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Worksheets

Rational -Je

Total questions: 188

Worksheet time: 14hrs 38mins

Name
Class
Date
1.

 2x(x2)(x2)(x+5)\ \frac{2x\left(x-2\right)}{\left(x-2\right)\left(x+5\right)}

 State the values of x which must be excluded to prevent division by zero.

a)

-2 and 5

b)

2 and -5

c)

0, 2, and -5

d)

0, -2, and 5

2.
Which value of x makes the expression undefined?
a)
-2
b)
2
c)
-6
d)
-3
3.
Factor
n2 + 5n - 6
a)
(n - 2)(n - 3)
b)
(n - 1)(n + 6)
c)
(n + 1)(n - 6)
d)
(n + 2)(n - 3)
4.
Factor x2-2x-15
a)
(x+5)(x-3)
b)
(x-5)(x-3)
c)
(x-5)(x+3)
d)
(x+5)(x+3)
5.

Simplify

a)

x+9x9\frac{x+9}{x-9}

b)

1(x9)\frac{1}{(x-9)}

c)

x9x-9

d)

1(x+9)\frac{1}{(x+9)}

e)

x+9x+9

6.
Simplify. 
a)
(x+6)/(x+4)
b)
(x+6)(x+4)
c)
(x+6)
d)
(x+6)/(x-5)
7.

Simplify.

a)

m+6m3\frac{m+6}{m-3}

b)

7m3\frac{7}{m-3}

c)

7m+6\frac{7}{m+6}

d)

1m+6\frac{1}{m+6}

8.

Simplify and make sure final answer is in standard form.

a)

A

b)

B

c)

C

d)

D

9.

Simplify:  x2+6x7x249Simplify:\ \ \frac{x^2+6x-7}{x^2-49}  

a)

x1x+7\frac{x-1}{x+7}  

b)

x+1x+7\frac{x+1}{x+7}  

c)

x1x7\frac{x-1}{x-7}  

d)

x+1x7\frac{x+1}{x-7}  

10.

Simplify.

a)

1n7\frac{1}{n-7}

b)

n7n-7

c)

(n6)(n7)\frac{(n-6)}{(n-7)}

d)

n6n-6

11.

Simplify:  x2+6xx2+3x18Simplify:\ \ \frac{x^2+6x}{x^2+3x-18}  

a)

xx+3\frac{x}{x+3}  

b)

xx3\frac{x}{x-3}  

c)

x+6x3\frac{x+6}{x-3}  

d)

xx+6\frac{x}{x+6}  

12.

Simplify:  x2+7x+12x2+4xSimplify:\ \ \frac{x^2+7x+12}{x^2+4x}  

a)

x+3x+4\frac{x+3}{x+4}  

b)

x3x\frac{x-3}{x}  

c)

x+3x\frac{x+3}{x}  

d)

x+3x2\frac{x+3}{x^2}  

13.

Simplify:   x24x45x281Simplify:\ \ \ \frac{x^2-4x-45}{x^2-81}  

a)

x+5x9\frac{x+5}{x-9}  

b)

x+5x+9\frac{x+5}{x+9}  

c)

x5x9\frac{x-5}{x-9}  

d)

x5x+9\frac{x-5}{x+9}  

14.
Factor completely: 
3x2 + 18x +15
Hint: Factor GCF first.
a)
3(x2 + 6x + 5)
b)
(x + 5)(x + 1)
c)
3(x + 5)(x + 1)
d)
Prime
15.

Simplify:  x2+7x+10x24Simplify:\ \ \frac{x^2+7x+10}{x^2-4}  

a)

x5x+2\frac{x-5}{x+2}  

b)

x5x2\frac{x-5}{x-2}  

c)

x+5x+2\frac{x+5}{x+2}  

d)

x+5x2\frac{x+5}{x-2}  

16.
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)
17.

Simplify:  x225x26x+5Simplify:\ \ \frac{x^2-25}{x^2-6x+5}  

a)

x+5x1\frac{x+5}{x-1}  

b)

x5x1\frac{x-5}{x-1}  

c)

x+5x+1\frac{x+5}{x+1}  

d)

x5x+1\frac{x-5}{x+1}  

18.
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)
19.
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
20.

We can't factor using difference of two square this

49x2 + 4y2. Why?

a)

Because 4 is not a perfect cubed number.

b)

Because 4 is not a perfect squared number.

c)

Because 49 is not a perfect squared number.

d)

Because we can't factor using difference of two squares if it is addition sign.

21.

Find the domain of the function. f(x)=3xx2121f\left(x\right)=\frac{3x}{x^2-121}  

a)

{x6,5}\left\{x\ne-6,5\right\}  

b)

{x121}\left\{x\ne121\right\}  

c)

{x11}\left\{x\ne11\right\}  

d)

{x11,11}\left\{x\ne-11,11\right\}  

22.
State the domain restrictions. 
a)
x ≠ -2
b)
x ≠ 2, 1
c)
x ≠ 2, -1
d)
x ≠ -2, 2, 1
23.
State the domain restrictions.
a)
x ≠ 3, -2, 6, -1
b)
x ≠ -1, 6
c)
x ≠ 3, -2
d)
No Domain Restrictions
24.

Find the excluded value(s).

a)

n = 0

b)

n = 24

c)

n = -24

d)

n can be any real number

25.

Find the excluded value(s).

a)

a = 0

b)

a = 10

c)

a = 1

d)

a = -1

26.

Find the excluded value(s).

a)

v = 5

b)

v = 10

c)

v = -25

d)

v = -5

27.

What are the domain restrictions of the following rational expression:

a)

x ≠ 4

b)

x ≠ -4, 4

c)

x ≠ -16, 16

d)

x ≠ 0, 4

28.
What value(s) make the expression undefined?
a)
x = - 3 and x = 4
b)
x = 3 and x = - 4
c)
x = 3 only
d)
x = - 4 only
29.
State the excluded (undefined) values for the given expression.
a)
8, -10
b)
8, 9
c)
-8, 10
d)
-8, -9
30.

What is an excluded value?

a)

A value that makes the denominator equal to 0

b)

A number that makes the numerator equal to 0

c)

The solution

d)

An ostracized number

31.
Which value of x makes the expression undefined?
a)
3
b)
-2
c)
-3
d)
5
32.
What is the non-permissible value of this rational expression.
a)
0 and 2
b)
2 and 3
c)
0 and 1.5
d)
1.5 and -1.5
33.
For which value is the expression undefined?
a)
-4
b)
-3
c)
3
d)
0
34.
State the excluded values. x ≠ ?
a)
A
b)
B
c)
C
d)
D
35.
State the excluded values. x ≠ ?
a)
A
b)
B
c)
C
d)
D
36.

Determine the excluded values.

a)

x = 0, 3

b)

x = 0, -3

c)

x = 0, -3, 5

d)

x = 0, 3, 5

37.

Determine the excluded values.

a)

x = 5, -1

b)

x = -5, 1

c)

x = 5, 1

d)

x = -5, -1

38.

Determine the excluded value.

a)

x = 6

b)

x = 0

c)

x = -6

d)

x = -6, 9

39.

Determine the excluded values.

a)

x = 0

b)

x = 2, 6

c)

x = -2, -6

d)

x = 0, -2, -6

40.
(x²+11x+24)/(x²+4x-32)
a)
A.(x+7)/(x+4)
b)
B.3/4
c)
C.(x+3)/(x+4)
d)
D.(x+3)/(x-4)
41.
20x³/(5x+10)
a)
A.4x³/(x+2)
b)
B.4x³/(x+10)
c)
C.2x³/(5x+1)
d)
D. 2x³/(x+5)
42.
(-x-5)/(x²+12x+35)
a)
A. 1/(x+7)
b)
B. 1/(x-7)
c)
C. -1/(x+7)
d)
D. -1/(x+6)
43.
Simplify by cancelling
a)
1
b)
-1
c)
Can't be simplified
44.
Which of the following is equivalent?
(7-m)
a)
(m-7)
b)
-(m+7)
c)
-(7+m)
d)
-(m-7)
45.
Simplify
a)
(x-9)/(x+9)
b)
1/(x-9)
c)
(x+9)
d)
1/(x+9)
46.
Simplify.
a)
A.
b)
B.
c)
C.
d)
D.
47.
Simplify
(x2-49)/(x2+9x+14)
a)
(x-7)/(x+2)
b)
(x+7)/(x+2)
c)
(x-7)/(x-2)
d)
(x+7)/(x+2)
48.
Simplify
(x2+6x+8)/(x2-x-6)
a)
(x+2)/(x-3)
b)
(x+4)/(x+2)
c)
(x+4)/(x-3)
d)
(x+2)/(x+2)
49.

Simplify

(8x + 32)/( x+4)

a)

8/(x - 4)

b)

-x/(x - 4)

c)

-8

d)

8

50.
(4 - x2) / (x2 - x - 2)
a)
4 / (-x - 2)
b)
-2 / (-X - 1)
c)
-1(x + 2) / (x + 1)
51.
What is the excluded value: 
7 / (x - 3)
a)
7
b)
There is not one.
c)
3
52.
(5x2 + 21x + 4) / (25x + 100)
a)
(x2 + 21x + 1) / (5x + 25)
b)
5x2 + 4 / 4x + 25
c)
(5x + 1) / 25
53.
Which value of x makes the expression undefined?
a)
-2
b)
2
c)
-6
d)
-3
54.
Simplify
(2x2-98)/(2x2+18x+28)
a)
(x-7)/(x+2)
b)
(x+7)/(x+2)
c)
(x-7)/(x-2)
d)
(x+7)/(x+2)
55.
a)
A
b)
B
c)
C
d)
D
56.

Simplify the expression

a)

1

b)

-1

c)

Can't be simplified

57.
Which of the following is equivalent?
(7-m)
a)
(m-7)
b)
-(m+7)
c)
-(7+m)
d)
-(m-7)
58.

Simplify

(8x + 32)/( x+4)

a)

8/(x - 4)

b)

-x/(x - 4)

c)

-8

d)

8

59.
Simplify.
a)
2p
b)
p/2
c)
2/p
d)
4p
60.

Simplify:  x2+6x7x249Simplify:\ \ \frac{x^2+6x-7}{x^2-49}  

a)

x1x+7\frac{x-1}{x+7}  

b)

x+1x+7\frac{x+1}{x+7}  

c)

x1x7\frac{x-1}{x-7}  

d)

x+1x7\frac{x+1}{x-7}  

61.

Simplify:  x2+6xx2+3x18Simplify:\ \ \frac{x^2+6x}{x^2+3x-18}  

a)

xx+3\frac{x}{x+3}  

b)

xx3\frac{x}{x-3}  

c)

x+6x3\frac{x+6}{x-3}  

d)

xx+6\frac{x}{x+6}  

62.

Simplify:  x2+7x+10x24Simplify:\ \ \frac{x^2+7x+10}{x^2-4}  

a)

x5x+2\frac{x-5}{x+2}  

b)

x5x2\frac{x-5}{x-2}  

c)

x+5x+2\frac{x+5}{x+2}  

d)

x+5x2\frac{x+5}{x-2}  

63.

Simplify:  x225x26x+5Simplify:\ \ \frac{x^2-25}{x^2-6x+5}  

a)

x+5x1\frac{x+5}{x-1}  

b)

x5x1\frac{x-5}{x-1}  

c)

x+5x+1\frac{x+5}{x+1}  

d)

x5x+1\frac{x-5}{x+1}  

64.

Simplify:   x24x45x281Simplify:\ \ \ \frac{x^2-4x-45}{x^2-81}  

a)

x+5x9\frac{x+5}{x-9}  

b)

x+5x+9\frac{x+5}{x+9}  

c)

x5x9\frac{x-5}{x-9}  

d)

x5x+9\frac{x-5}{x+9}  

65.

x2+8x+12x2+3x18\frac{x^2+8x+12}{x^2+3x-18}  

a)

x3x+2\frac{x-3}{x+2}  

b)

x+2x3\frac{x+2}{x-3}  

66.

2x2+10x488x+64\frac{2x^2+10x-48}{8x+64}  

a)

x38\frac{x-3}{8}  

b)

x34\frac{x-3}{4}  

67.

x211x+18x2+2x8\frac{x^2-11x+18}{x^2+2x-8}  

a)

x9x4\frac{x-9}{x-4}  

b)

x9x+4\frac{x-9}{x+4}  

68.

Simplify:  x8y12x4y15Simplify:\ \ \frac{x^8y^{12}}{x^4y^{15}}  

a)

x4y3\frac{x^4}{y^3}  

b)

x12y3\frac{x^{12}}{y^3}  

c)

x12y27x^{12}y^{27}  

d)

y3x4\frac{y^3}{x^4}  

69.

Simplify: 5a3c1020a5c4Simplify:\ \frac{5a^3c^{10}}{20a^5c^4}  

a)

4c6a2\frac{4c^6}{a^2}  

b)

1a2c64\frac{1a^2c^6}{4}  

c)

1c64a2\frac{1c^6}{4a^2}  

d)

1a24c6\frac{1a^2}{4c^6}  

70.

Simplify:  x8y12x4y15Simplify:\ \ \frac{x^8y^{12}}{x^4y^{15}}  

a)

x4y3\frac{x^4}{y^3}  

b)

x12y3\frac{x^{12}}{y^3}  

c)

x12y27x^{12}y^{27}  

d)

y3x4\frac{y^3}{x^4}  

71.

Simplify:  x2+6xx2+3x18Simplify:\ \ \frac{x^2+6x}{x^2+3x-18}  

a)

xx+3\frac{x}{x+3}  

b)

xx3\frac{x}{x-3}  

c)

x+6x3\frac{x+6}{x-3}  

d)

xx+6\frac{x}{x+6}  

72.

Simplify:  x2+6x7x249Simplify:\ \ \frac{x^2+6x-7}{x^2-49}  

a)

x1x+7\frac{x-1}{x+7}  

b)

x+1x+7\frac{x+1}{x+7}  

c)

x1x7\frac{x-1}{x-7}  

d)

x+1x7\frac{x+1}{x-7}  

73.

Which of the following statement describes a rational algebraic expression?

a)

It is the reverse process of multiplication.

b)

Fraction which numerator and denominator are polynomials

c)

Fraction which numerator and denominator are whole numbers

d)

It cannot be factored using only integers

74.

3x + 4x2  16  2xx216=\frac{3x\ +\ 4}{x^2\ -\ 16}\ -\ \frac{2x}{x^2-16}=

a)

11

b)

x+4x216\frac{x+4}{x^2-16}

c)

1x4\frac{1}{x-4}

d)

1x+4\frac{1}{x+4}

75.

xx+3+3x+3=\frac{x}{x+3}+\frac{3}{x+3}=  

a)

x2x^2  

b)

3xx + 3\frac{3x}{x\ +\ 3}  

c)

1

d)

3x3x\frac{3x}{3x}  

76.

Identify the given if it is rational expression or not. 

n8+n\frac{n}{8+\sqrt{n}}  

a)

rational expression

b)

not rational expression

77.

Which value of x is not allowed in the expression

x2x12x5\frac{x^2-x-12}{x-5}  ?

a)

0

b)

-3

c)

4

d)

5

78.

For what value of x will the expression

x+22x+4\frac{x+2}{2x+4}  be undefined?

a)

-1/2

b)

-1

c)

-2

d)

-4

79.

Add:

x+1x1+x+1x21\frac{x+1}{x-1}+\frac{x+1}{x^2-1}  

a)

x1x\frac{x-1}{x}  

b)

x2+2x\frac{x^2+2}{x}  

c)

x +1x 1\frac{x^{\ }+1}{x\ -1}  

d)

x+2x 1\frac{x^{ }+2}{x\ -1}  

80.

Simplify:  x8y12x4y15Simplify:\ \ \frac{x^8y^{12}}{x^4y^{15}}  

a)

x4y3\frac{x^4}{y^3}  

b)

x12y3\frac{x^{12}}{y^3}  

c)

x12y27x^{12}y^{27}  

d)

y3x4\frac{y^3}{x^4}  

81.

Simplify: 5a3c1020a5c4Simplify:\ \frac{5a^3c^{10}}{20a^5c^4}  

a)

4c6a2\frac{4c^6}{a^2}  

b)

1a2c64\frac{1a^2c^6}{4}  

c)

1c64a2\frac{1c^6}{4a^2}  

d)

1a24c6\frac{1a^2}{4c^6}  

82.

Simplify:  x2+6x7x249Simplify:\ \ \frac{x^2+6x-7}{x^2-49}  

a)

x1x+7\frac{x-1}{x+7}  

b)

x+1x+7\frac{x+1}{x+7}  

c)

x1x7\frac{x-1}{x-7}  

d)

x+1x7\frac{x+1}{x-7}  

83.

Which of the following is NOT a rational algebraic expression?

a)

3x\frac{3}{\sqrt{x}}

b)

a+46\frac{a+4}{6}

c)

x2+2xyx^2+2xy

d)

55

84.

Give the domain of     y+2y2\frac{y+2}{y-2}  

a)

all real numbers except   1-1  

b)

all real numbers except  11  

c)

all real numbers except  2-2  

d)

all real numbers except  22  

85.

8yz2+5z\frac{8-y}{z^2+5z}  

Give the values for which the given rational expression is undefined?

a)

z=0    and     z=5z=0\ \ \ \ and\ \ \ \ \ z=5  

b)

z =0    and    z=5z\ =0\ \ \ \ and\ \ \ \ z=-5  

c)

z=0    and    z=1z=0\ \ \ \ and\ \ \ \ z=-1  

d)

z=0    and    z=1z=0\ \ \ \ and\ \ \ \ z=1  

86.

xx+3+3x+3=\frac{x}{x+3}+\frac{3}{x+3}=  

a)

x2x^2  

b)

3xx + 3\frac{3x}{x\ +\ 3}  

c)

1

d)

3x3x\frac{3x}{3x}  

87.

3x + 4x2  16  2xx216=\frac{3x\ +\ 4}{x^2\ -\ 16}\ -\ \frac{2x}{x^2-16}=

a)

11

b)

x+4x216\frac{x+4}{x^2-16}

c)

1x4\frac{1}{x-4}

d)

1x+4\frac{1}{x+4}

88.
a)

4 / 7v2

b)

4 / 7v

c)

20 / 35v

d)

20 / 35v2

89.
a)

7(r + 2)/ (r + 2)

b)

(r - 8) / (r + 2)

c)

(r + 2) / 7

d)

(r - 8) / 7

90.
Simplify by cancelling
a)
1
b)
-1
c)
Can't be simplified
91.

A rational expression is said to be in lowest terms when its numerator and denominator have no common factors other than _____.

a)

1

b)

2

c)

3

d)

4

92.

What is 2yx2yless than 2x2yx?What\ is\ \frac{2y}{x-2y}less\ than\ \frac{2x}{2y-x}?  

a)


2x+2y2y x\frac{2x+2y}{2y-\ x}  

b)

2x+2yx2y\frac{2x+2y}{x-2y}  

c)

-1

d)

2x2yx2y\frac{2x-2y}{x-2y}  

93.

Dividev293v2+12by v+3v2+4Divide\frac{v^2-9}{3v^2+12}by\ \frac{v+3}{v^2+4}  

a)

v33\frac{v-3}{3}  

b)

v+33\frac{v+3}{3}  

c)

(v+3)(v-3)

d)

3

94.

Add:

x+1x1+x+1x21\frac{x+1}{x-1}+\frac{x+1}{x^2-1}  

a)

x1x\frac{x-1}{x}  

b)

x2+2x\frac{x^2+2}{x}  

c)

x +1x 1\frac{x^{\ }+1}{x\ -1}  

d)

x+2x 1\frac{x^{ }+2}{x\ -1}  

95.

x+3x1+x11(x1)(x+5)\frac{x+3}{x-1}+\frac{x-11}{\left(x-1\right)\left(x+5\right)}  

a)

x2+4x5x2+9x+4\frac{x^2+4x-5}{x^2+9x+4}  

b)

x2+9x+4(x+5)(x1)\frac{x^2+9x+4}{\left(x+5\right)\left(x-1\right)}  

c)

2x8x2+5x6\frac{2x-8}{x^2+5x-6}  

d)

2x83x+3\frac{2x-8}{3x+3}  

96.

x5x+8xx2\frac{x-5}{x+8}-\frac{x}{x-2}  

a)

15x+10(x+8)(x2)\frac{-15x+10}{\left(x+8\right)\left(x-2\right)}  

b)

2x2+x+10(x+8)(x2)\frac{2x^2+x+10}{\left(x+8\right)\left(x-2\right)}  

c)

2x52x+6\frac{2x-5}{2x+6}  

d)

12-\frac{1}{2}  

97.

x+310x+20x+2x2+4x+3\frac{x+3}{10x+20}\cdot\frac{x+2}{x^2+4x+3}  

a)

x2+6x2+40x+60\frac{x^2+6}{x^2+40x+60}  

b)

2x+5x2+14x+23\frac{2x+5}{x^2+14x+23}  

c)

110x+1\frac{1}{10x+1}  

d)

110(x+1)\frac{1}{10\left(x+1\right)}  

98.

9x+18x22x83x126x\frac{9x+18}{x^2-2x-8}\cdot\frac{3x-12}{6x}  

a)

92x\frac{9}{2x}  

b)

27x6x\frac{27x}{6x}  

c)

12x+6x2+4x8\frac{12x+6}{x^2+4x-8}  

d)

6x30x28x8\frac{6x-30}{x^2-8x-8}  

99.

x25x+4x2÷x1x\frac{x^2-5x+4}{x^2}\div\frac{x-1}{x}  

a)

x4x3\frac{x-4}{x^3}  

b)

4-4  

c)

x4x\frac{x-4}{x}  

d)

x(x4)x2\frac{x\left(x-4\right)}{x^2}  

100.

x25x65x+15÷x23x47x+21\frac{x^2-5x-6}{5x+15}\div\frac{x^2-3x-4}{7x+21}  

a)

7x65x4\frac{7x-6}{5x-4}  

b)

7(x+2)(x+3)5(x4)\frac{7\left(x+2\right)\left(x+3\right)}{5\left(x-4\right)}  

c)

(x6)(x4)(x+1)235(x+3)2\frac{\left(x-6\right)\left(x-4\right)\left(x+1\right)^2}{35\left(x+3\right)^2}  

d)

7(x6)5(x4)\frac{7\left(x-6\right)}{5\left(x-4\right)}  

101.
Find the least common denominator of the expression
a)
18
b)
6x
c)
3xy
d)
6xy
102.
Simplify the expression
a)
6x / 20xy
b)
3 / 10y
c)
(6x+1) / (20xy)
d)
3 / 20xy
103.
Simplify the expression
a)
n / 2m 
b)
n / 3m 
c)
(m+ 4n2) / 12m
d)
n / 4m 
104.
Simplify the expression
a)
(5x + 4y) / 9y
b)
(6y + 3x) / 3y
c)
(2y + x) / y
d)
(6y + 3x) / 9y 
105.
a)

n - 1

b)

2(n - 1) / 2

c)

2(n - 1)

d)

1

106.
a)

7v2(v + 1) / 10

b)

(v + 1)

c)

1 / 10

d)

(v + 1) / 10

107.

Simplify:  36y72z\frac{36y}{72z}  

a)

4y9z\frac{4y}{9z}  

b)

y2z\frac{y}{2z}  

c)

2y3z\frac{2y}{3z}  

d)

18y38z\frac{18y}{38z}  

108.

Simplify: xyyx\frac{x-y}{y-x}  

a)

xyyx\frac{x-y}{y-x}  

b)

1x\frac{1}{-x}  

c)

1-1  

d)

1y\frac{-1}{y}  

109.

Simplify: b2b6b2+4b+4\frac{b^2-b-6}{b^2+4b+4}  

a)

b6b+4\frac{b-6}{b+4}  

b)

b+3b+2\frac{b+3}{b+2}  

c)

b+3b+4\frac{b+3}{b+4}  

d)

b3b+2\frac{b-3}{b+2}  

110.

Simplify: r3+j3r2ry+j2\frac{r^3+j^3}{r^2-ry+j^2}  

a)

r+jrj\frac{r+j}{r-j}  

b)

(r2+rj+j2)(r2j)\frac{\left(r^2+rj+j^2\right)}{\left(r-2j\right)}  

c)

r+jr+j  

d)

(r+j)(r2+rj+j2)(r2j)(r+j)\frac{\left(r+j\right)\left(r^2+rj+j^2\right)}{\left(r-2j\right)\left(r+j\right)}  

111.

Find the quotient: a243a÷5a2a2\frac{a^2-4}{3a}\div\frac{5a^2}{a-2}  

a)

5a(a+4)3\frac{5a\left(a+4\right)}{3}  

b)

a32a24a+815a3\frac{a^3-2a^2-4a+8}{15a^3}  

c)

5a2+20a3\frac{5a^2+20a}{3}  

d)

a36a+815a\frac{a^3-6a+8}{15a}  

112.

Write the following quotient in simplest form:

8(p1)p+3÷p1p+3\frac{8\left(p-1\right)}{p+3}\div\frac{p-1}{p+3}  

a)

88  

b)

8p1p+3\frac{8p-1}{p+3}  

c)

8(p1)(p+3)(p+3)(p1)\frac{8\left(p-1\right)\left(p+3\right)}{\left(p+3\right)\left(p-1\right)}  

d)

8(p1)(p+3) + (p1)(p+3)(p+3)(p1)\frac{8\left(p-1\right)\left(p+3\right)\ +\ \left(p-1\right)\left(p+3\right)}{\left(p+3\right)\left(p-1\right)}  

113.

a)

A

b)

B

c)

C

d)

D

114.
Simplify
a)
(x-9)/(x+9)
b)
1/(x-9)
c)
(x+9)
d)
1/(x+9)
115.
Simplify the expression
a)
n / 2m 
b)
n / 3m 
c)
(m+ 4n2) / 12m
d)
n / 4m 
116.

What do you call the vertical number line in a Rectangular Coordinate System?

a)

x-axis

b)

y-axis

c)

origin

d)

plane

117.

What do you call the center where x and y-axis intersect?

a)

point

b)

coordinate

c)

plane

d)

origin

118.

The Cartesian Plane is divided by a horizontal number line called what?

a)

plane

b)

y-axis

c)

x-axis

d)

coordinates

119.

In which quadrant is the point with coordinates (-3, -2)?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

120.

In which quadrant is the point with coordinates (7, -15)?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

121.

In which quadrant is the point with coordinates (1, 1)?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

122.

Which describes the order of the signs of an ordered pair in the second quadrant?

a)

positive, negative

b)

negative, positive

c)

positive, positive

d)

negative, negative

123.

Which describes the order of the signs of an ordered pair in the fourth quadrant?

a)

positive, negative

b)

negative, positive

c)

positive, positive

d)

negative, negative

124.

He is the proponent of Rectangular Coordinate System or also known as the Cartesian Plane.

a)

Pythagoras

b)

Rene Descartes

c)

Albert Einstein

d)

Isaac Newton

125.

How many quadrants are there in a coordinate plane?

a)

1

b)

3

c)

4

d)

5

126.
Which quadrant contains the point named by (2, 5)?
a)
Quadrant I
b)
Quadrant II
c)
Quadrant III
d)
Quadrant IV
127.
In which quadrant is the following point?
(-3, 12)
a)
Quadrant I
b)
Quadrant II
c)
Quadrant III
d)
Quadrant IV
128.
The vertical number line in the coordinate plane is called what? 
a)
y-axis
b)
origin
c)
quadrant
d)
x-axis
129.
The coordinate plane is divided by a horizontal number line called what? 
a)
y-axis
b)
origin
c)
x-axis
d)
quadrant
130.
The coordinates for the origin in the coordinate plane are________?
a)
(1,1)
b)
(0,0)
c)
(0,1)
d)
(1,0)
131.
Where is Point A on the coordinate plane?
a)
(7,4)
b)
(1,3)
c)
(9,3)
d)
(4,7)
132.
Ordered pair (0,0) is also known as the ___.
a)
y-axis
b)
x-axis
c)
origin
d)
I love Math!
133.
How many quadrants are in a coordinate plane?
a)
1
b)
2
c)
3
d)
4
134.
The __ - axis is vertical in the coordinate plane.
a)
X
b)
Y
c)
Z
d)
None of the above
135.
The __ - axis is the horizontal axis of the coordinate plane.  
a)
X
b)
Y
c)
Z
d)
None of the above
136.

a)

A(4, 5); B(-5, 5)

b)

A(4, 5); B(5, 5)

c)

A(4, 5); B(5, -5)

d)

A(5, 24); B(5, -5)

137.

a)

A(-4, 0); B(-2, -6)

b)

A(-4, 4); B(2, -6)

c)

A(4, 0); B(2, -6)

d)

A(-4, 0); B(2, -6)

138.

a)

G(-6, 28); H(-2, -7)

b)

G(6, -6); H(-2, -7)

c)

G(6, -2); H(-6, -2)

d)

G(6, -6); H(-7, -2)

139.

a)

A(5, -5); B(1, -2)

b)

A(-5, 5); B(0, 2)

c)

A(5, 5); B(0, 2)

d)

A(5, 5); B(0, -2)

140.

a)

C(3, 4); D(-3, 7)

b)

C(-6, 3); D(7, -3)

c)

C(-6, -3); D(3, -3)

d)

C(-6, 3); D(-3, 7)

141.

State the quadrant in which or axis on which the point is located.

(-10, -16)

a)

II

b)

IV

c)

III

d)

I

142.

(-15, 0)

a)

y-axis

b)

II

c)

x-axis

d)

IV

143.

(7, 7)

a)

II

b)

I

c)

III

d)

IV

144.

(-4.9, -3.1)

a)

II

b)

III

c)

I

d)

IV

145.

(0, -11)

a)

x-axis

b)

y-axis

c)

II

d)

III

146.

a)

A(4, 5); B(-5, 5)

b)

A(4, 5); B(5, 5)

c)

A(4, 5); B(5, -5)

d)

A(5, 24); B(5, -5)

147.

a)

A(-4, 0); B(-2, -6)

b)

A(-4, 4); B(2, -6)

c)

A(4, 0); B(2, -6)

d)

A(-4, 0); B(2, -6)

148.

a)

G(-6, 28); H(-2, -7)

b)

G(6, -6); H(-2, -7)

c)

G(6, -2); H(-6, -2)

d)

G(6, -6); H(-7, -2)

149.

a)

A(5, -5); B(1, -2)

b)

A(-5, 5); B(0, 2)

c)

A(5, 5); B(0, 2)

d)

A(5, 5); B(0, -2)

150.

a)

C(3, 4); D(-3, 7)

b)

C(-6, 3); D(7, -3)

c)

C(-6, -3); D(3, -3)

d)

C(-6, 3); D(-3, 7)

151.

State the quadrant in which or axis on which the point is located.

(-10, -16)

a)

II

b)

IV

c)

III

d)

I

152.

(-15, 0)

a)

y-axis

b)

II

c)

x-axis

d)

IV

153.

(7, 7)

a)

II

b)

I

c)

III

d)

IV

154.

(-4.9, -3.1)

a)

II

b)

III

c)

I

d)

IV

155.

(0, -11)

a)

x-axis

b)

y-axis

c)

II

d)

III

156.
What is at (1,2)?
a)
the moon
b)
the sun
c)
a blue planet
d)
a robot
157.
Ordered pair (0,0) is also known as the ___.
a)
y-axis
b)
x-axis
c)
origin
d)
I love Math!
158.
In an ordered pair the first number represents which axis?
a)
x
b)
y
c)
z
d)
w
159.
In the ordered pair (4,9), which number is the y-coordinate?
a)
4
b)
9
c)
neither
d)
both
160.
How do you write an ordered pair?
a)
(X,X)
b)
(Y,X)
c)
(X,Y)
d)
(Y,Y)
161.
In which quadrant is the following point found?
(-3, -12)
a)
Quadrant I
b)
Quadrant II
c)
Quadrant III
d)
Quadrant IV
162.
If you were to plot the point (4, -12) what would be the correct method?
a)
Up 4, left 12
b)
Right 4, up 12
c)
Down 4, left 12
d)
Right 4, down 12
163.
What is the vertical number line in the coordinate plane called? 
a)
y-axis
b)
origin
c)
quadrant
d)
x-axis
164.

The horizontal axis is called __________.

a)

x - axis

b)

y - axis

165.

The vertical axis is called __________

a)

x - axis

b)

y - axis

166.

The first number in an ordered pair is called __________.

a)

x - coordinate

b)

y - coordinate

167.

The second number in an ordered pair is called __________.

a)

x - coordinate

b)

y - coordinate

168.

Point (0, 0) where the x-axis and y-axis intersect is called __________.

a)

Coordinate

b)

Origin

169.

The ordered pair (4, 7) lies on quadrant _____.

a)

I

b)

II

c)

III

d)

IV

170.

The ordered pair (3, -2) lies on quadrant _____.

a)

I

b)

II

c)

III

d)

IV

171.

The ordered pair ( -5, 2 ) lies on quadrant _____.

a)

I

b)

II

c)

III

d)

IV

172.

The ordered pair pair ( -1, 7) lies on quadrant _____.

a)

I

b)

II

c)

III

d)

IV

173.

The ordered pair ( -3, -1) lies on quadrant _____.

a)

I

b)

II

c)

III

d)

IV

174.
Which axis runs horizontally?
a)
x
b)
y
175.

How do you write a pair of coordinates?

a)

(X,X)

b)

(Y,X)

c)

(X,Y)

d)

(Y,Y)

176.

In a pair of coordinates the first number represents which axis?

a)

x

b)

y

177.

In the coordinate (4,9), which number is the y-coordinate?

a)

4

b)

9

c)

neither

d)

both

178.

What is the coordinate of this point?

a)

(8, 2)

b)

(2,7)

c)

(2,8)

d)

(8,3)

179.

In the coordinate point (2,7) the 2 represents

a)

y

b)

origin

c)

x

d)

point

180.
The coordinate (0,0) is also known as the ___.
a)
y-axis
b)
x-axis
c)
origin
181.
Where is point E located?
a)
( 2, 0 )
b)
( 2 , 2 )
c)
( 0 , 2 )
d)
( 0 , 0 )
182.
Where is T?
a)
(-3, -2)
b)
(-2,-3)
c)
(3,2)
d)
(-3,2)
183.

The coordinate (4, -3) is in which quadrant?

a)

Quadrant 1

b)

Quadrant 2

c)

Quadrant 3

d)

Quadrant 4

184.

In which quadrant is the point A located?

a)

1st Quadrant

b)

2nd Quadrant

c)

3rd Quadrant

d)

4th Quadrant

185.

In which quadrant is the point A located?

a)

1st Quadrant

b)

2nd Quadrant

c)

3rd Quadrant

d)

4th Quadrant

186.
What is at (1,2)?
a)
the moon
b)
the sun
c)
a blue planet
d)
a robot
187.
In an ordered pair the first number represents which axis?
a)
x
b)
y
c)
z
d)
w
188.
In which quadrant is the following point found?
(-3, -12)
a)
Quadrant I
b)
Quadrant II
c)
Quadrant III
d)
Quadrant IV