Free Printable Algebra II Semester I Review

1.

$f\left(x\right)=5x^2+2$

a)

Stretch of 5

Up 2

b)

Shrink of 5

Up 2

c)

Stretch of 5

Down 2

d)

Shrink of 5

Down 2

2.

Does this parabola have a minimum or maximum and what is its value?

a)

minimum: 2

b)

maximum: 2

c)

minimum: 5

d)

maximum: 5

3.

Find the vertex of
$f\left(x\right)=-x^2-4x+12$

a)

$\left(-2,\ 16\right)$

b)

$\left(2,\ 0\right)$

c)

$\left(2,\ 4\right)$

d)

$\left(-2,\ 4\right)$

4.

Does the following quadratic equation have a maximum or minimum value? How can you tell?
$f\left(x\right)=x^2+2x-3$

a)

Minimum value, because the a value is positive

b)

Maximum value, because the b value is positive

c)

Maximum value, because the a value is positive

d)

Minimum value, because the c value is negative

5.

Has at most 3 roots

a)

$f\left(x\right)=x^3$

b)

$f\left(x\right)=\sqrt{x}$

c)

$f\left(x\right)=x$

d)

$f\left(x\right)=x^2$

6.

Which standard form function matches the factored form:
$f\left(x\right)=\left(x+1\right)\left(x-1\right)\left(x+4\right)$

a)

$f\left(x\right)=x^3-x^2-4x$

b)

$f\left(x\right)=x^3+4x^2-x-4$

c)

$f\left(x\right)=x^3-4x^2+x+4$

d)

$f\left(x\right)=x^3+x^2-x-4$

7.

$i^{13}$

a)

$-1$

b)

$1$

c)

$i$

d)

$-i$

8.

What is $i^{129}$ ?

a)

$-i$

b)

$i$

c)

$1$

d)

$-1$

9.

What is the vertex of the quadratic function: $f\left(x\right)=\frac{1}{2}\left(x-3\right)^2+8$

a)

$\left(3,\ 8\right)$

b)

$\left(-3,\ -8\right)$

c)

$\left(-3,\ 8\right)$

d)

$\left(3,\ -8\right)$

10.

Factor:
$k^2+7k+10$

a)

$\left(k+2\right)\left(k+5\right)$

b)

$\left(k-2\right)\left(k-5\right)$

c)

$\left(k+10\right)\left(k+4\right)$

d)

$\left(k+2\right)\left(k-5\right)$

11.

Factor:
$5n^3-10n^2+3n-6$

a)

$\left(5n^2+3\right)\left(n-2\right)$

b)

$\left(5n^2-3\right)\left(n-2\right)$

c)

$\left(5n^3+3\right)\left(n-2\right)$

d)

$10n\left(n^2-6\right)$

12.

Solve:
$a^2+2a-24=0$

a)

$a=6,\ a=-4$

b)

$a=-6,\ a=4$

c)

$a=12,\ a=-2$

d)

$a=8,\ a=-3$

13.

Solve:
$7x^2-28x=0$

a)

$x=4,\ x=7$

b)

$x=0,\ x=4$

c)

$x=0,\ x=-4$

d)

$x=-4,\ x=-7$

14.

What is the following called?
$b^2-4ac$

a)

Axis of symmetry

b)

Quadratic Formula

c)

Vertex

d)

Discriminant

15.

Solve:
$2x^2+7x-15=0$

a)

$x=-1.5,\ x=5$

b)

No Solution

c)

$x=-5,\ x=1.5$

d)

$x=0.7,\ x=5$

16.

Write in standard form:
$\left(x-7\right)\left(2x+8\right)$

a)

$2x^2-7x-55$

b)

$2x^2-6x-56$

c)

$2x^2-12x-56$

17.

a)

$f\left(x\right)=x^3$

b)

$g\left(x\right)=x^2$

c)

$h\left(x\right)=2^x$

d)

$k\left(x\right)=x$

18.

What function family do I belong to?

a)

Linear

b)

Quadratic

c)

Exponential

d)

LInear Absolute Value

19.

What is this logo?

a)

Starbucks

b)

Starz

c)

Encore

d)

Target

20.

What is this logo? (Look at the letters it makes!)

a)

Sony

b)

Microsoft

c)

Playstation

d)

Xbox

21.

What is the equation for the axis of symmetry?

a)

$y=3$

b)

$x=3$

c)

$x=5$

d)

$y=1$

22.

Find the y-intercept of
$f\left(x\right)=2x^2-2x+1$

a)

$\left(0,\ 2\right)$

b)

$\left(0,\ -2\right)$

c)

$\left(0,\ 1\right)$

d)

$\left(0,\ -1\right)$

23.

Does $f\left(x\right)=-4x^2$ have a minimum or maximum value?

a)

maximum

b)

minimum

24.

Which of the following is the correct equation for the given graph?

a)

$f\left(x\right)=\left(x-2\right)^2-1$

b)

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

c)

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

d)

$f\left(x\right)=-\left(x-2\right)^2-1$

25.

What is the formula to find the vertex of a quadratic function?

a)

$x=\frac{-b}{2}$

b)

$x=-b$

c)

$x=\frac{-b}{2a}$

26.

The axis of symmetry line passes through which point?

a)

y-intercept

b)

any random point

c)

vertex

d)

none of these

27.

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

a)

$\left(-1,\ 4\right)$ ; opens up

b)

$\left(-1,\ 4\right)$ ; opens down

c)

$\left(1,\ 4\right)$ ; opens up

d)

$\left(1,\ 4\right)$ ; opens down

28.

What is another name for the x-intercepts of a quadratic?

a)

y-intercepts

b)

zeros

c)

x-axis

d)

none of these

29.

Number of solutions? Using the discriminant.

a)

0

b)

1

c)

2

30.

Determine the types of solutions for the given quadratic:
$2x^2+12x=-18$

a)

2 real

b)

2 real--double

c)

2 imaginary

31.

Calculate:
$\left(4-7i\right)-\left(-3+6i\right)$

a)

$7-13i$

b)

$7-i$

c)

$1-13i$

d)

$1-i$

32.

Calculate:
$\left(1-2i\right)+\left(-4+2i\right)$

a)

$-3$

b)

$-3-4i$

c)

$5-4i$

d)

$5$

33.

Calculate:
$-4\left(13+5i\right)$

a)

$-52-20i$

b)

$9+i$

c)

$17-20i$

d)

$-52+20i$

34.

Calculate:
$\left(4+3i\right)\left(4-3i\right)$

a)

$16-9i^2$

b)

$25$

c)

$7$

d)

$8-6i$

35.

Simplify: $\sqrt{-64}$

a)

$-8$

b)

$8i$

c)

$-8i$

d)

$8$

36.

What is the degree of this polynomial function? Is the leading coefficient positive or negative?

a)

A quartic polynomial with a negative leading coefficient.

b)

A quartic polynomial with a positive leading coefficient.

c)

A cubic polynomial with a negative leading coefficient.

d)

A cubic polynomial with a positive leading coefficient.

37.

Factor completely:
$3x^2+18x+15$

a)

$3\left(x^2+6x+5\right)$

b)

$\left(x+5\right)\left(x+1\right)$

c)

$3\left(x+5\right)\left(x+1\right)$

d)

Prime

38.

Perform the indicated operation:
$\left(3-2x+2x^2\right)-\left(4x-5+3x^2\right)$

a)

$x^2+6x+8$

b)

$2x^2+5x-7$

c)

$-x^2-6x+8$

d)

$-2x^2+11x-4$

39.

What is the y-value of the relative maximum?

a)

4

b)

2

c)

1

d)

-1

40.

How many roots or zeros does the equation
$f\left(x\right)=5x^4-8x^3+4x^2-6x+3$ have?

a)

3

b)

4

c)

5

d)

0

41.

What is the end behavior for the function
$f\left(x\right)=-3x^5+4x^4+2x^3-8x+1$

a)

$x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$
$x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

b)

$x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$
$x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

c)

$x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$
$x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$

d)

$x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$
$x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$

42.

What is the degree of the function graphed here?

a)

2

b)

3

c)

4

d)

5

43.

Classify the function:

a)

quadratic

b)

cubic

c)

quartic

d)

linear

44.

What room is Ms. Webb in?

a)

D303

b)

D3

c)

D324

d)

No Where

45.

What is Ms. Webb's first name?

a)

Amanda

b)

Jennifer

c)

Elizabeth

d)

Lisa

46.

Which transformation transforms the graph of $f\left(x\right)=x^2$ to the graph of $g\left(x\right)=\left(x+4\right)^2$

a)

a vertical translation 4 units up

b)

a vertical translation 4 units down

c)

a horizontal translation 4 units to the left

d)

a horizontal translation 4 units to the right

47.

How do we transform from $f\left(x\right)=x^2$ to $g\left(x\right)=-3x^2$

a)

reflection in x-axis and vertical shift down

b)

reflection x-axis and vertical stretch

c)

horizontal stretch

d)

reflection x-axis and vertical compression

48.

What is the vertical shift of this equation: $f\left(x\right)=-\left(x+3\right)^2-5$

a)

left 5

b)

right 5

c)

up 5

d)

down 5

49.

If the blue graph is $f\left(x\right)=x^2$
then the red must be...

a)

$g\left(x\right)=x^2-5$

b)

$g\left(x\right)=x^2+5$

c)

$g\left(x\right)=\left(x-5\right)^2$

d)

$g\left(x\right)=\left(x+5\right)^2$

50.

What transformations occurred to get $f\left(x\right)$ , the red graph, to become $g\left(x\right)$ , the blue graph?

a)

horizontal shift down and vertical shift left

b)

horizontal shift left and vertical shift down

c)

horizontal shift right and vertical shift up

d)

horizontal shift up and vertical shift right

51.

Factor:

$8x^3-20x^2+18x-45$

a)

$\left(2x-3\right)\left(2x+3\right)\left(2x+5\right)$

b)

$\left(2x+3\right)2\left(2x-5\right)$

c)

$\left(4x^2+9\right)\left(2x-5\right)$

d)

$\left(4x^2+9\right)\left(2x+5\right)$

52.

Factor:

$4x^4-81$

a)

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

b)

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

c)

$\left(2x^2-9\right)\left(2x^2+9\right)$

d)

$\left(2x^2-9\right)2$

53.

Factor:

$x^4+5x^2-6$

a)

$\left(x^2+6\right)\left(x-1\right)\left(x+1\right)$

b)

$\left(x^2-6\right)\left(x^2+1\right)$

c)

$\left(x^2-5\right)\left(x-1\right)\left(x+1\right)$

d)

$\left(x^2+6\right)\left(x-1\right)2$

54.

Factor:

$3x^4-11x^2+10$

a)

$\left(3x^2-5\right)\left(x^2-2\right)$

b)

$\left(3x^2-2\right)\left(x^2-5\right)$

c)

$\left(x^2-6\right)\left(x^2-5\right)$

d)

$3\left(x^2-6\right)\left(x^2-5\right)$

55.

Solve:

$x^3+3x^2-16x-48=0$

a)

$x=4,\ x=3$

b)

$x=4,\ x=-3$

c)

$x=\pm4,\ x=3$

d)

$x=\pm4,\ x=-3$

56.

Solve: $x^4-x^2-56=0$

a)

$x=\pm2i\sqrt{2},\ x=\pm\sqrt{7}$

b)

$x=\pm2\sqrt{2},\ x=\pm\sqrt{7}$

c)

$x=\pm3,\ x=\pm i\sqrt{7}$

d)

$x=\pm3i,\ x=\pm\sqrt{7}$

57.

How many tests did you take Semester I?

a)

3

b)

4

c)

5

d)

6

58.

When is your Period 5 Final Exam?

a)

12/18

b)

12/19

c)

12/20

59.

When is your Period 3 Final Exam

a)

12/18

b)

12/19

c)

12/20

60.

Mathematics is the Best, Most Fantabulous Class!!!!!

a)

True

b)

False

Algebra II Semester I Review

Total questions: 60

Worksheet time: 5hrs 10mins

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