Font size
WorksheetsRational -Je
Total questions: 188
Worksheet time: 14hrs 38mins
(x−2)(x+5)2x(x−2)
State the values of x which must be excluded to prevent division by zero.
-2 and 5
2 and -5
0, 2, and -5
0, -2, and 5
n2 + 5n - 6
Simplify
x−9x+9
(x−9)1
x−9
(x+9)1
x+9
Simplify.
m−3m+6
m−37
m+67
m+61
Simplify and make sure final answer is in standard form.
A
B
C
D
Simplify: x2−49x2+6x−7
x+7x−1
x+7x+1
x−7x−1
x−7x+1
Simplify.
n−71
n−7
(n−7)(n−6)
n−6
Simplify: x2+3x−18x2+6x
x+3x
x−3x
x−3x+6
x+6x
Simplify: x2+4xx2+7x+12
x+4x+3
xx−3
xx+3
x2x+3
Simplify: x2−81x2−4x−45
x−9x+5
x+9x+5
x−9x−5
x+9x−5
3x2 + 18x +15
Hint: Factor GCF first.
Simplify: x2−4x2+7x+10
x+2x−5
x−2x−5
x+2x+5
x−2x+5
3v2 - 4v - 7
Simplify: x2−6x+5x2−25
x−1x+5
x−1x−5
x+1x+5
x+1x−5
25x2 - 81?
We can't factor using difference of two square this
49x2 + 4y2. Why?
Because 4 is not a perfect cubed number.
Because 4 is not a perfect squared number.
Because 49 is not a perfect squared number.
Because we can't factor using difference of two squares if it is addition sign.
Find the domain of the function. f(x)=x2−1213x
{x=−6,5}
{x=121}
{x=11}
{x=−11,11}
Find the excluded value(s).
n = 0
n = 24
n = -24
n can be any real number
Find the excluded value(s).
a = 0
a = 10
a = 1
a = -1
Find the excluded value(s).
v = 5
v = 10
v = -25
v = -5
What are the domain restrictions of the following rational expression:
x ≠ 4
x ≠ -4, 4
x ≠ -16, 16
x ≠ 0, 4
What is an excluded value?
A value that makes the denominator equal to 0
A number that makes the numerator equal to 0
The solution
An ostracized number
Determine the excluded values.
x = 0, 3
x = 0, -3
x = 0, -3, 5
x = 0, 3, 5
Determine the excluded values.
x = 5, -1
x = -5, 1
x = 5, 1
x = -5, -1
Determine the excluded value.
x = 6
x = 0
x = -6
x = -6, 9
Determine the excluded values.
x = 0
x = 2, 6
x = -2, -6
x = 0, -2, -6
(7-m)
(x2-49)/(x2+9x+14)
(x2+6x+8)/(x2-x-6)
Simplify
(8x + 32)/( x+4)
8/(x - 4)
-x/(x - 4)
-8
8
7 / (x - 3)
(2x2-98)/(2x2+18x+28)
Simplify the expression
1
-1
Can't be simplified
(7-m)
Simplify
(8x + 32)/( x+4)
8/(x - 4)
-x/(x - 4)
-8
8
Simplify: x2−49x2+6x−7
x+7x−1
x+7x+1
x−7x−1
x−7x+1
Simplify: x2+3x−18x2+6x
x+3x
x−3x
x−3x+6
x+6x
Simplify: x2−4x2+7x+10
x+2x−5
x−2x−5
x+2x+5
x−2x+5
Simplify: x2−6x+5x2−25
x−1x+5
x−1x−5
x+1x+5
x+1x−5
Simplify: x2−81x2−4x−45
x−9x+5
x+9x+5
x−9x−5
x+9x−5
x+2x−3
x−3x+2
8x−3
4x−3
x−4x−9
x+4x−9
Simplify: x4y15x8y12
y3x4
y3x12
x12y27
x4y3
Simplify: 20a5c45a3c10
a24c6
41a2c6
4a21c6
4c61a2
Simplify: x4y15x8y12
y3x4
y3x12
x12y27
x4y3
Simplify: x2+3x−18x2+6x
x+3x
x−3x
x−3x+6
x+6x
Simplify: x2−49x2+6x−7
x+7x−1
x+7x+1
x−7x−1
x−7x+1
Which of the following statement describes a rational algebraic expression?
It is the reverse process of multiplication.
Fraction which numerator and denominator are polynomials
Fraction which numerator and denominator are whole numbers
It cannot be factored using only integers
x2 − 163x + 4 − x2−162x=
1
x2−16x+4
x−41
x+41
x+3x+x+33=
x2
x + 33x
1
3x3x
Identify the given if it is rational expression or not.
rational expression
not rational expression
Which value of x is not allowed in the expression
x−5x2−x−12 ?0
-3
4
5
For what value of x will the expression
2x+4x+2 be undefined?-1/2
-1
-2
-4
Add:
xx−1
xx2+2
x −1x +1
x −1x+2
Simplify: x4y15x8y12
y3x4
y3x12
x12y27
x4y3
Simplify: 20a5c45a3c10
a24c6
41a2c6
4a21c6
4c61a2
Simplify: x2−49x2+6x−7
x+7x−1
x+7x+1
x−7x−1
x−7x+1
Which of the following is NOT a rational algebraic expression?
x3
6a+4
x2+2xy
5
Give the domain of y−2y+2
all real numbers except −1
all real numbers except 1
all real numbers except −2
all real numbers except 2
z2+5z8−y
Give the values for which the given rational expression is undefined?
z=0 and z=5
z =0 and z=−5
z=0 and z=−1
z=0 and z=1
x+3x+x+33=
x2
x + 33x
1
3x3x
x2 − 163x + 4 − x2−162x=
1
x2−16x+4
x−41
x+41
4 / 7v2
4 / 7v
20 / 35v
20 / 35v2
7(r + 2)/ (r + 2)
(r - 8) / (r + 2)
(r + 2) / 7
(r - 8) / 7
A rational expression is said to be in lowest terms when its numerator and denominator have no common factors other than _____.
1
2
3
4
What is x−2y2yless than 2y−x2x?
x−2y2x+2y
-1
x−2y2x−2y
Divide3v2+12v2−9by v2+4v+3
3v−3
3v+3
(v+3)(v-3)
3
Add:
xx−1
xx2+2
x −1x +1
x −1x+2
x−1x+3+(x−1)(x+5)x−11
x2+9x+4x2+4x−5
(x+5)(x−1)x2+9x+4
x2+5x−62x−8
3x+32x−8
x+8x−5−x−2x
(x+8)(x−2)−15x+10
(x+8)(x−2)2x2+x+10
2x+62x−5
−21
10x+20x+3⋅x2+4x+3x+2
x2+40x+60x2+6
x2+14x+232x+5
10x+11
10(x+1)1
x2−2x−89x+18⋅6x3x−12
2x9
6x27x
x2+4x−812x+6
x2−8x−86x−30
x2x2−5x+4÷xx−1
x3x−4
−4
xx−4
x2x(x−4)
5x+15x2−5x−6÷7x+21x2−3x−4
5x−47x−6
5(x−4)7(x+2)(x+3)
35(x+3)2(x−6)(x−4)(x+1)2
5(x−4)7(x−6)
n - 1
2(n - 1) / 2
2(n - 1)
1
7v2(v + 1) / 10
(v + 1)
1 / 10
(v + 1) / 10
Simplify: 72z36y
9z4y
2zy
3z2y
38z18y
Simplify: y−xx−y
y−xx−y
−x1
−1
y−1
Simplify: b2+4b+4b2−b−6
b+4b−6
b+2b+3
b+4b+3
b+2b−3
Simplify: r2−ry+j2r3+j3
r−jr+j
(r−2j)(r2+rj+j2)
r+j
(r−2j)(r+j)(r+j)(r2+rj+j2)
Find the quotient: 3aa2−4÷a−25a2
35a(a+4)
15a3a3−2a2−4a+8
35a2+20a
15aa3−6a+8
Write the following quotient in simplest form:
p+38(p−1)÷p+3p−1
8
p+38p−1
(p+3)(p−1)8(p−1)(p+3)
(p+3)(p−1)8(p−1)(p+3) + (p−1)(p+3)
A
B
C
D
What do you call the vertical number line in a Rectangular Coordinate System?
x-axis
y-axis
origin
plane
What do you call the center where x and y-axis intersect?
point
coordinate
plane
origin
The Cartesian Plane is divided by a horizontal number line called what?
plane
y-axis
x-axis
coordinates
In which quadrant is the point with coordinates (-3, -2)?
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
In which quadrant is the point with coordinates (7, -15)?
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
In which quadrant is the point with coordinates (1, 1)?
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
Which describes the order of the signs of an ordered pair in the second quadrant?
positive, negative
negative, positive
positive, positive
negative, negative
Which describes the order of the signs of an ordered pair in the fourth quadrant?
positive, negative
negative, positive
positive, positive
negative, negative
He is the proponent of Rectangular Coordinate System or also known as the Cartesian Plane.
Pythagoras
Rene Descartes
Albert Einstein
Isaac Newton
How many quadrants are there in a coordinate plane?
1
3
4
5
(-3, 12)
A(4, 5); B(-5, 5)
A(4, 5); B(5, 5)
A(4, 5); B(5, -5)
A(5, 24); B(5, -5)
A(-4, 0); B(-2, -6)
A(-4, 4); B(2, -6)
A(4, 0); B(2, -6)
A(-4, 0); B(2, -6)
G(-6, 28); H(-2, -7)
G(6, -6); H(-2, -7)
G(6, -2); H(-6, -2)
G(6, -6); H(-7, -2)
A(5, -5); B(1, -2)
A(-5, 5); B(0, 2)
A(5, 5); B(0, 2)
A(5, 5); B(0, -2)
C(3, 4); D(-3, 7)
C(-6, 3); D(7, -3)
C(-6, -3); D(3, -3)
C(-6, 3); D(-3, 7)
State the quadrant in which or axis on which the point is located.
(-10, -16)
II
IV
III
I
(-15, 0)
y-axis
II
x-axis
IV
(7, 7)
II
I
III
IV
(-4.9, -3.1)
II
III
I
IV
(0, -11)
x-axis
y-axis
II
III
A(4, 5); B(-5, 5)
A(4, 5); B(5, 5)
A(4, 5); B(5, -5)
A(5, 24); B(5, -5)
A(-4, 0); B(-2, -6)
A(-4, 4); B(2, -6)
A(4, 0); B(2, -6)
A(-4, 0); B(2, -6)
G(-6, 28); H(-2, -7)
G(6, -6); H(-2, -7)
G(6, -2); H(-6, -2)
G(6, -6); H(-7, -2)
A(5, -5); B(1, -2)
A(-5, 5); B(0, 2)
A(5, 5); B(0, 2)
A(5, 5); B(0, -2)
C(3, 4); D(-3, 7)
C(-6, 3); D(7, -3)
C(-6, -3); D(3, -3)
C(-6, 3); D(-3, 7)
State the quadrant in which or axis on which the point is located.
(-10, -16)
II
IV
III
I
(-15, 0)
y-axis
II
x-axis
IV
(7, 7)
II
I
III
IV
(-4.9, -3.1)
II
III
I
IV
(0, -11)
x-axis
y-axis
II
III
(-3, -12)
The horizontal axis is called __________.
x - axis
y - axis
The vertical axis is called __________
x - axis
y - axis
The first number in an ordered pair is called __________.
x - coordinate
y - coordinate
The second number in an ordered pair is called __________.
x - coordinate
y - coordinate
Point (0, 0) where the x-axis and y-axis intersect is called __________.
Coordinate
Origin
The ordered pair (4, 7) lies on quadrant _____.
I
II
III
IV
The ordered pair (3, -2) lies on quadrant _____.
I
II
III
IV
The ordered pair ( -5, 2 ) lies on quadrant _____.
I
II
III
IV
The ordered pair pair ( -1, 7) lies on quadrant _____.
I
II
III
IV
The ordered pair ( -3, -1) lies on quadrant _____.
I
II
III
IV
How do you write a pair of coordinates?
(X,X)
(Y,X)
(X,Y)
(Y,Y)
In a pair of coordinates the first number represents which axis?
x
y
In the coordinate (4,9), which number is the y-coordinate?
4
9
neither
both
What is the coordinate of this point?
(8, 2)
(2,7)
(2,8)
(8,3)
In the coordinate point (2,7) the 2 represents
y
origin
x
point
The coordinate (4, -3) is in which quadrant?
Quadrant 1
Quadrant 2
Quadrant 3
Quadrant 4
In which quadrant is the point A located?
1st Quadrant
2nd Quadrant
3rd Quadrant
4th Quadrant
In which quadrant is the point A located?
1st Quadrant
2nd Quadrant
3rd Quadrant
4th Quadrant
(-3, -12)
