Free Printable Honors Algebra II Fall Final Review

1.

What is the equation of the graph below?

a)

f(x) = I x + 2 I

b)

f(x) = I x + 2 I +2

c)

f(x) = I x - 2 I +2

d)

f(x) = I x - 2 I

2.

What is the equation of the graph below?

a)

f(x) = I x I + 1

b)

f(x) = I x I - 1

c)

f(x) = -I x I + 1

d)

f(x) = -I x I - 1

3.

Describe the transformations of Function

from Parent Function

$g\left(x\right)=\sqrt[]{x+4}-6$

a)

Shift Left 4

and

Shift Down 6

b)

Shift Left 4

and

Shift Up 6

c)

Shift Right 4

and

Shift Down 6

d)

Shift Up 4

and

Shift Left 6

4.

State the transformations of the function from the Parent Function

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

a)

Shift Left 2

and

Shift Down 3

b)

Shift Right 2

and

Shift Up 3

c)

Shift Right 2

and

Shift Down 3

d)

Shift Left 2

and

Shift Up 3

5.

Describe the transformation of

the function from its Parent Function

$g\left(x\right)=2\left|x-7\right|-3$

a)

Vertical Stretch by 2, Shift Right 3 and Shift Down 7

b)

Vertical Stretch by 2, Shift Right 7 and Shift Down 3

c)

Vertical Stretch by 2, Shift Left 7 and Shift Down 3

d)

Horizontal Stretch by 2, Shift Right 7 and Shift Down 3

6.

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation

s(t) = –16t² + 64t + 80

What will be the object's maximum height?

a)

2 ft

b)

80 ft

c)

144 ft

d)

64 ft

7.

You jump off a 24 foot high cliff and your fall is modeled by the function:

h(t) = -16t² + 8t + 24

How long would it take you to hit the water?

a)

8 seconds

b)

1 second

c)

1.5 seconds

d)

1/4 second

8.

The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function:

p= -15x² +600x +60

What is the maximum profit you can make from selling tickets?

a)

$6060

b)

$20

c)

$600

d)

$10,250

9.

Heather dropped a water balloon over the side of her school building from a height of 80 feet. The approximate height of the balloon at any point during its fall can be represented by the following quadratic equation:

h = -16t² + 80

About how long did it take for the balloon to hit the ground?

a)

1.73 seconds

b)

2.24 seconds

c)

2.45 seconds

d)

2.83 seconds

10.

A ball is thrown into the air with an upward velocity of 40ft/s. Its height h in feet after t seconds is given by the function :

h(t) = -16t² + 40t + 10

How many seconds does it take the ball to reach its maximum height?

a)

1.25 seconds

b)

1.4 seconds

c)

2.5 seconds

d)

2 seconds

11.

What are the factors of
25x² - 81?

a)

(5x - 9)(5x + 9)

b)

(5x - 9)(5x - 9)

c)

(5x + 9)(5x + 9)

d)

Cannot be factored

12.

Factor 4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

13.

Factor completely:
3x² + 5x - 12

a)

(3x + 4)(x-3)

b)

(3x - 4)(x + 3)

c)

(3x + 3)(x -4)

d)

(3x - 3)(x + 4)

14.

Factor:
p² - 14p

a)

p(1 - 14)

b)

2p(p - 7)

c)

p²(1-14)

d)

p(p - 14)

15.

x²- 16

a)

Prime

b)

( x - 4) ( x + 4)

c)

( x - 8) ( x + 8)

d)

( x - 4) ( x - 4)

16.

The degree and the sign of the leading coefficient (positive or negative) of a polynomial determines the behavior of the ends for the graph.

Determine the end behavior of this equation.

f(x) = -x⁵ - 4x +2

a)

As x goes to negative infinity, y goes to positive infinity. As x goes to positive infinity, y goes to positive infinity.

b)

As x goes to negative infinity, y goes to positive infinity. As x goes to positive infinity, y goes to negative infinity.

c)

As x goes to negative infinity, y goes to negative infinity. As x goes to positive infinity, y goes to positive infinity.

d)

As x goes to negative infinity, y goes to negative infinity. As x goes to positive infinity, y goes to negative infinity.

17.

What are the zeros of the graph?

a)

-4, -1, 2, 1 multiplicity 2

b)

-4, -1, 1, 2

c)

4, 1, -2, -1 multiplicity 2

d)

4, 1, -1, -2

18.

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

19.

What is the degree of the following graph?

a)

3

b)

4

c)

5

d)

6

20.

Factor completely:
2x³+ 5x² - 8x - 20

a)

(x² - 4)(2x + 5)

b)

(2x - 5)(x² + 4)

c)

(2x² - 4)(x + 5)

d)

(x - 2)(x + 2)(2x + 5)

21.

Find all zeros for the polynomial
P(x) = x³ -3x²-5x+15

a)

3, √5

b)

3, √5, -√5

c)

-3, √5, -√5

d)

-3, 5i, -5i

22.

FInd all zeros for the polynomial
f(x) = x⁴+8x²-9

a)

-1, ⅓, ±3i

b)

½, -1, ±3i

c)

1, -1, ±i√11

d)

1, -1, ±3i

23.

x²+ 12x + 32 = 0

a)

x = -4, 8

b)

x = 4, 8

c)

x = -4, -8

d)

x = 0, 12

24.

Find the root(s) of the function.

a)

x = 3

b)

x = {-3, -1, 2}

c)

x = {-3, 2}

d)

x = -1

25.

Which of the following is NOT a solution to the function?

a)

x = -2

b)

x = -1

c)

x = 1

d)

x = 2

26.

Which of the following is not an x-intercept of the function.

a)

x = -1

b)

x = 2

c)

x = 4

d)

x = 5

27.

Solve using the quadratic formula.
2x² - 9x - 35 = 0

a)

x = 7/2, x = -6

b)

x = -5/2, x =5

c)

x = -3/7, x =6

d)

x = -5/2, x = 7

28.

If the discriminant equals 0, then the quadratic has:

a)

1 Rational Solution

b)

2 Rational Solutions

c)

No solutions

d)

2 Complex Solutions

29.

If the discriminant is negative, then the quadratic has:

a)

1 Rational Solution

b)

2 Rational Solutions

c)

2 Irrational Solutions

d)

2 Complex Solutions

30.

Solve by completing the square.
x² +12x = 5

a)

X = 6 + √41 or 6 − √41

b)

X= 35 or 47

c)

X = −6 + √41 or −6 − √41

d)

X = √35 or √47

31.

Solve by completing the square:
k² − 12k + 23 = 0

a)

{6 + √13, 6 - √13}

b)

{-6 + √13, -6 - √13}

c)

{6 + √59, 6 - √59}

d)

{-6 + √59, -6 - √59}

32.

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

a)

75-24i

b)

63 - 24i - 12i²

c)

51 - 24i

d)

58 + 60i

33.

Write the polynomial in standard form given the following zeros. x = -2, 1, 4

a)

f(x) = (x+2)(x-1)(x-4)

b)

f(x) =x³ - 3x² - 6x + 8

c)

f(x) = x³+ 8

d)

f(x) = x³ - 3x² + 8

34.

x³ - 27

a)

(x - 4)(x² + 4x + 16)

b)

(x + 3)(x² - 4x + 16)

c)

(x - 1)(x² + 1x + 1)

d)

(x - 3)(x² + 3x + 9)

35.

Simplify the following expression:

a)

b)

c)

d)

36.

i² equals...

a)

1

b)

-1

c)

-i

d)

0

37.

Expand (x + 2)³

a)

x³+ 6x²- 12x + 8

b)

x³+ 6x²+ 12x + 8

c)

x³- 6x²+ 12x - 8

d)

x³+ 4x²+ 12x + 6

38.

Simplify: (v²- v - 56) ÷ (v - 8)

a)

(v + 8)

b)

(v - 7)

c)

v - 8 R(0)

d)

v + 7

39.

What are the first and second steps in solving the equation $\sqrt{x\ -\ 3}+8\ =\ 10$ ?

a)

Subtract 8, then square both sides

b)

Square both sides, then subtract 8

c)

Square both sides, then add 3

d)

Subtract 8, then add 3

40.

Find the vertex

$y=\left(x+3\right)^2-1$

a)

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

b)

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

c)

$\left(3,1\right)$

d)

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

41.

Find the vertex

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

a)

$\left(3,4\right)$

b)

$\left(-3,4\right)$

c)

$\left(6,4\right)$

d)

$\left(-6,4\right)$

42.

Simplify the expression

$\sqrt{-24}$

a)

$\sqrt{3}\sqrt{8}$

b)

$2\sqrt{6}$

c)

$\sqrt{3}\sqrt{8}i$

d)

$2\sqrt{6}i$

43.

Solve for x

$x^2+3x+6=0$

a)

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

b)

$\left\{3,6\right\}$

c)

$\frac{3}{2}\pm\frac{\sqrt{15}}{2}$

d)

$\frac{3}{2}\pm\frac{\sqrt{15}}{2}i$

44.

Determine the number of solutions to the given linear-quadratic system.

a)

0 solutions

b)

1 solution

c)

2 solutions

d)

3 solutions

45.

Based on the table, which function can best be used to model this situation?

a)

h(t) = 99t² + 858

b)

h(t) = -4.9t² + 295t + 0.6

c)

h(t) = -4.9t² + 295t + 2

d)

h(t) = 99t² + 1,470.3

46.

a)

$f\left(x\right)=192x^2-16x+0$

b)

$f\left(x\right)=-16x^2+192x+0$

c)

$f\left(x\right)=-4.9x^2+5x+19$

d)

$f\left(x\right)=3.37x^2-1.98x-7$

47.

What could be the equation for this graph?

a)

y = -2x³+ 1x + 3

b)

y = (x - 2)(x + 1)(x + 3)

c)

y = (x + 2)(x - 1)(x - 3)

d)

y = -2x² + 1x + 3

48.

What could be the equation for this graph?

a)

y = -2x³+ 1x + 3

b)

y = (x - 2)(x + 1)(x + 3)

c)

y = (x + 2)(x - 1)(x - 3)

d)

y = -2x² + 1x + 3

Honors Algebra II Fall Final Review

Total questions: 48

Worksheet time: 4hrs 53mins

Similar Resources on Wayground