Algebra 2 Honors: Final Exam Review

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Algebra 2 Honors: Final Exam Review

Directions: You may write on this review packet. Remember that this packet is similar to the questions that you will have on your final exam. Attempt all problems!!!! You will be able to use a calculator on the exam.

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1. Find the product (5x - 3)(x3 - 5x + 2). a. 5x4 - 3x3 - 25x2 + 25x - 6 b. 5x3 + 22x2 - 5x - 6 c. 5x3 - 28x2 + 25x - 6 d. 5x4 - 3x3 + 25x2 - 5x - 6

Simplify the given expression.

5(a 2 + 5a + 6) 41(a + 3) 2. 3(a 2 - 36) ? 6(a + 6)

10(a + 3)(a - 2) 10(a + 2) 10(a + 2) 10(a + 3)(a + 2) a. 41(a - 6) b. 41(a - 6) c. 41(a + 6) d. 41(a + 6)(a - 6)

3.

12x 2y

3y 2 24x 3

3y

3y 2

a. 4x b. 4x2

3y c. 4x2

4y d. 3x2

4. Which gives the solution(s) of the equation 3 x - 5 = -6? a. ?211, 221 b. 41 c. 221 d. ?211

Solve the given equation.

5. 9x - 9 + 5 = 10

a.

104 9

b.

34 9

c.

109 9

d.

14 9

6. 2 9n - 11 = 1 16

a.

n =

7 9

b.

n =

5 3

c.

n =

8 9

d.

n= 7

7. 625x - 4 = 25x + 5

a. 14 b. 13 c. ?13 d. ?3 8. Solve the equation. -x2 + 4 = 2x2 - 5

Factor the polynomial completely.

9. 30x3 - 50x2 + 27x - 45 a. 10x2 (3x - 5) - 9(3x - 5) b. (10x2 + 9)(3x - 5) c. 10x2 (3x - 5) - 27x + 45 d. (30x3 - 50x2) + (27x - 45)

10. 8a 4 b 2 - 12a 3 b 2 a. 4(2a 4 b 2 - 3a 3 b 2 ) b. a 3 b 2 (8a - 12) c. 4a 3 b 2 (2a - 3) d. 4a 2 b 2 (2a 2 - 3)

1

Graph:

11. Which is the graph of f(x) = 3 x + 1 - 5?

a.

c.

b.

d.

12.

Evaluate

the

expression

log3

???????

1 27

^?~~~~~

.

a.

-

1 3

b. -3

c.

1 3

d. 3

13. Identify the vertex and the axis of symmetry of the graph of the function y = 2(x + 2)2 - 4.

a. vertex: (?2, 4); axis of symmetry: x = -2

b. vertex: (2, ?4); axis of symmetry: x = 2

c. vertex: (?2, ?4); axis of symmetry: x = -2

d. vertex: (2, 4); axis of symmetry: x = 2

14. The price per person of renting a bus varies inversely with the number of people renting the bus. It costs $15 per person if 44 people rent the bus. About how much will it cost per person if 71 people rent the bus? a. $9.30 b. $24.20 c. $208.27 d. $6.21

Solve for x.

15. 3x2 = 147 a. ?21 b. ? 144 c. ? 441 d. ?7

2

16.

Graph

the

rational

function

f (x)

=

1 x- 1

.

Then

find

its

domain

and

range.

a.

c.

Domain: all real numbers except 1 Range: all real numbers except 1 b.

Domain: all real numbers except ?1 Range: all real numbers except 1 d.

Domain: all real numbers except ?1 Range: all real numbers except 0

Domain: all real numbers except 1 Range: all real numbers except 0

Simplify the given expression. Assume that no variable equals 0.

17. ????19x-6 y11 ^?~~ ????-6xy5 ^?~~

a. -114x -5 y 16

b.

13y 16 x5

-114y 16 c. x5

d. -114x -7 y -24

18.

??????????

32x 18 y 10 16x 9 y 20

^?~~~~~~~~

2

a. 2x 9 y 20

b.

4x 18 y20

c.

4x 9 y 10

d. 4x 18 y -20

Simplify the expression.

19.

245 64

75

49

5 77

a. 8 b. 8 c. 8 d. 8

20. (11 + i) + (3 - 15i) a. 14 - 14i b. - 4 + 4i c. 12 - 12i d. 14 + 16i

21. (-4 + 4i)(-3 - 3i) a. 16 + 12i b. 12 + 0i - 12i2 c. 24 + 0i d. 12 + 0i + 12

3

22. Divide x3 + x2 - x + 2 by x + 4. a. x2 - 3x + 11, R ?42 b. x2 - 3x + 11 c. x2 + 5x - 13 d. x2 + 5x - 13, R 46

23.

Divide

5x 3 3x2 y

?

25 3y 9

.

Assume

that

all

expressions

are

defined.

xy 8 a. 5

b.

125x 9y 1 0

c.

x 5y 8

d.

5 xy 8

24. Suppose that x and y vary inversely, and x = 2 when y = 8. Write the function that models the inverse variation.

16

10

6

a. y = b. y = c. y = 4x d. y =

x

x

x

25. Solve 8x + 8 = 32x . a. x = ?12 b. x = 22 c. x = 12 d. x = ?22

26. Identify the maximum or minimum value and the domain and range of the graph of the function

y = 2(x + 2)2 - 3.

a. minimum value: 3 domain: all real numbers 3 range: all real numbers

b. maximum value: ?3 domain: all real numbers -3 range: all real numbers

c. maximum value: 3 domain: all real numbers range: all real numbers 3

d. minimum value: ?3 domain: all real numbers range: all real numbers -3

27. Which is an equation for the inverse of the relation y = 4x + 2?

a. y = 2x + 4

b.

y

=

4x - 4

2

c.

y

=

x+2 4

d.

y

=

x-2 4

What are the solutions?

28. 9x2 + 16 = 0

a.

-

4 3

i,

4 3

i

b.

-

16 9

i,

16 9

i

c.

-

3 4

i,

3 4

i

d.

-

4 3

,

4 3

29.

Use

inverse

operations

to

write

the

inverse

of

f(x)

=

x 4

?

5.

a.

f -1 (x) = 4x + 5

b.

f -1 (x) = ?5x - 4

c.

f -1 (x) = 4(x + 5)

d.

f -1 (x)

=

x 4

+ 5

30. Write the equation of the parabola y = x2 - 4x - 15 in standard form.

a. y + 4 = (x - 2) 2 b. y + 19 = (x - 2) 2 c. y - 2 = (x - 2) 2 d. y + 15 = (x - 2) 2

4

31. Consider the function f(x) = -4x2 - 8x + 10. Determine whether the graph opens up or down. Find the axis of

symmetry, the vertex and the y-intercept. Graph the function.

a. The parabola opens downward.

c. The parabola opens upward.

The axis of symmetry is the line x = -1. The vertex is the point (-1,14).

The axis of symmetry is the line x = -1. The vertex is the point (-1,-6).

The y-intercept is 10.

The y-intercept -5.

b. The parabola opens upward.

d. The parabola opens downward.

The axis of symmetry is the line x = -1.

The axis of symmetry is the line x = -1.

The vertex is the point (-1,14).

The vertex is the point (-1,7).

The y-intercept 10.

The y-intercept is 5.

Simplify.

32. 3 + 5 4- 5

17 + 7 5 17 + 7 5 17 - 7 5 17 - 7 5

a.

11

b.

2

c.

11

d.

2

33. 192 - 245 + 27 + 80 a. 11 3 - 3 5 b. 11 3 + 3 5 c. 3 3 - 11 5 d. 3 3 + 11 5

5

Divide.

34. ????2x4 - 4x3 - 12x - 15^?~~ ? (x - 3)

a.

2x2 + 2x + 6 +

3 x-3

b.

2x2 + 2x + 6 + 3

c.

2x3 + 2x2 + 6x + 6 + 3

d.

2x 3

+ 2x2

+ 6x

+6+

3 x-3

35. Tell whether the function y = 2(5) x shows growth or decay. Then graph the function. a. This is an exponential growth function. c. This is an exponential decay function.

b. This is an exponential growth function. d. This is an exponential growth function.

36. 16x2 - 25 a. (4x - 5)2 b. (4x + 5)(-4x - 5) c. (4x + 5)(4x - 5) d. (-4x + 5)(4x - 5)

Solve the equation. Check for extraneous solutions.

37.

3 k2 -1

=

k

3 +1

a. 3 b. 0 c. 2 d. 1

6

Find the sum or difference.

38. ????6q 5 + 8q 2 + 3^?~~ + ????8q 5 - 3q - 7^?~~ a. -2q 5 + 8q 2 - 3q + 10 b. 14q 5 + 8q 2 - 3q - 4 c. -2q 5 + 8q 2 + 3q + 10 d. 14q 5 + 5q 2 - 4

Solve the system by graphing.

39.

?????????? -x 2-x

= 3y - y = -4

2

a.

c.

(?2, ?2) b.

(2, ?2) d.

(?2, ?2)

(?2, 2)

What is the quotient in simplified form? State any restrictions on the variable.

x2 - 16

x2 + 5x + 4

40. x2 + 5x + 6 ? x2 - 2x - 8

(x - 4)2

(x + 4)2 (x + 1)

(x - 4)2

1

a. (x + 3)(x + 1) b. (x + 2)2 (x + 3) c. (x + 3)(x + 1) d. (x + 3)(x + 1)

7

Solve the equation.

41. 5n - 2(n - 2) = -11

42.

1 4

??? 3y

+

2^?~

=

7

43. 3x + 17 - 5x = 12 - (6x + 3)

44. ?3x + 25 + x + 21 = 2 a. 22 b. ?3 c. ?22 d. 3

What is the graph of the rational function?

-3x + 5 45. y =

-5x + 2

a.

b.

c.

d.

Solve the equation. 46. x3 + 4x2 - 25x - 100 = 0

a. -4, 25 b. -5, 4, 5 c. 4, 5 d. -4, - 5, 5 47. x3 - x2 - 6x = 0

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