Free Printable Algebra 2 Fall Semester Final Review

1.

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient

a)

Leading Coefficient Positive
Degree - Even

b)

Leading Coefficient Positive
Degree - Odd

c)

Leading Coefficient Negative
Degree - Even

d)

Leading Coefficient Negative
Degree - Odd

2.

Simplify the expression...

12÷4+12×(9−5)

a)

51

b)

60

c)

130

d)

39

3.

Evaluate if x=2 and y=3
$\left(x+y\right)^3\div5\left(2\right)-30\ \div x$

a)

5

b)

4

c)

-5

d)

-4

4.

Simplify $2^{3\ }+\ \frac{4}{2}\left(3\right)\ \div3$

a)

14/3

b)

7/3

c)

12

d)

10

5.

Solve for x:
2(3x + 4) + 2 = 4 + 3x

a)

2

b)

-2/3

c)

10

d)

-2

6.

Solve for b: $\frac{4b+8}{-2}=10$

a)

3

b)

-7

c)

7

d)

-3

7.

solve for x

a)

5

b)

-25

c)

15

d)

1/5

8.

Which line is being represented by the graph?

a)

y = 3/4 X -3

b)

y = -3/4x + 4

c)

y = 3/4x + 4

d)

y = -3/4 x - 3

9.

Find the slope of the line that passes through the points (2, 4) and (6, 12)

a)

1/2

b)

-1/2

c)

2

d)

-2

10.

Write a linear equation in slope-intercept form give the point and slope. (-6, -11); slope = 1/2

a)

$y+6=\frac{1}{2}\left(x+6\right)$

b)

$x-2y=16$

c)

$y=\frac{1}{2}x-8$

d)

$y=\frac{1}{2}x-11$

11.

What is the y-intercept in the equation
y= -2x + 5

a)

-2

b)

3

c)

5

d)

Cannot be Determined

12.

What is the correct equation in
Slope-Intercept Form?
(y = mx +b)

a)

x = 4

b)

y = 4

13.

What is the equation of the line that goes through the points (2, 9) and (3, 1) ?

a)

y= 8x - 5

b)

y= -8x + 25

c)

y= (1/8)x - 2

d)

y= (-1/8)x + 1

14.

What is an equation of line that is perpendicular to the line y = -3x + 5?

a)

$y\ =\ -3x\ +\ 7$

b)

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

c)

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

15.

Name the x- and y-intercepts for the equation:
5x - 3y = 15

a)

(3, 0) and (0, -5)

b)

(0, 3) and (-5, 0)

c)

(5, 15) and (15, 3)

d)

(0, -3) and (5, 0)

16.

The Maplewood Symphony Orchestra sold 146 tickets and collected a total of $1036 in ticket sales. Admission was $5 for children and $8 for adults. Write two equations that would be used to solve the system.

a)

c+a=146

5c+8a=1036

b)

c-a=146

8c+5a=1036

c)

c+a=1036

8c+5a=146

d)

c+a=146

5c-8a=1026

17.

Tania had 35 coins in pennies and nickels. She had $1.03. Which system of equations could be used to determine the number of coins she has?

a)

.01p + .05n = 35

p + n = 103

b)

1p + 5n = 1.03

p + n = 35

c)

.01p + .05n = 1.03

p + n = 35

d)

.05p + .01n = 1.03

p + n = 35

18.

How many solutions does this system have?

a)

One

b)

None

c)

Infinite

19.

What is the solution to this system?

a)

(1, -2)

b)

No Solutions

c)

Infinite Solutions

d)

(0, -3)

20.

Find the solution:
2x-5y=15
3x+y=31

a)

(10,1)

b)

(13, -8)

c)

(-10,-7)

d)

No Solution

21.

Describe the transformation that is applied to the parent function.
f(x) = 3 Ix+8I

a)

Stretches by 3, Shifts left 8

b)

Stretches by 3, Shifts right 8

c)

Stretches by 3, Shifts up 8

d)

Stretches by 3, Shifts down 8

22.

What is the equation to this graph?

a)

f(x)= Ix+2I +1

b)

f(x)= Ix-2I +1

c)

f(x)= Ix+2I -1

d)

f(x)= Ix-2I -1

23.

Which parent function matches the graph?

a)

y = |x|

b)

y = x

c)

y = x²

24.

Describe the transformation

a)

left 2 up 5

b)

right 2 up 5

c)

left 2 down 5

d)

right 2 down 5

25.

Which equation below is a quadratic function translated left 4 units?

a)

y = x² + 4

b)

y = (x + 4)²

c)

y = (x - 4)²

d)

y = 4x²

26.

Describe the transformation of the equation below from the absolute value parent function
$y=-2\left|x-3\right|+3$

a)

reflected over x axis, stretched by 2, right 3, up 3

b)

reflected over x axis, stretched by 2, left 3 up 3.

c)

reflected over x axis, shrunk by 2, right 3, up 3

d)

reflected over the x axis, shrunk by 2, left 3, up 3

27.

What type of function is shown?

a)

absolute value

b)

quadratic

c)

linear

d)

exponential

28.

Is this a max or min?

a)

max

b)

min

c)

cannot be determined

29.

What is a parabola?

a)

The straight graph of a quadratic function

b)

The circular graph of a quadratic function

c)

The V-shaped graph of a quadratic function

d)

The U-shaped graph of a quadratic function

30.

Using the graph of the quadratic function, identify the y-intercept.

a)

(4, -6)

b)

(0, 2)

c)

(.5, 0)

d)

(7.5, 0)

31.

Using the graph of the quadratic function, identify the range.

a)

y < -6

b)

-2 < x < 10

c)

-∞ < x < ∞

d)

-6 ≤ y < ∞

32.

Which of the following graphs appropriately marks the axis of symmetry?

a)

b)

c)

d)

33.

What is the vertex of the parabola: y=2(x-3)²+4

a)

(3,4)

b)

(-3,4)

c)

(3, -4)

d)

(-3,-4)

34.

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

a)

(-2, 16)

b)

(2, 0)

c)

(2, 4)

d)

(-2, 4)

35.

What are the x-intercept(s) of the function
g(x) = -9(x-3)(x+2)?

a)

(3,0) and (-2,0)

b)

(-3,0) and (2,0)

c)

(3,-2)

d)

(-9,0), (3,0), and (-2,0)

36.

Use the graph to determine the solutions.
*Hint: Solutions = roots = zeros = x-intercepts

a)

-1 and -3

b)

1 and -3

c)

1 and 3

d)

-1 and 3

37.

Determine the domain and range of the function below.

$y=-2\left|x\right|+5$

a)

Domain: x > 0

Range: y > 5

b)

Domain: all real numbers

Range: y < 5

c)

Domain: all real numbers

Range: y > -2

d)

Domain: x < -2

Range: y < 5

38.

Determine the interval in which this function is DECREASING.

a)

(-3, ∞)

b)

(-3, ∞)

c)

(-∞, -4)

d)

(-∞, -3)

39.

As X → ∞, f(x) →______?

a)

∞

b)

-∞

c)

Neither

d)

Both ∞ & -∞

40.

The height of a water balloon that is launched into the air is given by h(t) = -5x²+20x+25. When will the balloon explode on the ground?

a)

5 seconds

b)

1 second

c)

2 seconds

d)

3 seconds

41.

A dolphin jumps from the water at at initial velocity of 16 feet per second. The equation h = -8t² + 16t models the dolphin's height at any given time, t. What is the maximum height the dolphin jumps?

a)

1 foot

b)

5 feet

c)

7 feet

d)

8 feet

e)

12 feet

42.

Your nephew is standing on his deck, which is 4 feet off the ground. He tosses his toy up into the air. The equation

h = -2t²+ 7t + 4 models the toy's height, h, from the ground at t seconds after he threw it. How high is the toy after 1 second?

a)

2

b)

4

c)

9

d)

10

e)

15

43.

(3 + 2i) + (4 - 5i)

a)

7 + 7i

b)

1 - 3i

c)

1 - 7i

d)

7 - 3i

44.

(3i)(-2+4i)

a)

-6+12i

b)

-12-6i

c)

-2+7i

d)

12+6i

45.

Simplify $\frac{5}{-1-9i}$

a)

$\frac{-2+18i}{41}$

b)

$\frac{-5+45i}{82}$

c)

$\frac{-5+45i}{86}$

d)

$\frac{-2+9i}{17}$

46.

(3 + 8i)(-2 - i)

a)

2-19i

b)

23-i

c)

34+5i

d)

23-i

47.

i^{26}

a)

1

b)

-1

c)

$i$

d)

$-i$

48.

Simplify:

\left(4i^6\right)\left(-3i\right)^2

Hint: Use the POWER rule, then the PRODUCT rule for your laws of exponents! Then simplify your powers of i

a)

-12

b)

12

c)

-36

d)

36

49.

Simplify √-28

a)

-√28

b)

-2i√7

c)

2i√7

d)

28i

50.

$\sqrt{48}$

a)

4√2

b)

6√3

c)

4√3

d)

4√2

51.

Solve the Following Quadratic Equations

2x^2+5x-12=0

?

a)

$\left\{4,\ -7\right\}$

b)

$\left\{-2,\ 14\right\}$

c)

$\left\{-4,\ \frac{3}{2}\right\}$

d)

$\left\{-25,\ 28\right\}$

52.

$x^2-2x-15=0$

Solve by factoring

a)

x=5,-3

b)

x=-5,3

c)

x=5,3

d)

x=-5,-3

53.

$16x^2-4x=0$

Solve with any method

a)

$x=\pm\frac{1}{4}$

b)

$x=0,\ 4$

c)

$x=\frac{1}{4},\ 0$

d)

$x=-\frac{1}{4},\ 0$

54.

If the discriminant is negative, you will have....

a)

two real solutions

b)

two irrational solutions

c)

two imaginary solutions

d)

one solution

55.

Use the Quadratic Formula to solve $3x^2=-5-10x$

a)

$x=3,\ x=5$

b)

$x=\frac{-10+\sqrt{10}}{6},\ \ x=\frac{-10-\sqrt{10}}{6}$

c)

$x=\frac{-5+\sqrt{5}}{3},\ \ x=\frac{-5-\sqrt{5}}{3}$

d)

$x=\frac{-10+\sqrt{40}}{6},\ \ x=\frac{-10-\sqrt{40}}{6}$

e)

No Solution

56.

$x^2-6x+4=0$

a)

$3\pm\sqrt{5}$

b)

$\frac{6\pm\sqrt{20}}{2}$

c)

$3\pm\sqrt{20}$

d)

$3\pm i\sqrt{13}$

57.

Simplify. Express using exponents. $\left(2h^7\right)\left(7h^{ }\right)$

a)

$14h^7$

b)

$14h^8$

c)

$14h^6$

58.

Simplify. Express using exponents. $\frac{12n^5}{4n^2}$

a)

$8n^3$

b)

$3n^3$

c)

$3n^7$

59.

1.) Simplify
(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

60.

a)

2a²b⁶

b)

$\frac{1}{2a^2b^6}$

c)

$\frac{b^6}{2a^2}$

d)

$\frac{2b^6}{a^2}$

61.

(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

62.

The binomial 3x² - 4 has degree...

a)

1

b)

2

c)

3

d)

4

63.

This polynomial: 3x²- 4x⁴ + 7x³ - 1 + 5x ,written in standard form would be

a)

3x²- 4x⁴ + 7x³ - 1 + 5x

b)

- 4x⁴ + 7x³ + 3x²+ 5x - 1

c)

- 1 + 5x + 3x²+ 7x³- 4x⁴

d)

7x³+ 5x- 4x⁴+ 3x² - 1

64.

What is the degree of this polynomial? 7x - 4x⁵ + 3x⁴ - 6x²

a)

1

b)

2

c)

4

d)

5

65.

Simplify (-4m³-m+9)-(4m²+m-12)

a)

-4m³-4m²-2m-21

b)

-4m³-4m²-2m+21

c)

-8m³-2m+21

d)

-4m³+4m²+2m+21

66.

Classify this polynomial by its degree and number of terms: x³ + 2x + 6

a)

Cubic polynomial

b)

Quadratic binomial

c)

Quadratic trinomial

d)

Cubic trinomial

67.

The multiplicity at x=2 is odd.

a)

TRUE

b)

FALSE

68.

What is the equation in factored form of this graph?

a)

f(x) = (x-4)(x-1)²(x+2)(x+4)

b)

f(x) = (x-4)(x+1)²(x+2)(x+4)

c)

f(x) = (x-4)(x-1)²(x-2)(x+4)

d)

f(x) = (x+4)(x+1)²(x-2)(x-4)

69.

What are the roots of the polynomial function?
y = (x + 2)(x - 7)³

a)

-2, 7 multiplicity 3

b)

-2, 7, 3

c)

2, -7 multiplicity 3

d)

2, -7, 3

70.

Solve $4x^4+12x^3+9x^2=0$

a)

$\left\{-\frac{3}{2},\ \frac{3}{2}\right\}$

b)

$\left\{0,-\frac{3}{2},\ \frac{3}{2}\right\}$

c)

$\left\{0,-\frac{3}{2}\right\}$

d)

$\left\{0,\ \frac{3}{2}\right\}$

71.

Find the zeros of the function

$f\left(x\right)=x^3+2x^2-9x-18$

a)

$\left\{-3,\ 2,\ 3\right\}$

b)

$\left\{-3,\ -2,\ 3\right\}$

c)

$\left\{-3,2\right\}$

d)

$\left\{-2,\ 3\right\}$

72.

Factor this difference of cubes:
x³ - 343

a)

(x + 7) (x² - 7x + 49)

b)

(x² + 1) (x - 343)

c)

(x - 7) (x² + 7x + 49)

d)

(x² - 343) (x + 1)

73.

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

a)

1

b)

2

c)

3

d)

4

74.

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

75.

(2x³ - 5x - 7) ÷ (x - 2)

a)

2x³ - 4x² + 3x - 13

b)

2x³ + 4x² +3x - 1

c)

2x² - 4x + 3 - 13/x-2

d)

2x² + 4x + 3 - 1/x-2

Algebra 2 Fall Semester Final Review

Total questions: 75

Worksheet time: 3hrs 26mins

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