Free Printable Fall Semester Review

1.

What is the degree of this equation? 5x + 4x² + 3x³ - 5x

a)

1

b)

2

c)

3

d)

4

2.

Based on the graph of the polynomial function, what can you determine about the degree?

a)

negative

b)

odd

c)

positive

d)

even

3.

Based on the graph of the polynomial function, what can you determine about the leading coefficient?

a)

positive

b)

negative

c)

even

d)

even

4.

What would you put to complete the end behavior statement below using the polynomial funciton shown?

$As\ \ x\rightarrow\infty,\ \ f\left(x\right)\rightarrow_{ }$ ___

a)

$\infty$

b)

$-\infty$

c)

2

d)

-2

5.

Based on the graph of the polynomial function, what can you determine about the degree?

a)

positive

b)

odd

c)

negative

d)

even

6.

Based on the graph of the polynomial function, what can you determine about the leading coefficient?

a)

positive

b)

odd

c)

even

d)

positive

7.

What possible degree is the polynomial shown?

a)

2

b)

4

c)

3

d)

5

8.

Which lists the correct end behavior statements for the polynomial funciton shown?

a)

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

b)

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

c)

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

d)

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

9.

Which end behavior statements match the polynomial shown?

a)

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

b)

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

c)

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

d)

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

10.

What possible degree does the polynomial function shown have?

a)

4

b)

3

c)

5

d)

6

11.

Based on the graph shown, what can you determine about the leading coefficient of the polynomial?

a)

even

b)

odd

c)

positive

d)

negative

12.

Identify the domain of the function.

a)

$\left[-2,3\right]$

b)

$\left(-2,3\right)$

c)

$\left[-5,5\right]$

d)

$\left(-5,5\right)$

13.

Identify the domain of the function.

a)

$\left[-1,3\right]$

b)

$\left(-1,3\right]$

c)

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

d)

$\left[-1,3\right)$

14.

Describe the function between $x=-2$ and $x=2$ .

a)

Increasing

b)

Decreasing

c)

Constant

15.

Identify the range of the function.

a)

$\left[-5,3\right)$

b)

$\left[-5,4\right)$

c)

$\left[-5,4\right]$

d)

$\left(-5,4\right)$

16.

Identify the minimum of the function.

a)

$y=-5$

b)

$y=0$

c)

$y=3$

d)

$y=4$

17.

Identify the maximum of the function.

a)

$y=-5$

b)

$y=0$

c)

$y=3$

d)

$y=4$

18.

Where is the root?

a)

(6, 0)

b)

(0, 6)

c)

(-3, 0)

d)

(0, -3)

19.

What are the zeros?

a)

0 and 2

b)

-4 and 0

c)

2 and 3

d)

0 and 4

20.

On what interval is the graph decreasing?

a)

∞ < x < 3

b)

3 < x < -∞

c)

3 < x < ∞

d)

-∞ < x < 3

21.

What is the vertex?

a)

(-3, 0)

b)

(3, 0)

c)

(0, 18)

d)

(18, 0)

22.

Where is the function positive?

a)

$0<x<4$

b)

$at\ the\ vertex\ \left(2,4\right)$

c)

$y\le4$

d)

$-\infty<x<\infty$

23.

What is the domain of the function?

a)

(-∞,5]

b)

(-∞,5)

c)

(-∞,2]

d)

(-∞,2)

24.

What is the range of the function?

a)

(-∞,5]

b)

(-∞,5)

c)

(-∞,2]

d)

(-∞,2)

25.

Where is the function positive and where is it negative?

a)

positive (1,∞) and negative (-∞,1)

b)

positive (0,∞) and negative (-∞,-1)

c)

positive (-∞,∞) and negative nowhere

d)

positive (∞,1) and negative (1,-∞)

26.

Where is the function increasing and decreasing?

a)

increasing (-∞,∞) and decreasing nowhere

b)

increasing nowhere and decreasing (-∞,∞)

c)

increasing (1,∞) and decreasing (-∞,1)

d)

increasing (-1,∞) and decreasing (-∞,-1)

27.

y = 6x - 11

-2x - 3y = -7

(a)

28.

-4x + y = 6

-5x - y = 21

(a)

29.

-2x + 6y = 6

-7x + 8y = -5

(a)

30.

How many solutions will this system have?

a)

No solution

b)

One Solution

c)

I Don't Know

d)

Infinitely Many Solutions

31.

^{What is the solution?}

a)

1

b)

-2

c)

(1, 2)

d)

(1, -1)

32.

For $y=x^2-2x+3$ and $y=x+1$ , what are the points of intersection?

a)

$x=5$ and $x=-3$

b)

$x=2$ and $x=1$

c)

(0, 0) and (4, 2)

d)

(1, 1) and (5, 5)

33.

What shape does the graph of a quadratic equation form?

a)

Circle

b)

Line

c)

Parabola

d)

Ellipse

34.

What values of x and y make the equation true?

a)

x = 5

y = -2

b)

x = 3

y = -5

c)

x = 9

y = 10

d)

x = 16

y = -5

35.

Given these matrices find A + B

a)

b)

c)

d)

36.

Given these matrices find B - A

a)

b)

c)

d)

37.

What is the inverse of this matrix?

a)

_{(1/25) (-4/25)}
_{(3/25) (13/25)}

b)

_{(1/5) (-4/5)}
_{(3/5) (13/5)}

c)

_{(6/25) (-2/25)}
_{(2/25) (9/25)}

d)

_{(1/150) (-4/150)}
_{(3/150) (13/150)}

38.

find: B*A

a)

47 30
9 5

b)

17 15
42 35

c)

10 25
7 1

d)

not possible because rows do not match columns

39.

Find the product.

a)

undefined

b)

-3 16
17 12
8 -10

c)

3 12
-15 -8
-1 -3

40.

What is the determinant of this matrix?

a)

5

b)

25

c)

-25

d)

1

41.

Determine the axis of symmetry for the following function.

a)

x=2

b)

x=3

c)

x= -2

d)

x= -3

42.

What is the vertex of the following function? Is it a maximum or a minimum?

a)

Minimum

(-2,-1)

b)

Maximum

(-2,-1)

c)

Minimum

(-1,-2)

d)

Maximum

(-1,-2)

43.

Solve the following quadratic equation...

x² + 3x + 2 = 0

a)

x = -1

x = -2

b)

x = 1

x = 2

c)

x = -1

x = 2

d)

x = 1

x = -2

44.

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.

45.

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.

46.

Solve Using the Quadratic Formula
x² + 4x - 40 = -8

a)

-10 & -4

b)

-4 & 10

c)

-8 & 4

d)

8 & -4

47.

Solve by taking the square root: (x - 2) ² = 49

a)

9 or -5

b)

± 9

c)

± 5

d)

± 7

48.

Find the missing value "c" to create a perfect square trinomial:
x² – 8x + ___

a)

-4

b)

16

c)

4

d)

8

49.

Complete the square.
x² + 14x + ____

a)

x² + 14x - 196

b)

x² + 14x + 49

c)

x² + 14x - 49

d)

x² + 14x + 196

50.

Solve by Factoring: 4x² + 11x - 3 = 0

a)

x = -3/4 and x = -1

b)

x = 4 and x = 3

c)

x = 1/4 and x = -3

d)

x = -1/4 and x = 3

51.

Solve x⁴ - 256 = 0

a)

x = 4, x = - 4

b)

x = 4, x = 4i

c)

x = 4, x -4, x = 4i

d)

x = 4, x -4, x = 4i, x = -4i

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.

a)

x+7

b)

x+2

c)

X-10

d)

X-7

54.

Divide: $\frac{6x^2+7x-20}{2x+5}$

a)

$6x^2-8x$

b)

$6x-8$

c)

$3x-4$

d)

$3x^2-4x$

55.

Divide: $\frac{5x^3-x^2+6}{x-4}$

a)

$5x^2-21x+84-\frac{330}{x-4}$

b)

$5x^2+19x+82$

c)

$5x^2+19x+76+\frac{310}{x-4}$

d)

$5x^2+19x+\frac{82}{x-4}$

56.

Divide: $\frac{2x^3-9x^2+15}{2x-5}$

a)

$2x^2-4x-10-\frac{10}{2x-5}$

b)

$x^2-2x-5-\frac{10}{2x-5}$

c)

$x^2-2x-5-\frac{5}{2x-5}$

d)

$2x^2-4x+5$

57.

Divide: $\frac{9x^3+12x^2+15x+4}{3x+1}$

a)

$9x^2+9x+12-\frac{8}{3x+1}$

b)

$3x^2+3x+12-\frac{8}{3x+1}$

c)

$9x^2+9x+12$

d)

$3x^2+3x+4$

Fall Semester Review - AdvAlg2

Total questions: 57

Worksheet time: 5hrs 45mins

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