Free Printable December Review of Units 1-4 and 6.

1.

Is the relation a function? Why.

a)

Yes, because the x-value 11 has two y-values pair with it.

b)

Yes, because each x-value has only one y-value paired with it.

c)

No, because the x-value 11 has two y-values pair with it.

d)

No, because each x-value has only one y-value paired with it.

2.

Which set of values is a function?

a)

(9,5) (10,5) (9,-5) (10,-5)

b)

(3,4) (4,-3) (7,4) (3, 8)

c)

(6,-5) (7, -3) (8, -1) (9, 1)

d)

(2, -2) (5, 9) (5, -7) (1, 4)

3.

All of the y values or outputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

4.

All of the x values or inputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

5.

Is this table a function or not a function?

a)

Function

b)

Not a Function

6.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

7.

What is the range of the graph?

a)

-2 < y < 10

b)

-3 < x < 3

c)

-2 ≤ y ≤ 10

d)

-3≤ x ≤ 3

8.

What is the domain of the graph?

a)

{x| -∞ ≤ x ≤ ∞}

b)

(-∞,∞)

c)

-3 ≤ x ≤ 3

d)

-15 ≤ y ≤ 9

9.

What is the domain of the function?

a)

{x| x = all real numbers}

b)

{x| -2 < x < 4}

c)

{x| -2 ≤ x ≤ 4}

d)

{x| -6 ≤ x ≤ 3}

10.

What is the range of this functions?

a)

{y| -6 ≤ y ≤ 3}

b)

{y| -6 < y < 3}

c)

{y|y = all real numbers}

d)

{y| -2 ≤ y ≤ 4}

11.

a)

-8

b)

-6

c)

-4

d)

-2

12.

What is the average rate of change from x=0 to x=1

a)

-3

b)

3

c)

0

d)

2

13.

Find the average rate of change of f(x)=2x²+3x-1 on the interval 1≤ x ≤ 2.

a)

18

b)

-9

c)

9

d)

3

14.

What is the average rate of change of f(x) = 5x - 7 on the interval -3 ≤ x ≤ 7 ?

a)

$\frac{1}{2}$

b)

5

c)

10

d)

2

15.

What is the average rate of change of the function from x=2 to x=4?

a)

20

b)

100

c)

300

d)

600

16.

Find the product.

( 9x - y ) ²

a)

81x² - 9xy + y²

b)

81x² - y²

c)

81x² - 18xy + y²

d)

81x² + y²

17.

Simplify: (2a - 3) (3a + 1)

a)

6a²+ 7a - 3

b)

6a²+ 5a - 3

c)

6a² - 7a - 3

d)

6a²- 9a + 3

18.

Simplify the expression.
(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

a)

-8n² - 8n + 3

b)

-7n² - 8n + 3

c)

-6n²- 8n + 3

d)

-7n² - 4n + 3

19.

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

a)

1

b)

2

c)

3

d)

4

20.

What is the standard form of the polynomial,
9x² + 5x + 27 + 2x³

a)

27 + 5x + 9x² + 2x³

b)

9x² + 5x + 2x³ + 27

c)

9x² + 5x + 27 + 2x³

d)

2x³ + 9x² + 5x + 27

21.

Simplify the expression
(2x - 2)(4x + 1)

a)

8x² - 10x + 2

b)

8x² + 2

c)

8x² + 16x + 2

d)

8x² - 6x - 2

22.

In a Mathematics class there are $x^2-121$ students. You are asked to group the number of students into $x-11$ . How many groups can you form?

a)

$x+121$

b)

$x-11$

c)

$x-121$

d)

$x+11$

23.

Find the product:
(2x+3)²

a)

2x+3+2x+3

b)

4x²+12x+9

c)

4x²+9

d)

16x²+9

24.

(2x + 3)(x² + 4x + 1)

a)

2x³ + 10x² + 14x + 4

b)

2x³ + 11x² + 14x + 3

c)

-2x³ - 11x² + 14x + 5

d)

x³ - 11x² + 14x + 3

25.

Solve the system of equations to find the value of y.

a)

-2

b)

3

c)

-3

d)

2

26.

(-2)³⋅(-2)⁶

a)

(-2)⁹

b)

(-2)¹⁸

c)

(-2)⁻³

d)

(-2)

27.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

28.

Simplify (-4r⁵)(2r⁸)

a)

-8r¹³

b)

-2r¹³

c)

-8r⁴⁰

d)

-2y⁴⁰

29.

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

30.

According to exponent rules, when we multiply the same base we _______ the exponents.

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

31.

According to exponent rules, when we divide the expressions we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

32.

According to exponent rules, when we raise the coefficients to a power we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

33.

Which expression is NOT equivalent to $3^8$ ?

a)

$\left(3^6\right)\left(3^2\right)$

b)

$\left(3^4\right)^2$

c)

$\left(3^4\right)\left(3^4\right)$

d)

$\left(3^4\right)^4$

34.

Which expression is equivalent to $\frac{x^2y^2z^2}{4y^4}$ ?

a)

$4y^6$

b)

$y^6$

c)

$\frac{x^2z^2}{4y^2}$

d)

$4x^2y^6z^2$

35.

Which expression represents the product of $\left(2x^2y^2\right)\left(3x^3y^3\right)$ ?

a)

$6x^6y^6$

b)

$5x^5y^5$

c)

$5x^6y^6$

d)

$6x^5y^5$

36.

Simplify: $\left(s^2r^{-4}\right)\left(s^6r^{-2}\right)$

a)

$\frac{s^8}{r^6}$

b)

$\frac{s^{15}}{r^8}$

c)

$r^6s^8$

d)

$r^7s^{13}$

37.

a)

b)

c)

d)

38.

What is the value of the power?

a)

$\frac{1}{9}$

b)

$9$

c)

$-1$

d)

$1$

e)

$-\frac{1}{9}$

39.

$\left(\frac{125}{64}\right)^{\frac{4}{3}}=$

a)

$\left(^3\sqrt{\frac{125}{64}}\right)^4$

b)

$\left(^4\sqrt{\frac{125}{64}}\right)^3$

40.

Rewrite in radical form.

a)

A

b)

B

c)

C

d)

D

41.

Factor
n²-13n+40

a)

(n-5)(n-8)

b)

(n+5)(n-8)

c)

(n-5)(n+8)

d)

(n+6)(n+1)

42.

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)

43.

w⁴ - 625

a)

(w² + 25) (w² - 25)

b)

(w² - 25) (w² - 25)

c)

(w²+ 25) (w+5) (w-5)

d)

(w+25)(w-25)

44.

x⁶- 400

a)

( x³ - 200) ( x³ + 200)

b)

( x² + 20) ( x² + 20)

c)

( x - 20) ( x + 20)

d)

( x³ - 20) ( x³ + 20)

45.

x⁴ - 100y²

a)

(x² + 10y) (x² - 10y)

b)

(x + 10y) (x - 10y)

c)

(x + 10y) (x³ - 10y)

d)

(x³ + 10y) (x - 10y)

46.

Factor: x³+ 1

a)

(x + 1)³

b)

(x+1)(x²- x + 1)

c)

(x - 1) (x² + x - 1)

d)

(x + 1)(x² - 2x + 1)

47.

Factor: 8x³ - 1

a)

(2x - 1)(4x² + 2x + 1)

b)

(2x + 1)(4x² - 2x + 1)

c)

(2x - 1)(4x² - 2x - 1)

d)

(2x + 1)(4x² +2x + 1)

48.

Factor: 27x³ + 8

a)

(3x + 2)(9x² - 6x + 4)

b)

(9x + 2)(3x² + 18x + 4)

c)

(3x²+4)(9x + 2)

d)

(27x + 8)(x² - 216x + 64)

49.

Complete the formula
a³-b³=

a)

(a-b)(a²+ab+b²)

b)

(a+b)(a²-ab+b²)

c)

(a-b)(a²-ab+b²)

d)

(a+b)(a²+ab+b²)

50.

Factor
27x³-64

a)

(3x-4)(9x²+12x+16)

b)

(3x-4)(9x²-12x+16)

c)

(3x+4)(9x²-12x+16)

d)

(3x+4)(9x²+12x+16)

51.

Factor this sum of cubes:
2x³ + 128

a)

2(x³ + 64)

b)

(x + 4)(x² - 4x + 16)

c)

2(x - 4)(x² + 4x + 16)

d)

2(x + 4)(x² - 4x + 16)

52.

7r³-8r²+42r-48

a)

(r²+6)(7r+8)

b)

(r²+6)(7r-8)

c)

(r²+6)(r²+8)

d)

(r²+6)(7r+6)

53.

20x³-25x²+4x-5

a)

(5x²-5)(4x+1)

b)

5(x²-1)(4x+5)

c)

(5x²+1)(4x-5)

d)

(5x²+1)(4x-1)

54.

Factor

2x⁴ - 13x² - 70

a)

(2x+7)(x-10)

b)

(7x+5)(x+2)

c)

(2x²+7)(x²-10)

d)

2(x²+7)(x²+10)

55.

Rewrite log_x95 = 2.3

a)

x^2.3 = 95

b)

95^2.3 = x

c)

2.3⁹⁵ = x

d)

x⁹⁵= 2.3

56.

Rewrite 1.6^(x+2) = 14.1

a)

log_1.614.1 = x+2

b)

log_1.6(x+2) = 14.1

c)

log_14.1(x+2) = 1.6

d)

log_(x+2)1.6 = 14.1

57.

Which of the following has a domain of all real numbers, x > 2 ?

a)

y = log₂ x

b)

y = log₃ (x+2)

c)

y = log₄ (x - 2)

d)

y = log₇x - 2

58.

Which of the following is the sketch of the graph of y = -log₃ (x+5) ?

a)

b)

c)

d)

59.

log_x1000=3

a)

1

b)

10

c)

30

d)

3

60.

log₈(4x+4)=2

a)

15

b)

12

c)

10

d)

3

61.

log₆(2x + 3) = 3

a)

x = 106.5

b)

x = 100

c)

x = 16

d)

x = 50

62.

a)

5

b)

13

c)

84

d)

-20

63.

What is a, the starting term, for the function: f(x) = 300(1.16)^x?

a)

300

b)

1.16

c)

.16

d)

x

64.

What is b, the common ratio, for the function: f(x) = 300(1.16)^x?

a)

300

b)

1.16

c)

.16

d)

x

65.

Joe deposits $500 in an account with 3% interest compounded quarterly for a period of 5 years. What expression would you type into the calculator to calculate the total amount of money Joe will have after the 5 year period?

a)

500(1+.03)⁴⁽⁵⁾

b)

500(1+.03/4)⁽⁴⁾⁽⁵⁾

c)

500(1+3)⁵

d)

500e^(.03)(5)

66.

Jasmine puts $4000 into an a savings account which offers 8% interest and compounds interests continuously for 3 years. Which expression could be typed into the calculator to see how much money Jasmine will have after 3 years?

a)

4000(1+.08)³

b)

4000e^(.08)(3)

c)

4000(1+3)^.08

d)

4000(1+.08/3)³⁽³⁾

67.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

68.

Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?

a)

$23,219.72

b)

$136.72

c)

$51,710.94

d)

$16,710.94

69.

Hannah invested $4000. How much money will she have in 15 years if the interest rate of 6% is being compounded continuously?

a)

9839.42

b)

32412.71

c)

9838.41

d)

32412.72

70.

Which reindeer does not belong below?

a)

Dancer

b)

Comet

c)

Roger

d)

Dasher

71.

On the 7th day of Christmas what did my true love bring?

a)

geese a laying

b)

swans a swimming

c)

ladies dancing

d)

maids a milking

72.

"Oh what fun it is to ride" is a line from which song?

a)

Away in the Manger

b)

Jingle Bells

c)

White Christmas

d)

Frosty the Snowman

73.

Christmas Island is a territory of which country?

a)

Australia

b)

France

74.

Where are the traditional Christmas plant poinsettias from?

a)

France

b)

Mexico

75.

Which country banned Christmas in 1644?

a)

France

b)

England

c)

Canada

76.

19. In what year was the Christmas card invented?

a)

a) 1834

b)

b) 1852

c)

c) 1901

77.

How many points does a snowflake have?

a)

6

b)

9

c)

8

d)

12

December Review of Units 1-4 and 6.

Total questions: 77

Worksheet time: 6hrs 51mins

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