Free Printable Algebra II second semester review

Worksheets

Algebra II second semester review

Total questions: 53

Worksheet time: 2hrs 41mins

Name

Class

Date

log₃27=x

x=1

x=9

x=3

Does Not Exist

Solve for x.
log₇70=log₇(10x-30)

x=1

x=2

x=10

x=-2

Write as one logarithm. Simplify, if possible.
log₆3 + log₆2

log₆5

log₆1

Write as one logarithm. Simplify, if possible.
log₂800 - log₂100

-3

Expand
(b - 2)³

b³ - 2b² + 4b - 8

5b³ - 20b² + 40b - 40

b³ - 6b² + 12b - 8

4b³ - 12b² + 16b - 8

Name the polynomial based on its degree and the number of terms:
4x² + 3x+ 7

quadratic trinomial

cubic trinomial

cubic binomial

quadratic binomial

Find the value of the discriminant: 4x²-7x+8

√79

√-79

-79

-7±i√79/8

The polynomial is...

Odd degree, positive leading coefficient.

Odd degree, negative leading coefficient.

Even degree, positive leading coefficient.

Even degree, negative leading coefficient.

Which inequality is shown?

y < -5(x-2)(x-4)

y < -5(x+2)(x+4)

y > -5(x-2)(x-4)

y > -5(x+2)(x+4)

10.

Factor Completely: 3x² + 5x - 12

(3x + 4)(x-3)

(3x - 4)(x + 3)

(3x + 3)(x -4)

(3x - 3)(x + 4)

11.

How is the graph y = (x - 8)² - 9 translated from y = x²?

Moved down 8 and right 9

Moved up 9 and left 8

Moved down 9 and right 8

Moved up 8 and left 9

12.

Describe the transformation that occurred
m(x) = f(x + 1)

Left 1 Unit

Right 1 unit

Steeper

Up 1 unit

13.

Factor
27x³-64

(3x-4)(9x²+12x+16)

(3x-4)(9x²-12x+16)

(3x+4)(9x²-12x+16)

(3x+4)(9x²+12x+16)

14.

What is the solution to 5+√3x=11?

-12

No solution

15.

Solve

104/5

124/5

14/5

16.

Simplify the expression completely and write it in radical form if necessary.
x^3/4⋅x^1/2

∜x⁵

√x

∜x²

17.

Find the discriminant & describe the number & type of solutions:
-2x² -6x = -28

-260; two imaginary solutions

260; two imaginary solutions

-260; two real solutions

260; two real solutions

18.

Divide (2x³+4x²-5) by (x+3).

2x²+2x-4 R(-12)

2x²-2x+6 R(-23)

2x²-2x+8 R(-20)

2x²-4x+1 R0

19.

The y-intercept of the function y = 3 · 2^x is -

(0, 2)

(0, 1)

0, 3)

(0, 0)

20.

Directions: Select all correct answers.

Identify each expression below that is a factor of the polynomial shown in the graph.

x + 1

x - 1

x - 3

2x - 3

3x - 2

21.

The quadratic equation 0 = -16t² + 80t gives the time t in seconds when a golf ball is at a height of 0 feet. How do you find how many seconds until the ball is at its maximum height?

Find the x-coordinate of the maximum

find the y-coordinate of the maximum

find the zero

Use the table to find the y-intercept

find the x-intercept

22.

Condense the logarithmic expression:
3 log x - 2 log 8

log (x³ - 64)

log (3x - 16)

log (3x / 16)

log (x³ / 64)

23.

Solve the equation:
log ₂ (x - 7) = 5

x = 39

x = 32

x = 17

x = 25

24.

Find the horizontal asymptote.
4x-16
_______
x²-16

y=2

y=1

y=0

none

25.

What is the y-intercept?

(0,1)

(0,1/9)

(0,-1/9)

(0,-1)

26.

Find the constant of variation for the direct variation 4x = −6y

−2/3

2/3

−3/2

−6

27.

In a direct variation, if y = 4 when x = −2 , find x when y = 6.

−2

−3

28.

You have inherited land that was purchased for $30,000 in 1960. The value of the land increased by approximately 5% per year. What is the approximate value of the land in the year 2011?

$344,022

$31,500

$15,000

$28,500

29.

Expand:

2lnx - ln 6

ln6 - 2lnx

ln6 + 2lnx

2ln6x

30.

log₃4x = 2

x=4/9
x=4/9

x=9/4

x=3/2

x=2/3

31.

log₂(x + 5) = 3

32.

Solve for x:
(2x - 1)^3/4 + 9 = 36

33.

Simplify completely.

34.

Parts of Parabola can be shown in the picture above...

Find the vertex of f(x)= x²+2x-15

(-5, 0)

(3, 0)

(0, -15)

(-1, -16)

35.

What are the vertical and horizontal asymptotes for the function shown?

VA: x=-5 HA: y=0

VA: x=0 HA: y=-5

VA: x=3 HA: y=3

VA: x=-5 HA" y=-3

36.

What transformations were use to obtain the graph of g(x)= 4 log(x-3)-7 from the graph of f(x)= log(x)?

Stretch by 4, left 3, down 7

Stretch by 4, right 3, down 7

Compress by 4, left 3, down 7

Compress by 4, right 3, down 7

37.

Solve.

[Hint: You can always check answer choices]

x=2

x=9

x=4

x=1

38.

What is the name of this function?

Parabola

Rational Function

Ellipse

Cubic

39.

What type of function is shown?

cube root

square root

logarithm

exponential

40.

Which parent function matches the graph?

y = |x|

y = ∛(x)

y = x²

y = a⋅b^x

41.

What type of function is shown?

absolute value

quadratic

linear

exponential

42.

What type of function is shown?

linear

quadratic

square root

absolute value

43.

What type of function is shown?

exponential

logarithm

quadratic

square root

44.

A person puts $4000 in the bank with a 6% annual interest rate. How much would he have after 1 year if it is compounded continuously?

$4247.35

$4345.25

$3679.42

$6738.12

45.

Simplify:

46.

What is the domain of the graph of the radical function?

(-infinity, infinity)

(-7, infinity)

(0, infinity)

(4, infinity)

47.

What is the range of the graph of the radical function?

(-infinity, infinity)

(-7, infinity)

(0, infinity)

(4, infinity)

48.

What is the point of intersection for f(x)=2^xand g(x)=(1/2)^x

(0,1)

(1,0)

(1,1/2)

(2,4)

49.

Ellis is studying the graph of a function with the general equation f(x) = a(x-h)²+k. If Ellis only changes the value of a, from 1 to 5, what happens to the graph?

It becomes wider.

It becomes narrower.

It moved up 4 units.

It moved to the right 4 units.

50.

What is the end behavior as x → +∞, f(x)→ ?

-∞

∞

51.

Find the vertical asymptote(s).

None

x = 0

x= 4

x = -4, 4

52.

The holes of a rational function occur when :

my pencil pokes a hole in the paper I'm working on

there is something left in the denominator

the value of f(0)

a factor in the denominator cancels with a factor in the numerator

53.

Anything raised to a power of zero is always:

itself

negative

100 %

Algebra II second semester review

Total questions: 53

Worksheet time: 2hrs 41mins

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