Free Printable Algebra 2 Honors Semester 1 Final Review

1.

Which function is graphed?

a)

f(x) = 2|x + 2| -4

b)

f(x) = 2|x - 4| + 2

c)

f(x) = |x + 2| - 4

d)

f(x) = -2|x - 4|

2.

What is the equation of this graph?

a)

y=2|x-3|+1

b)

y=2|x+1|+3

c)

y=-2|x-1|+3

d)

y=-2|x-1|+3

3.

What is another word for zeros?

a)

y-intercepts

b)

roots

c)

vertex

d)

axis of symmetry

4.

Find the vertex of
f(x) = -x²- 4x + 12

a)

(-2, 16)

b)

(2, 0)

c)

(2, 4)

d)

(-2, 4)

5.

Find the y-intercept of
f(x) = 2x²-2x + 1

a)

2

b)

-2

c)

1

d)

-1

6.

Use the graph to determine the solutions.

a)

-1 and -3

b)

1 and -3

c)

1 and 3

d)

-1 and 3

7.

Does
y = -4x²
have a maximum or minimum value?

a)

maximum

b)

minimum

8.

What is the vertex of
f(x) = 2(x - 5)² + 12

a)

(-5, -12)

b)

(5,-12)

c)

(5, 12)

d)

(-5, 12)

9.

Solve 3x² - 192 = 0

a)

-32 or 32

b)

No Solution

c)

-8 or 8

d)

-64 or 64

10.

If the graph of a quadratic does not intercept the x-axis at any point, then it has:

a)

1 Real Solution

b)

2 Real Solutions

c)

Half a Solution

d)

No Real Solution

11.

Convert the equation y= 8x²-16x+27 into vertex form.

a)

y=8(x+1)²+19

b)

y= -8(x-1)²+19

c)

y=8(x-1)²+19

d)

y=(x-1)²+8

12.

Rewrite into standard form: f(x) = 2(x-3)²-1

a)

f(x)=2x²-17

b)

f(x)=2x²-12x+8

c)

f(x)=2x²-12x+17

d)

f(x)=2x²-19

13.

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

14.

Solve by factoring.
15 = 8x² - 14x

a)

x = -5 or x = 3/8

b)

x = -2/5 or x = 4/3

c)

x = -3 or x = 5/8

d)

x = -3/4 or x = 5/2

15.

Solve by factoring:
n² - 2n = 0

a)

n = 2 and 0

b)

n = -2 and 0

c)

n = 2

d)

n = 0

16.

What does the discriminant tell us?

a)

The maximum or minimum

b)

The y-intercept

c)

The number and type of solutions

d)

The axis of symmetry

17.

If the discriminant is negative, how many solutions and of what type?

a)

1 real solution

b)

2 irrational solutions

c)

no real solutions

d)

2 rational solutions

18.

Which of the following is a factor of
1-8x³

a)

(1-2x)

b)

(1+2x)

c)

(2x+1)

d)

(2x+2)

19.

Fill in the missing number that will make the quadratic finction a perfect square trinomial
x²- ( )x + 100

a)

50

b)

25

c)

10

d)

20

20.

What is the range?

a)

y≥-3

b)

y≥-1

c)

All real numbers

d)

y≤-1

21.

Solve
x² -6x +2 = 0

a)

3+√7 &
3-√7

b)

3/2+√7 &
3/2-√7

c)

-3+√-7
& -3-√-7

d)

-3+√7
& -3-√7

22.

Which graph has a discriminant = 0?

a)

None of them

b)

Red

c)

Blue

d)

Green

23.

(-5 + 6i)(3 - 2i)

a)

-15 + 18i

b)

-3 + 28i

c)

-3 - 28i

d)

27 + 8i

24.

Simplify i³

a)

1

b)

-1

c)

i

d)

-i

25.

33 = 18 - 3x²

a)

x = ±5i

b)

x = ±i√5

c)

x = ±√5

d)

x = i√5

26.

What is i¹²⁹?

a)

-i

b)

i

c)

1

d)

-1

27.

Calculate(Divide, multiply by conjugate):

a)

-3/4 − 1/4i

b)

3/4 + 1/4i

c)

-3/4 + 1/4i

d)

3/4 − 1/4i

28.

Simplify the expression.
-3x²( 7x²- x + 4)

a)

-21x⁴ + 3x³ -12x²

b)

7x² - x + 4 (-3x²)

c)

21x⁴+ 3x³+ 12x²

d)

-12x²+ 3x³-21x⁴

29.

(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

30.

Factor completely: 3x² - 7x + 2

a)

(x - 1) (3x + 2)

b)

(x - 2) (3x -1)

c)

(x - 1) (3x - 2)

d)

(x + 2) (3x + 1)

31.

Give the correct name for
2x³+5x

a)

Linear Binomial

b)

Cubic Binomial

c)

Quadratic Trinomial

d)

Linear Trinomial

32.

Give the correct name for
-3x⁴-3x²+5

a)

Constant Trinomial

b)

Quartic Trinomial

c)

quadratic Trinomial

d)

Linear Trinomial

33.

(3x + 4y - 3z) - (2x - 6y + 7z)

a)

x + 10y - 10z

b)

-x +10y - 10z

c)

x -10y - 10z

d)

-x -10y - 10z

34.

(4x³-5x²+3x)+(-2x³-x²+6x)

a)

2x³-6x²-9x

b)

2x³+6x²+9x

c)

-2x³-6x²+9x

d)

2x³-6x²+9x

35.

Expand:
(x - 2y)³

a)

x³ - 8y³

b)

x² - 4xy + 4y²

c)

x³ + 6x²y + 12xy² + 8y³

d)

x³ - 6x²y + 12xy² - 8y³

36.

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

37.

Decide if (x-3) is a factor of 3x³+10x²-x-12

a)

Yes, it is a factor!

b)

No, it is not a factor!

38.

What does multiplicity of a zero mean?

a)

Look at the number of terms

b)

How many times the zero repeats

c)

Find the sum of all the coefficients

d)

Ratio your x and y

39.

What are the zeros of the polynomial and state their multiplicity at each.
y = (x - 5)(x + 2)²

a)

x = 5 multi 1, x = 2 multi 2

b)

x = -5 multi 2, x = -2 multi 1

c)

x = 5 multi 1, x = -2 multi 2

d)

x = 5 multi 2, x = -2 multi 1

40.

a)

2

b)

1

c)

4

d)

None

41.

How many zeros does the polynomial function
P(x) = 3x⁴+4x-8 have?

a)

1

b)

2

c)

3

d)

4

42.

a)

The function has an Odd degree

b)

The function has an Even degree

c)

The function has 5 real zeros

d)

The function has a Positive coefficient

43.

What is the degree?

a)

Positive

b)

Negative

c)

Odd

d)

Even

44.

What is the leading coefficient?

a)

Positive

b)

Negative

c)

Odd

d)

Even

45.

What is the leading coefficient?

a)

Positive

b)

Negative

c)

Odd

d)

Even

46.

Simplify the radical - 6√90

a)

10√8

b)

10√18

c)

18√10

d)

18√9

47.

Simplify:
(x²^/³)²^/⁵

a)

x⁴^/¹⁵

b)

b. x¹⁶^/¹⁵

c)

c. x⁶

d)

d. 6x

48.

Simplify

a)

2x²yz² ⁵√(xy³)

b)

2x²yz⁴ ⁵√(xy³)

c)

2xyz ⁵√(xy³z)

d)

2x²yz⁴ ⁵√(xy³z)

49.

Rewrite in Exponential Form.

a)

A

b)

B

c)

C

d)

D

50.

What is the RANGE of the function?

a)

All real numbers

b)

y ≤ 4

c)

y < 4

d)

0 ≤ y ≤ 4

51.

Which piecewise function corresponds to this graph? (Take your time)

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

52.

Find f(-2)

a)

-3

b)

6

c)

8

d)

-6

53.

f(x) = 9-3x
g(x) = 5x-7
Find f(x)+g(x).

a)

14x-10

b)

-8x+2

c)

2x+2

d)

2x-2

54.

f(x)=x²+1
g(x)=2x-5
Find f(x)-g(x)

a)

x²-2x+6

b)

-x²+2x+4

c)

-x²-2x-6

d)

x²-2x-4

55.

f(x)=2x + 4

g(x)=3x²- 1

Find f(x) ⋅ g(x)

a)

6x⁴+ 12x³- 4x²- 8x

b)

-6x³+ 12x²+ 2x - 4

c)

6x³+ 12x²- 2x - 4

d)

5x²- 18x + 20

56.

p(x) = 3x + 4
q(x) = 2x²
Find q(p(-2))

a)

8

b)

-8

c)

28

d)

None of these.

57.

When f(x) = x²- 9

and g(x) = x + 3 ,

find f(x) / g(x).

a)

x - 3

b)

x + 3

c)

x - 12

d)

x - 6

58.

Describe the transformation

a)

Left 4 units, up 1 unit

b)

Right 4 units, up 1 unit

c)

Left 4 units, down 1 unit

d)

Right 4 units, down 1 unit

59.

Describe the transformation.

a)

Left 1, Reflect over x-axis, up 2

b)

Left 1, Reflect over y-axis, down 2

c)

Right 1, Reflect over x-axis, up 2

d)

Right 1, Reflect over y-axis, uo 2

60.

a)

y ≤ 3

b)

x ≥ 2

c)

y ≥ 3

d)

x ≤ 2

61.

Graph the function $y=-\sqrt{x-3}\ +2$

a)

b)

c)

d)

62.

a)

x = 2

b)

x = 4

c)

x = 7

d)

x = 9

63.

Solve and check your solution(s).

a)

x = 2, 3

b)

x = -2, -3

c)

x = -1, -6

d)

No solution

64.

a)

A

b)

B

c)

C

d)

D

65.

Are the following inverses of each other?

a)

True

b)

False

66.

$g\left(x\right)=-7x^5+7$ Find the inverse of the function.

a)

$g^{-1}\left(x\right)=^5\sqrt{\frac{x-7}{7}}$

b)

$g^{-1}\left(x\right)=-^5\sqrt{\frac{x-7}{7}}$

c)

$g^{-1}\left(x\right)=^5\sqrt{-\frac{x-7}{7}}$

d)

$g^{-1}\left(x\right)=-^5\sqrt{\frac{x-7}{7}}$

67.

Find the inverse function

a)

b)

c)

d)

68.

Find f(2)

a)

f(2) = 0

b)

f(2) = 1

c)

f(2) = 3

d)

f(2) = 4

69.

A house painter charges $12 per hour for the first 40 hours he works, $18 for the ten hours after that, and $24 for all hours after that.

How much does he earn for a 70 hour week?

a)

$1020

b)

$1140

c)

$840

d)

He works for free!

70.

Graph

a)

b)

c)

d)

71.

How many solutions does the polynomial have?

a)

2

b)

3

c)

4

d)

5

72.

Solve: $4x^3-3x^2+16x-12=0$

a)

$x=\pm2,\ \frac{3}{4}$

b)

$x=\pm2i,\ \frac{3}{4}$

c)

$x=\pm4,\ \frac{4}{3}$

d)

$x=\pm i\sqrt{2},\ \frac{3}{4}$

73.

a)

A

b)

B

c)

C

d)

D

74.

f(x)= x²(x – 2)³(x – 7)

State the zeros, include multiplicity.

a)

0 (Mult of 2), 2 (Mult of 3), 7 (mult 1)

b)

2 (Mult of 3), 7 (mult 1)

c)

0, 2, 7

d)

2 (mult of 2), 7 (mult of 3)

75.

Write a polynomial function of least degree with integral coefficients that has the given zeros.

-1, 5, -3+2i

a)

x⁴+2x³-16x²-82x-69

b)

x⁴+7x³-16x²-82x-65

c)

x⁴+2x³-16x²-82x-65

d)

x⁴+2x³-16x²-82x-68

76.

Given f(x)= -3x+7 and g(x)=2x² - 8, find f(g(x)).

a)

f(g(x))= -6x²+31

b)

f(g(x))= -6x²+24

c)

f(g(x))=18x²-84x+6

d)

f(g(x))=9x²-42x-1

77.

Simplify
3√5 + √20 - √45

a)

3√-20

b)

2√-20

c)

3√5

d)

2√5

78.

Simplify the expression:

a)

$-15+8\sqrt{9}$

b)

9

c)

$2+8\sqrt{3}+6\sqrt{6}$

d)

$9+14\sqrt{3}$

79.

$\left(-2x\sqrt{7x}\right)\left(3\sqrt{28x^3}\right)$

a)

$-6x^2\sqrt{4x}$

b)

$12x^3\sqrt{14}$

c)

$-84x^3$

d)

$-78x^2\sqrt{x}$

80.

$\frac{\sqrt{10}}{\sqrt{3}+\sqrt{2}}$

a)

$\frac{\sqrt{30}\ +2\sqrt{5}}{5}$

b)

$\sqrt{30}+2\sqrt{5}$

c)

$\sqrt{30}-2\sqrt{5}$

d)

$\frac{\sqrt{30}+2\sqrt{5}}{6}$

Algebra 2 Honors Semester 1 Final Review

Total questions: 80

Worksheet time: 4hrs 51mins

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