Free Printable Algebra 2 Final 22/23

1.

(6x + 3y + 4) – (x + y – 5)

a)

5x + 2y + 9

b)

7x + 2y + 9

c)

7x + 4y + 9

d)

5x + 2y -1

2.

WRITE AN EQUATION

331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus?

a)

7x+6=331

b)

13x=331

c)

6x+7=331

d)

331-7=6x

3.

10x + 9 = 4x - 9

a)

x = 0

b)

x = 3

c)

x = -3

d)

x = -18

4.

−2|−2r − 4| = -12

a)

{3,1}

b)

{-3,-1}

c)

{-3}

d)

No Solution

5.

4x - 10 ≤ 22

a)

x ≤ 8

b)

x ≥ 8

c)

x ≤ 3

d)

x ≥ 3

6.

Match the graph with its inequality.

a)

11 < a

b)

11 > a

c)

11 ≤ a

d)

11 ≥ a

7.

−6 < 2t − 5 < 3

a)

−0.5 < t < 1

b)

0.5 < t < −1

c)

−11/2 < t < 2

d)

11/2 < t < −2

8.

If f(x)=6x²-4,
what is f(-1)?

a)

-2

b)

13

c)

2

d)

0

9.

Given f(x) = -4x - 10 and f(x) = 10. Find x.

Hint: f(x) is the same as y.

a)

x = -5

b)

x = 5

c)

x = -50

d)

x = 30

10.

Write an equation that includes point (4, 5) and is parallel to

$y=\frac{3}{4}x-5$

a)

$y=\frac{3}{4}x+2$

b)

$y=-\frac{4}{3}x+2$

c)

$y=\frac{3}{4}x+5$

d)

$y=-\frac{4}{3}x+5$

11.

-4x-2y=-12
4x+8y=-24

a)

(5,6)

b)

(6,-6)

c)

(6,-2)

d)

(4,-3)

12.

Which point below is NOT part of the solution set?

a)

(0, 0)

b)

(-10, -10)

c)

(-1, 5)

d)

(5, 20)

13.

Select the correct graph for each inequality. y≤ -¾x -1

a)

A

b)

B

c)

C

d)

D

14.

Match the system to the graph (solution set is on the left)

a)

y ≤ 3x and y ≤ -2x + 4

b)

y > 3x and y > -2x + 4

c)

y < 3x and y > -2x + 3

d)

y > 3x and y < -2x + 4

15.

a)

10

b)

-10

c)

10i

d)

-10i

16.

What is the complex conjugate of 4-3i?

a)

A. 1/(4-3i)

b)

B. 1/(4+3i)

c)

C. -4 + 3i

d)

D. 4 + 3i

17.

(5-2i) + (-7+8i)

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

18.

a)

-2, 4

b)

-8

c)

±8

d)

No real solution

19.

Solve by completing the square. $x^2-8x=20$

a)

$x=\left\{-2,\ 10\right\}$

b)

$x=\left\{-10,\ 2\right\}$

c)

$x=\left\{-20,\ -8\right\}$

d)

$x=\left\{8,\ 20\right\}$

20.

Find the sum.
(2x² + 5x - 7) + ( 3 - 4x² + 6x)

a)

2x²+ 3x +1

b)

-2x²- 11x -4

c)

2x² + 5x -7

d)

-2x² + 11x -4

21.

Find the product:
(3r-4)(7r-5)

a)

21r²-43r+20

b)

21r+43r²+9

c)

7r+12r

d)

r+2r

22.

Factor Completely

x^2-49

a)

$\left(x+7\right)\left(x-7\right)$

b)

$7\left(x-7\right)$

c)

$\left(x-7\right)\left(x-7\right)$

d)

$x\left(x-7\right)$

23.

a)

x⁴(x² - 5x - 24)

b)

(x - 8)(x + 3)

c)

x⁴(x - 8)(x + 3)

d)

(x³ - 8)(x³ +3)

24.

Solve the following equation. x⁴+4x³ + 3x²= 0

a)

x = 0, x = 3, x = 1

b)

x = -3, x = -1

c)

x = 3, x = 1

d)

x = 0, x = -3, x = -1

25.

Use synthetic division.

(2x³ - 5x² + 3x + 7) ÷ (x - 2)

a)

2x³ - x² + x + 9

b)

2x² - x + 1

c)

2x² - x + 1 + 9/x-2

d)

2x² - 9x - 15 - 23/x-2

26.

Given
f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f + g)(x).

a)

11x² - 1

b)

5x⁴ + 6x² - 1

c)

5x² + 6x - 1

d)

5x² + 8x - 1

27.

Given f(x) = 2x and
g(x) = x²+3 , find f(g(x)).

a)

x²+2x+3

b)

4x²+3

c)

2x²+3

d)

2x²+6

28.

$-3\sqrt{8}+3\sqrt{18}$

a)

$-3\sqrt{2}$

b)

$6\sqrt{2}$

c)

$15\sqrt{2}$

d)

$3\sqrt{2}$

29.

$2\sqrt{3}\left(\sqrt{6}-\sqrt{3}\right)$

a)

$6\sqrt{2}-6$

b)

$3\sqrt{2}+3$

c)

$6-\sqrt{3}$

d)

$\sqrt{3}-\sqrt{2}$

30.

$\sqrt[]{5x-1}+4=11$

a)

x=10

b)

x=15

c)

x=7

d)

No solution

31.

$Simplify:\ \frac{5a^3c^{10}}{20a^5c^4}$

a)

$\frac{4c^6}{a^2}$

b)

$\frac{1a^2c^6}{4}$

c)

$\frac{1c^6}{4a^2}$

d)

$\frac{1a^2}{4c^6}$

32.

Simplify.

a)

(x+6)/(x+4)

b)

(x+6)(x+4)

c)

(x+6)

d)

(x+6)/(x-5)

33.

$\frac{\frac{2x}{x+1}}{\frac{3}{x+1}}$

a)

$\frac{2x\left(x+1\right)}{3}$

b)

$\frac{2x}{3}$

c)

$\frac{3}{2x}$

d)

$\frac{2x\left(x+1\right)}{x+1}$

34.

$\frac{7x-49}{x^2+8x+12}=\frac{3}{x+6}+\frac{1}{x+2}$

a)

$-2$

b)

$5$

c)

$6$

d)

$\frac{61}{3}$

35.

$1-\frac{1}{r-2}=\frac{2}{r-2}$

a)

5

b)

- 5, 4

c)

- 5

d)

5, 4

Algebra 2 Final 22/23

Total questions: 35

Worksheet time: 4hrs 51mins

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