, integers, rational numbers, real numbers c. whole numbers, integers, real numbers d. rational numbers, real numbers

3. An irrational number can ________ be expressed as a quotient of integers.

a. always

b. sometimes

c. never

Insert , or = to make the sentence true.

____ 4. a. <

b. >

c. =

Name the property of real numbers illustrated by the equation.

____ ____ ____

5.

a. Distributive Property b. Associative Property of Multiplication c. Commutative Property of Multiplication d. Associative Property of Addition

6. ?6 + 6 = 0 a. Identity Property of Multiplication b. Inverse Property of Multiplication c. Associative Property of Addition d. Inverse Property of Addition

7. ?2.5 + 0 = ?2.5 a. Inverse Property of Multiplication b. Identity Property of Addition c. Inverse Property of Addition d. Identity Property of Multiplication

Evaluate the expression for the given value of the variable(s).

____ 8. a. 19

; b = 2 b. 17

c. ?11

d. 21

Algebra 2 ---- 1st Semester Final Exam Review

____ 9. a. 3

; x = ?3 b. ?1

c. 11

d. ?17

Simplify by combining like terms.

____ 10.

a.

b.

c.

d.

____ 11. Find the perimeter of the figure. Simplify the answer.

x + y

2x 4 x

y 2x

x

a. 9x + 2y

b. 10x + y

Solve the equation.

c. 10x + 2y

d. 9x + 3y

____ 12.

a.

b.

c.

d.

____ 13.

a.

x

=

8 9

or

x

=

-

2 9

b. x = 0 or x = -223

c.

x

=

8 9

or

x

=

-223

d.

x

=

8 9

or

x

=

0

Solve the equation or formula for the indicated variable.

____ 14.

, for t

a.

b.

c.

d.

____ 15. The formula for the time a traffic light remains yellow is

, where t is the time in seconds and s is

the speed limit in miles per hour. a. Solve the equation for s. b. What is the speed limit at a traffic light that remains yellow for 4.5 seconds?

a.

; s = 28 mi/h

b.

; s = 36 mi/h

c.

; s = 35

d. ; s = 28 mi/h

Algebra 2 ---- 1st Semester Final Exam Review

Solve for x. State any restrictions on the variables.

____ 16. a.

b.

; ;

c.

;

d. ;

____ 17. A rectangle is 3 times as long as it is wide. The perimeter is 60 cm. Find the dimensions of the rectangle.

Round to the nearest tenth if necessary.

a. 7.5 cm by 22.5 cm

c. 20 cm by 60 cm

b. 7.5 cm by 52.5 cm

d. 15 cm by 22.5 cm

____ 18. The sides of a triangle are in the ratio 3 : 4 : 5. What is the length of each side if the perimeter of the triangle

is 90 cm?

a. 10.5 cm, 11.5 cm, and 12.5 cm

c. 7.5 cm, 11.5 cm, and 32.1 cm

b. 22.5 cm, 30 cm, and 37.5 cm

d. 19.3 cm, 25.7 cm, and 32.1 cm

____ 19. Two cars leave Denver at the same time and travel in opposite directions. One car travels 10 mi/h faster than

the other car. The cars are 500 mi apart in 5 h. How fast is each car traveling?

a. 35 mi/h and 45 mi/h

c. 45 mi/h and 55 mi/h

b. 55 mi/h and 35 mi/h

d. 55 mi/h and 65 mi/h

Solve the inequality. Graph the solution set.

____ 20. ?4k + 5 21 a. k ?4

c. k ?4

?8 ?6 ?4 ?2 0 2 4 6 8

b. k -612

?8 ?6 ?4 ?2 0 2 4 6 8

d. k -612

?8 ?6 ?4 ?2 0 2 4 6 8

____ 21. 26 + 6b 2(3b + 4) a. all real numbers

?8 ?6 ?4 ?2 0 2 4 6 8

b. b 112

?8 ?6 ?4 ?2 0 2 4 6 8

?8 ?6 ?4 ?2 0 2 4 6 8

c. b 112

?8 ?6 ?4 ?2 0 2 4 6 8

d. no solutions

?8 ?6 ?4 ?2 0 2 4 6 8

Algebra 2 ---- 1st Semester Final Exam Review

Solve the compound inequality. Graph the solution set.

____ 22. 4x ? 5 < ?17 or 5x + 6 > 31 a. x < ?3 or x > 5

?8 ?6 ?4 ?2 0 2 4 6 8

b. x < -512 or x > 725

c. x < ?3 or x > 725

?8 ?6 ?4 ?2 0 2 4 6 8

d. x < -512 or x > 5

____ 23. a.

b.

?8 ?6 ?4 ?2 0 2 4 6 8

?8 ?6 ?4 ?2 0 2 4 6 8

c.

?8 ?6 ?4 ?2 0 2 4 6 8

d.

?8 ?6 ?4 ?2 0 2 4 6 8

?8 ?6 ?4 ?2 0 2 4 6 8

?8 ?6 ?4 ?2 0 2 4 6 8

Solve the inequality. Graph the solution.

____ 24. a.

?40 ?30 ?20 ?10 0 10 20 30 40

b.

?20 ?15 ?10 ?5 0 5 10 15 20

____ 25. a. ?18 > x > 8

?20 ?15 ?10 ?5 0 5 10 15 20

b. ?18 < x < 8

?20 ?15 ?10 ?5 0 5 10 15 20

c.

?20 ?15 ?10 ?5 0 5 10 15 20

d.

?20 ?15 ?10 ?5 0 5 10 15 20

c. ?36 < x < 16

?40 ?30 ?20 ?10 0 10 20 30 40

d.

?20 ?15 ?10 ?5 0 5 10 15 20

Short Answer 26. Name the property used in each step of simplification.

Algebra 2 ---- 1st Semester Final Exam Review

1st Semester Final Exam Review Chapter 2

Multiple Choice Identify the choice that best completes the statement or answers the question.

____ 1. Find the domain and range of the relation and determine whether it is a function.

y

4

2

?4

?2 O

2

4

x

?2

?4

____

a. Domain: all real numbers; range: all real numbers; yes, it is a function b. Domain: x > 0; range: y > 0; yes, it is a function.

c. Domain: positive integers; range: positive integers; no, it is not a function. d. Domain: x 0; range: y 0; no, it is not a function.

2. Use the vertical-line test to determine which graph represents a function.

a.

y

c.

y

4

4

2

2

?4 ?2 O ?2

?4

24

x

?4 ?2 O ?2

?4

24

x

b.

y

4

2

d.

y

4

2

?4 ?2 O ?2

?4

24

x

?4 ?2 O ?2

?4

24

x

____ 3. For

,

.

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