Free Printable Algebra 2 Final Exam Part 1 Review

1.

Solve by factoring:

6v^2-18v-18=6

a)

$c=-2,\ 2$

b)

$c=\ -4,\ 1$

c)

$c=24,\ -1$

d)

$c\ =\ -\ 1,\ 4$

2.

Solve by factoring:

28y^2-63=0

a)

$y=-\ \frac{2}{3},\ \frac{2}{3}$

b)

$y=-\ \frac{3}{2},\ \frac{3}{2}$

c)

$y\ =\ -4,\ 9$

d)

$y\ =\ -4,\ -9$

3.

Solve by factoring:

8x^2+21=-59x

a)

$x=\frac{3}{8},\ 7$

b)

$x=\frac{1}{7},\ \frac{8}{3}$

c)

$x=-\frac{8}{3},\ -\frac{1}{7}$

d)

$x=-7,\ -\frac{3}{8}$

4.

Solve by factoring:

40k^2-22k+7=5k^2+4

a)

$k=-\frac{1}{5},\ -\frac{3}{7}$

b)

$k=\frac{1}{5},\ \frac{3}{7}$

c)

$k=\frac{7}{3},\ 5$

d)

$k=-\frac{7}{3},\ -5$

5.

Factor: 27x³ + 8

a)

(3x + 2)(9x² - 6x + 4)

b)

(9x + 2)(3x² + 18x + 4)

c)

(3x²+4)(9x + 2)

d)

(27x + 8)(x² - 216x + 64)

6.

Complete the formula
a³-b³=

a)

(a-b)(a²+ab+b²)

b)

(a+b)(a²-ab+b²)

c)

(a-b)(a²-ab+b²)

d)

(a+b)(a²+ab+b²)

7.

Factor
27x³-64

a)

(3x-4)(9x²+12x+16)

b)

(3x-4)(9x²-12x+16)

c)

(3x+4)(9x²-12x+16)

d)

(3x+4)(9x²+12x+16)

8.

Factor using difference/sum of cubes.

a³ + b³

a)

(a-b)(a²+ab+b²)

b)

(a+b)(a²-ab+b²)

c)

(a-b)(a²-ab+b²)

d)

(a+b)(a²+ab+b²)

9.

Factor by grouping.

30x³+15x²-18x-9

a)

(5x²-3)(6x+1)

b)

(5x²-3)(6x+3)

c)

3(5x²+3)(2x-1)

d)

3(5x²-3)(2x+1)

10.

Factor: 8a³+c³

a)

(2a+c)(2a+c)(2a+c)

b)

(2a+c)(4a²-2ac+c²)

c)

(2a-c)(4a²+2ac+c²)

d)

(2a-c)(4a²+4ac+c²)

11.

$Factor:\ \ 27x^3-8y^3$

a)

$\left(3x-2y\right)\left(6x^2-12xy+4y^2\right)$

b)

$\left(3x-2y\right)\left(9x^2-6xy+4y^2\right)$

c)

$\left(6x-4y\right)\left(36x^2-24xy+16y^2\right)$

d)

$\left(3x-2y\right)\left(9x^2+6xy+4y^2\right)$

12.

Choose the equivalent expression.

a)

b)

c)

13.

Choose the equivalent expression.

a)

b)

c)

d)

None of the above.

14.

What is the conjugate of (x - 3)?

a)

( x - 3)

b)

x²- 9

c)

( x + 3)

15.

a)

A

b)

B

c)

C

d)

D

16.

What is the product of the complex number and its conjugate?

(4 + 3i)

a)

16 − 9i²

b)

25

c)

7

d)

8 − 6i

17.

Find the conjugate of:
-4 − 8i

a)

-4 + 8i

b)

4 − 8i

c)

4 + 8i

18.

What do you do to determine the value of c when completing the square?

a)

square b

b)

divide b by 2 and square the result

c)

divide b by 2 and take the square root of the result

d)

divide b by 2 only

19.

Determine the value of c that will complete the square.

x² + 14x + ____

a)

x² + 14x - 196

b)

x² + 14x + 49

c)

x² + 14x - 49

d)

x² + 14x + 196

20.

What should be added to both sides of the following equation to complete the square?
x² + 12x = 5

a)

12

b)

6

c)

36

d)

5

21.

Describe the transformation of the equation below from the absolute value parent function
$y=-2\left|x-3\right|+3$

a)

reflected over x axis, stretched by 2, right 3, up 3

b)

reflected over x axis, stretched by 2, left 3 up 3.

c)

reflected over x axis, shrunk by 2, right 3, up 3

d)

reflected over the x axis, shrunk by 2, left 3, up 3

22.

What steps transform the graph y = x² to y = 2(x+2)² - 5?

a)

Compress by 2, shifted 2 units left and 5 down

b)

Stretch by 5, shifted 5 units left and 2 down

c)

Stretch by 2, shifted 2 units left and 5 down

d)

Compress by 5, shifted 2 units left and 2 down

23.

What steps transform the graph $y=x^2$ to $y=-\frac{1}{2}\left(x-4\right)^2+1$ ?

a)

Compressed by 1/2, shifted 4 units right and 1 unit up

b)

Reflected across x-axis, compressed by 1/2, shifted 4 units right and 1 unit up

c)

Reflected across x-axis, stretched by 1/2, shifted 4 units left and 1 unit up

d)

Stretched by 1/2, shifted 4 units right and 1 unit down

24.

What steps transform the graph y = x² to y = x² + 8

a)

shifted up 8 units

b)

shifted down 8 units

c)

shifted left 8 units

d)

shifted right 8 units

25.

Describe the transformations.

a)

Translate Right 2, Down 4

b)

Translate Left 2, Down 4

c)

Translate Left 2, Up 4

d)

Translate Right 2, Up 4

26.

Rewrite the expression using a rational exponent.

a)

4xy¹¹

b)

xy⁴⁴

c)

x^11/4y^11/4

d)

x^4/11y^4/11

27.

Write the following expression in exponential form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

28.

a)

2^3/5

b)

-2^3/5

c)

2^5/3

d)

8⁵

29.

f(x) = -4x - 12

Which is the inverse?

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = -4x - 3

30.

Which is the inverse?

a)

f^-1(x) = 3x + 5

b)

f^-1(x) = 3x - 5

c)

f^-1(x) = 3x - 15

d)

f^-1(x) = 3x + 15

31.

What is the inverse of the function
f(x) = 2x + 4 ?

a)

f^-1(x) = 4(x -2)

b)

f^-1(x) = (x-4)/2

c)

f^-1(x) = x/2 - 4

d)

f^-1(x) = x/4 + 2

32.

Are these functions inverses?

a)

No

b)

Yes

c)

No way to tell

33.

Are y=2x+3 and y=1/2 (x-3) inverse functions?

a)

yes

b)

no

c)

no way to tell

34.

Find the domain of

f\left(x\right)\ =\ \frac{x-3}{x+4}

.

a)

$\left(-\infty,\ \infty\right)$

b)

$\left(-\infty,3\right)\cup\left(3,\infty\right)$

c)

$\left(-\infty,-4\right)\cup\left(-4,\infty\right)$

d)

$\left(-\infty,-4\right)\cup\left(-4,3\right)\cup\left(3,\infty\right)$

35.

What is the domain?

a)

$\left(-\infty,-1\right)\cup\left(3,\infty\right)$

b)

$\left(-\infty,-3\right)\cup\left(-3,1\right)\cup\left(1,\infty\right)$

c)

$\left(-\infty,-1\right)\cup\left(-1,3\right)\cup\left(3,\infty\right)$

d)

$\left(-\infty,\ 1\right)\cup\left(1,\ 3\right)\cup\left(3,\ \infty\right)$

36.

What is the range of the graph?

a)

[1, ∞)

b)

(1, ∞)

c)

(-∞, ∞)

d)

none of these

37.

What is the range of the graph?

a)

(-∞,∞)

b)

[0,∞)

c)

(0,5)

d)

[-1,∞)

38.

What is the range?

a)

\left(0,\ \infty\right)

b)

$\left[0,\ \infty\right)$

c)

$\left(-\infty,\ \infty\right)$

d)

None of the answer choices

39.

What is the domain?

a)

[-2, 3]

b)

[-2, 3)

c)

(-2, 3]

d)

[-3, 4]

e)

(-3, 4]

40.

What is the range?

a)

$\left(-\infty,\ -3\right]$

b)

$\left[3,\ -\infty\right)$

c)

$\left(-\infty,3\right]$

d)

None of the answer choices

e)

$\left[-3,\ \infty\right)$

41.

What is the DOMAIN?

a)

[0, ∞)

b)

(-∞, 0)

c)

All real numbers

d)

{0, 1, 2, 3, 4,...}

42.

Which piecewise function corresponds to this graph?

a)

f(x) = { x if x < 4; -x+1 if x ≥ 4

b)

f(x) = { x if x ≤ 4; -x+1 if x > 4

c)

f(x) = { -x+1 if x < 4; x if x ≥ 4

d)

f(x) = { -x+1 if x ≤ 4; x if x > 4

43.

Match the graph with the correct equation.

a)

b)

c)

d)

44.

Match the graph with the correct equation.

a)

b)

c)

d)

45.

Solve for all the zeros.

a)

b)

c)

d)

46.

Solve for all the zeros.

a)

b)

c)

d)

47.

What are the zeros of the function?

a)

4,1

b)

3,1,-2,-5

c)

-3, -1, 2, 5

d)

-2,4

48.

What is another way to say "where a function crosses the x-axis"?

a)

x-intercept

b)

zero

c)

root

d)

all of these.

49.

Factor:

f(x) = x³- 12x²+ 47x - 60 given one of its factors is (x-5)

a)

(x-3)(x-4)(x-5)=0

b)

(x+1)(x-4)(x-5)=0

c)

(x-3)(x-4)(2x-5)=0

d)

(x-5)(x-4)(x-5)=0

50.

Find all the real zeros of the function
f(x) = 2x³ - 19x² + 38x + 24 given that x-4 is a factor.

a)

x = 1/2, -6

b)

x = -1/2, 6

c)

x = 4, -1/2, 6

d)

x = -4, 1/2, -6

51.

Find all the zeros, given that (x+3) is a factor.

f(x) = 2x³+5x²-6x-9

a)

-1,-3,-3

b)

-1,-3,3/2

c)

3,3,3

d)

-3,2/3,-1

52.

Find all zeros for the polynomial function P(x) = x³ -3x²-5x+15

a)

3, √5

b)

3, √5, -√5

c)

-3, √5, -√5

d)

-3, 5i, -5i

53.

Find all zeros of the polynomial function P(x) = x³+6x²+9x+54

a)

6, 3, -3

b)

-6, 3, -3

c)

-6, 3i, -3i

d)

6, 3i, -3i

54.

Solve. (3x - 5)^1/4+ 3 = 4

a)

4/3

b)

2

c)

-2

d)

-4/3

55.

Solve for x:
(2x - 1)^3/4 + 9 = 36

a)

27

b)

13

c)

41

d)

82

56.

Solve. (3x-5)^1/4+3=4

a)

4/3

b)

2

c)

-2

d)

-4/3

57.

In the above graph complete the following end behavior:
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

a)

-∞
-∞

b)

+∞
-∞

c)

-∞
+∞

d)

+∞
+∞

58.

Which function has this end behavior?

a)

-1x⁴-3x³+3

b)

-2x⁷+2x⁴+4

c)

3x⁸+3x⁵-4x+7

d)

4x⁵-4x⁴+2x³-9

59.

Which function has this end behavior?

a)

-1x⁴-3x³+3

b)

-2x⁷+2x⁴+4

c)

3x⁸+3x⁵-4x+7

d)

4x⁵-4x⁴+2x³-9

60.

Which function has this end behavior?

a)

-x²-3x+1

b)

-x³+2x²+3

c)

x⁴+3x³-4x+1

d)

x⁵-4x⁴+2x²-1

61.

Which function has this end behavior?

a)

-1x⁴-3x³+3

b)

-2x⁷+2x⁴+4

c)

3x⁸+3x⁵-4x+7

d)

4x⁵-4x⁴+2x³-9

62.

Write an equation for this polynomial in factored form.

a)

$\left(x-1\right)\left(x+3\right)^2=0$

b)

$\left(x+1\right)\left(x-3\right)^2=0$

c)

$\left(x-1\right)^2\left(x+3\right)=0$

d)

$\left(x+1\right)^2\left(x-3\right)=0$

63.

Find a polynomial function of degree 3 with zeros ±3i and -2.

a)

P(x) = x³+2x²+9x+11

b)

P(x) = x³-2x²+9x+18

c)

P(x) = x³+2x²+9x+18

d)

P(x) = x²-3ix+2x-6i

64.

a)

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

b)

y = x(x - 3)²(x+2)

c)

y = x(x + 3)²(x - 2)

d)

y = -x(x + 3)²(x - 2)

65.

Using the degree and leading coefficient, match the graph to an equation.

a)

y=-(x-1)²(x+2)²

b)

y=(x-1)²(x+2)²

c)

y=(x-1)(x+2)²

d)

y=-(x-1)²(x+2)²

Algebra 2 Final Exam Part 1 Review

Total questions: 65

Worksheet time: 4hrs 55mins

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