Free Printable #1 Semester Review

1.

Solve the cube root equation

a)

344

b)

21

c)

-344

d)

-21

2.

Solve the cube root equation

a)

27

b)

20

c)

3

d)

30

3.

Solve for x:

(3x + 1)³ = 64

a)

-1

b)

6

c)

1

d)

No real solution

4.

Solve $x^3=343$

a)

104

b)

6

c)

7

d)

no solution

5.

$\left(x+7\right)^3+8=16$

a)

5

b)

505

c)

-505

d)

-5

e)

None

6.

What are the shifts of the graph

f\left(x\right)=\left(x-2\right)^3-8

from the parent graph of

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

?

a)

Left 2 and Up 8

b)

Right 2 and Up 8

c)

Left 2 and Down 8

d)

Right 2 and Down 8

7.

What are the shifts of the graph

f\left(x\right)=\left(x+9\right)^3+4

from the parent graph of

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

?

a)

Left 9 and Up 4

b)

Right 9 and Up 4

c)

Left 9 and Down 4

d)

Right 9 and Down 4

8.

Identify the Transformations.

a)

Vertical stretch by 2 and down 4

b)

Horizontal compression by ½ and down 4

c)

Vertical stretch by 2 and up 4

d)

Horizontal compression by ½ and right 4

9.

If f(x) = x³ is changed to f(x) = - (x + 3)³ + 2, how is the graph transformed?

a)

3 units right, 2 units up, reflected across the y-axis

b)

3 units right, 2 units up, reflected across the x-axis

c)

3 units left, 2 units up, reflected across the y-axis

d)

3 units left, 2 units up, reflected across the x-axis

10.

If f(x) = ∛(x) is reflected over the x-axis, vertically compressed by a factor of 1/4, and shifted left 9, which equation is correct?

a)

1/4 ∛(x + 9)

b)

1/4 ∛(x - 9)

c)

- 1/4 ∛(x + 9)

d)

- 1/4 ∛(x - 9)

11.

x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Unfactorable

12.

Fully Factor the Following
25x²-81

a)

(5x-9)²

b)

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

c)

25(x-9)²

d)

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

13.

Factor the Trinomial:
x² - 8x + 15

a)

(x + 5) ( x + 3)

b)

(x - 5) (x - 3)

c)

(x + 15) (x - 1)

d)

(x - 7) (x - 8)

14.

Factor
x²+ 12x + 36

a)

(x + 6)(x +6)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 6)(x - 6)

15.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

16.

What is the mode?

a)

# happening the most

b)

the average

c)

biggest - smallest

d)

the middle #

17.

Find the mean of these numbers:
5,11,2,12,4,2

a)

4.1

b)

6

c)

4.5

d)

4

18.

Find the median of these numbers:
4,2,7,4,3

a)

2

b)

5

c)

7

d)

4

19.

In order to find the median, the data must be sorted from least to greatest first.

a)

True

b)

False

20.

Find the mode:
5, 0, 9, 9, 3, 0, 5, 5, 4

a)

9

b)

5

c)

3

d)

7

21.

If there is an even number of data in the data set how do you find the median?

a)

order the data and find the middle value

b)

order the data add the 2 middle values and divide by 2

22.

James purchased 3 shirts, 3 jackets and 2 pairs of pants. How many different outfits using a shirt, a jacket, and pants are possible?

a)

8

b)

18

c)

54

23.

At a New Car Dealership a particular model comes in 4 trim levels, 5 different colors, and 3 different interiors. How many different versions of this car model can be created from these options?

a)

180

b)

23

c)

12

d)

60

24.

A particular model of a new car comes in: 4 trim levels, 5 different colors, and 3 different interiors. How many different versions of this car model can be created from these options?

a)

180

b)

23

c)

12

d)

60

25.

How many ways can a club select a president, vice president, and a secretary from a group of 5 people?

a)

12

b)

60

c)

15

26.

How many ways can you listen to 3 songs from a CD that has 12 selections?

a)

1320

b)

33

c)

36

27.

5³⋅5⁴

a)

5⁷

b)

5⁻¹

c)

5¹²

d)

5

28.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

29.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

30.

n²⋅n⁴⋅n⁵

a)

n¹¹

b)

n⁴⁰

c)

n¹³

d)

n²²

31.

8⁷ ⁄ 8²

a)

8⁵

b)

8⁹

c)

8¹⁴

d)

1⁵

32.

The amount of money earned on a job is directly proportional to the number of hours worked. If $70.00 is earned in 5 hours, how much money is earned in 22 hours of work?

a)

$2

b)

$308

c)

$1.57

d)

$265

33.

Determine if the relationship between the two quantities is a direct variation. Explain your reasoning.

a)

yes, the constant of variation is 1/2

b)

yes, the constant of variation is 2

c)

no, there is constant of variation.

34.

Is this a direct variation? y =2x + 1

a)

Yes

b)

No

35.

Is this a direct variation?
y=2x

a)

yes

b)

no

36.

Is this a direct variation?

a)

yes

b)

no

37.

In a direct variation, y = 39 when x = 3.
Find the value of y when x = 2.

a)

26

b)

3

c)

58.5

d)

2

38.

Given that y varies inversely with x, if x =7 and y = 4, what is y when x = 2?

a)

14

b)

10

c)

2

d)

-14

39.

Does the equation show an inverse variation?
y=10/x

a)

yes

b)

no

40.

Given the following equation, identify the constant k.
y = 54/x

a)

There is one.

b)

k = x

c)

54

d)

y = k

41.

Which of the following represents indirect variation?

a)

y = kx

b)

y = k/x

c)

y = x/k

d)

y = mx + b

42.

If a varies jointly as b and the square root of c, and a = 21 when b = 5 and c = 36, find a when b = 9 and c = 225.

a)

126

b)

196

c)

256

d)

289

43.

(x − 3)(6x − 2)

a)

6x² − 20x + 6

b)

6x² + 20x - 6

c)

6x² +6

d)

6x + 6

44.

(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

45.

For synthetic division, what would be the number in the left hand box?

a)

0

b)

1

c)

2

d)

3

46.

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

a)

3 0 -4 6 1

b)

6 -4 3 1 0

c)

6 -4 0 3 1

d)

-6 4 0 -3 -1

47.

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

a)

Yes, (x-2) is a factor. There is a remainder.

b)

No, (x-2) is not a factor. The remainder is zero.

c)

Yes, (x-2) is a factor. The remainder is zero.

d)

No, (x-2) is not a factor. There is a remainder.

48.

Divide using synthetic division
(2x³ + 4x² - 5) by (x + 3).

a)

2x² + 2x - 4 R(-12)

b)

2x² - 2x + 6 R(-23)

c)

2x² - 2x + 8 R(-20)

d)

2x² - 4x + 1 R0

49.

Rewrite as an exponential: log₂8 = 3

a)

3² = 8

b)

2³ = 8

c)

2⁸ = 3

d)

8³ = 2

50.

Rewrite as an exponential: $\log_7\left(\frac{1}{49}\right)=-2$

a)

$7^{\frac{1}{49}}=-2$

b)

$\left(\frac{1}{49}\right)^{-2}=7$

c)

$7^{-2}=\frac{1}{49}$

d)

$\left(-2\right)^7=\frac{1}{49}$

51.

Rewrite as a log: y = 7^x

a)

log₇(x) = y

b)

log_y(7) = x

c)

log_x(y) = 7

d)

log₇(y) = x

52.

Rewrite as a log: x = 11^y

a)

log₁₁(y) = x

b)

log_y(11) = x

c)

log₁₁(x) = y

d)

log_x(y) = 11

53.

Expand $\log_4\left(x^5y^2\right)$

a)

$10\log_4\left(x\ +y\right)$ 1

b)

$5\log_4x+2\log_4y$

c)

$5\log_9x+2\log_9y$

d)

$\log_4\left(5x+2y\right)$

54.

$Expand\ \log_5\left(xy^5\right)^2$

a)

$2\log_5x\ +10\log_5y$

b)

$10\left(\log_5x\ +\log_5y\right)$

c)

$10\log_5x\ +10\log_5y$

d)

$10\log_5x\ +2\log_5y$

55.

$4\log_4u-6\log_4v$ Condense

a)

$\log_4\left(\frac{u}{v}\right)^{24}$

b)

$\log_4\left(\frac{u^6}{v^4}\right)^{ }$

c)

$\log_4\left(\frac{u^4}{v^6}\right)^{ }$

d)

$\log_4\left(\frac{v^6}{u^4}\right)^{24}$

56.

Condense $15\ \log_5a\ +3\ \log_5b$

a)

$15\log_5ab$

b)

$\log_5\left(a^{15}b^3\right)$

c)

$\log_5\left(b^{15}a^3\right)$

d)

$45\log_5\left(ab\right)$

57.

Solve for x

a)

x = 19.6

b)

x = 5/98

c)

x = 101/5

58.

Solve by cross-multiplying

a)

x = 6

b)

x = -6

c)

x = 6/7

d)

x = -6/7

59.

Solve by cross-multiplying.

a)

x = 2

b)

No Solution

c)

x = -10

d)

x = 10

60.

Which is better?

a)

Dogs!

b)

cats

#1 Semester Review

Total questions: 60

Worksheet time: 10hrs 0mins

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