Free Printable Algebra 2 Semester 1 Final

1.

Combine like terms to simplify:
(5x + 2) + (4x + 5)

a)

9x -7

b)

-9x-11

c)

9x+7

d)

x+7

2.

(4x²+ x) - (x²+ 2x)

a)

3x² - x

b)

4x²+ 2x

c)

3x² + 3x

d)

3x² + 2x

3.

Simplify each expression.
(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

a)

-8n² - 8n + 3

b)

-7n² - 8n + 3

c)

-6n²- 8n + 3

d)

-7n² - 4n + 3

4.

Add the polynomials.
(3x³ + 3x² – 4x + 5) + (x³ – 2x² + x – 4)

a)

4x³ + 1x² – 3x + 1

b)

2x³ + 1x² - 5x + 9

c)

6x³ + 1x - 1x² - 3

d)

3x⁵ +1x - 1x⁵ - 3x

5.

Add or Subtract to Simplify:
(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

a)

-8n² - 8n + 3

b)

-7n² - 8n + 3

c)

-6n²- 8n + 3

d)

-7n² - 4n + 3

6.

(d⁴)(d⁵)

a)

2d⁴

b)

d⁹

c)

d²

d)

2d

7.

1.) Simplify
(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

8.

Multiply.
(x + 2)(x + 3)

a)

x² + 5x + 6

b)

x² + x + 6

c)

x² + 5x + 5

d)

x² + 6x + 6

9.

Find the product.

(x - 2)²

a)

x²+ 2x + 2x + 4

b)

x²+ 2x + 2

c)

7x²+ x + 7

d)

x² - 4x + 4

10.

(5x+2)(x²-3x+6)

a)

5x³- 17x²+24x +12

b)

5x³+ 17x² - 24x +12

c)

5x³ - 13x² + 24x +12

d)

5x³ +13x² - 24x - 12

11.

(5x-1)(x+1)

a)

5x²+ 4x - 1

b)

5x²+6x - 1

c)

5x²- 4x -1

d)

5x² + 4x + 1

12.

What do we call the graph of a quadratic function?

a)

parabola

b)

linear

c)

cubic

d)

sinusoidal

13.

What is the green dot on the parabola called?

a)

maximum

b)

minumum

c)

roots

d)

zeros

14.

Identify the vertex

a)

(-1,-9)

b)

(0,-8)

c)

(-4,0)

d)

(0,0)

15.

If given the equation
y = 3(x + 5)² - 4,
what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

16.

What is the equation of this graph?

a)

f(x) = (x -5)² + 1

b)

f(x) = (x - 1)² - 5

c)

f(x) = (x + 1)² - 5

d)

f(x) = (x + 5)² +1

17.

Identify the vertex and whether the graph opens up or down.

a)

(5, 2); opens up

b)

(5, 2); opens down

c)

(-5, 2); opens up

d)

(-5, 2); opens down

18.

Convert the equation y= x²+4x into vertex form.

a)

y= (x+4)²-4

b)

y= (x-2)²+4

c)

y= (x+2)²-4

d)

y= (x+2)²

19.

Convert the equation y= x²+ 4x + 11 into vertex form.

a)

y = (x + 2)² - 4

b)

y = (x + 2)² + 7

c)

y = (x + 2)²

d)

y = (x - 2)² - 7

20.

Factor:

x² + 11x + 24

a)

(x + 6)(x + 4)

b)

(x + 12)(x + 2)

c)

(x - 8)(x - 3)

d)

(x + 8)(x + 3)

21.

Factor:
x² - 10x + 24

a)

(x - 6)(x - 4)

b)

(x + 6)(x + 4)

c)

(x - 12)(x + 2)

d)

(x - 8)(x - 3)

22.

Find GCF of 22x³+11x²

a)

11x

b)

11x²

c)

22x

d)

22x²

23.

Factor:
18b²-9b³

a)

9b²(18-9b)

b)

9b²(2-b)

c)

9b²(18-9b²)

d)

b²(2-b²)

24.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

25.

Factor: 5n² - 6n - 27

a)

(5n + 3)(n-9)

b)

(5n - 3)(n + 9)

c)

(5n + 9)(n - 3)

d)

(5n - 9)(n + 3)

26.

x² -4 = 77

a)

9

b)

-9

c)

No Real Solutions

d)

±9

27.

Solve by taking square roots:
5b² - 4 = 41

a)

b = 9, b = -9

b)

b = 3, b = -3

c)

b = 8, b = -8

d)

no solutionb

28.

What is this formula?

a)

This is the speed of light formula.

b)

This is the quadratic formula.

c)

This is the zero product property.

d)

This is scary.

29.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

Write down: a=1, b=6, c=-13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

30.

Solve Using the Quadratic Formula
2x² + 7x - 15 = 0

a)

-1.5 or 5

b)

No Solution

c)

-5 or 1.5

d)

0.7 or 5

31.

Solve using the quadratic formula...
9x² = 4 + 7x

a)

x = 2 and x = 3

b)

x = -1 and x = .25

c)

x = 1 and x = -.45

d)

x = 1.16, and x = -.38

32.

Express $\sqrt{-300}$ in terms of $i$

a)

$10\sqrt{3}$

b)

$i\sqrt{300}$

c)

$10i\sqrt{3}$

d)

$-\sqrt{300}$

33.

Express $\sqrt{-225}$ in terms of $i$

a)

$15i$

b)

$-15i$

c)

$i\sqrt{15}$

d)

$-i\sqrt{15}$

34.

What does i²= ?

a)

1

b)

-1

c)

√-1

d)

√1

35.

Simplify √-45

a)

3i√5

b)

-3i√5

c)

-i√45

d)

45i

36.

A complex number can be expressed as a + bi. What does a represent?

a)

the real part of the complex number

b)

the imaginary part of the complex number

c)

depends on the sign of the number

d)

the square root of the complex number

37.

What is the "real part" of this complex number:

8\ +\ 2i

a)

8

b)

2i

38.

What is the "imaginary part" of this complex number:

–14–5i

a)

-14

b)

-5i

c)

14

d)

5i

39.

Add/Subtract using the proper rules:
(7 + 2i) - (-12 - 4i)

a)

-5 - 2i

b)

19 - 2i

c)

-5 + 6i

d)

19 + 6i

40.

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

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

41.

Simplify:
(7 + 2i)(9 - 6i)

a)

75-24i

b)

63 - 24i - 12i²

c)

51 - 24i

d)

58 + 60i

42.

Multiply
(2i)(3i)

a)

5i

b)

-5

c)

6i

d)

-6

43.

Simplify:
-3i(4 + 2i)

a)

6 - 12i

b)

6 + 12i

c)

-12i - 6i²

d)

-12i + 6i²

44.

Solve:
$x^2+6x+27=0$

a)

$3\pm\sqrt{18}$

b)

$3\pm i\sqrt{18}$

c)

$-3\pm i\sqrt{18}$

d)

$-3\pm\sqrt{18}$

45.

Solve the equation $3x^2+96=0$

a)

$\pm4\sqrt{2}$

b)

$\pm4i\sqrt{2}$

c)

$2i\sqrt{4}$

d)

$\pm2\sqrt{4}$

Algebra 2 Semester 1 Final

Total questions: 45

Worksheet time: 4hrs 45mins

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