Free Printable Periodical Test

1.

Factor

8a^3-27

using difference of two cubes.

a)

$\left(2a-3\right)\left(4a^2+12a+9\right)$

b)

$\left(2a-3\right)\left(4a^2-6a+9\right)$

c)

$\left(2a-3\right)\left(4a^{2\ }+6a+9\right)$

d)

$\left(2a-3\right)\left(4a^{2\ }-12a+9\right)$

2.

To simplify

m^3\left(m^2\right)

, we need to apply the product of (a) .

3.

Monomial: xyz; (a) :

xy+z

.

4.

The result if you expand

\left(4m-n\right)^2

is a (a) .

5.

A polynomial which has no other factors other than 1 and itself.

(a)

6.

The common factor of the polynomial $5m^3n^2+40n^7+10n^3$ is a (a) .

7.

Simplify 6v(2v + 3).

a)

12v+18

b)

12v² + 18v

c)

15v² + 8v

d)

12v² + 18v²

8.

Simplify 2x ( -2x -3).

a)

-4x - 3

b)

x² - 3

c)

-4x² - 6x

d)

-4x - 6

9.

Simplify (4x - 1)(5x−2) using FOIL method.

a)

20x² + 3x − 2

b)

20x² − 11x + 5

c)

20x² − 13x + 2

d)

20x² − 3x − 2

10.

What is the simplified form of (4x+1)(5x−2)?

a)

20x² + 3x − 2

b)

20x² − 11x + 5

c)

20x² − 18x + 2

d)

20x² − 3x − 2

11.

Simplify: (x + 3) (x + 2)

a)

x² + 6x + 5

b)

x² + 5

c)

x² + 11

d)

x² + 5x + 6

12.

Simplify: (2x + y)(2x - y)

a)

4x² - y²

b)

4x - y

c)

4x² + y²

d)

2x² - y²

13.

Find the product using the distributive property.

-8x ( 4x² - 9x + 12)

a)

-32x² - 72x + 96

b)

-32x³ - 72x² - 96x

c)

-32x³ + 72x² - 96

d)

-32x³ + 72x² - 96x

14.

Multiply these monomials.

-12x⁴ ⋅ 11x

a)

132x⁴

b)

-132x⁴

c)

132x⁵

d)

-132x⁵

15.

Simplify (x+4)²

a)

x²+16

b)

x²-16

c)

x²+8x+16

d)

x²+8x-16

16.

Find the product of (7r+6)(7r+6) using distributive property.

a)

49r²+36

b)

49r²-36

c)

49r²+84r+36

d)

49r²+42r+36

17.

Simplify (3m + 1)(3m – 1).

a)

9m²– 1

b)

9m²– 6m – 1

c)

9m²+ 1

d)

9m²+ 6m – 1

18.

Simplify (-3m-1)(3m-1).

a)

-9m²+1

b)

-9m²-6m+1

c)

-9m²-1

d)

-9m²-6m+1

19.

What is the greatest common factor of the monomials a²b⁵ and a³b³

a)

a²b³

b)

a²b⁵

c)

a³b³

d)

a³b⁵

20.

What is the Greatest Common Factor of the following polynomial?
12t³ + 30t² + 48t

a)

12t

b)

6t³

c)

6t

d)

12t³

21.

Find the greatest common factor of 6x⁴y³- 12x⁴y²+ 6x³y²

a)

6

b)

6xy

c)

6x³y²

d)

6x⁹y⁶

22.

Which of the following is a good definition for the Greatest Common Factor of a polynomial?

a)

The constants and variables that are the smallest

b)

The constants and variables that are the largest

c)

The largest combination of constants and variables you can "pull out" of a polynomial

d)

The common factor that is the greatest

23.

Factor 5ab²c¹¹ + 2bc⁵

a)

bc⁵(5ab²c⁶ + 2b)

b)

bc⁵(5abc⁶ + 2)

c)

b²c⁵(5bc⁶ + 2)

d)

c4(5a²b²c⁷+ 2bc)

24.

Factor 10x² + 15x-5

a)

25(10x³+45x-15)

b)

5(2x³ + 3x²-x)

c)

x(10x³+15x-5)

d)

5(2x²+3x-1)

25.

Factor 2n³+16n+12.

a)

2n(n³+24n+6)

b)

2(n³+8n+6)

c)

2n(n³+8n+6)

d)

3(n³+8n+6)

26.

Find the factor of 169x²y⁶ - 196w⁴z⁸ using difference of two square.

a)

(13xy³ + 14w²z⁴) (13xy³ - 14w²z⁴)

b)

(13xy² + 14w³z⁴) (13xy² - 14w³z⁴)

c)

(13xy⁶ + 14w²z⁴) (13xy⁶ - 14w²z⁴)

d)

(13x²y + 14w³z⁴) (13x²y - 14w³z⁴)

27.

Factor 121x²y⁶z⁸ - 225w⁴using difference of two square.

a)

(11xy⁴z⁴ + 15w) (11xy²z⁴ - 15w)

b)

(11x²y³z⁴ + 15w) (11x²y³z⁴ - 15w)

c)

(11xy³z⁴ + 15w²) (11xy³z⁴ - 15w²)

d)

(11xy³z + 15w²) (11xy³z³ - 15w²)

28.

We can't factor using difference of two square this 25x² - 51y². Why?

a)

Because 51 is not a perfect cubed number.

b)

Because 51 is not a perfect squared number.

c)

Because 25 is not a perfect squared number.

d)

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

29.

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.

30.

Which of these can factor using difference of two squares?

a)

144x² - 49y²

b)

x² + 4x - 12

c)

100x² + 20x + 1

d)

14x - 16

31.

Simplify

\frac{x^2+11x+24}{x^2+4x-32}

.

a)

$\frac{x+7}{x+4}$

b)

$\frac{3}{4}$

c)

$\frac{x+3}{x+4}$

d)

$\frac{x+3}{x-4}$

32.

Simplify
$\frac{x+9}{x^2-81}$ .

a)

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

b)

$\frac{1}{x-9}$

c)

$x+9$

d)

$\frac{1}{x+9}$

33.

Simplify

\frac{x^2+10x+24}{x^2-x-20}

.

a)

$\frac{x+6}{x+4}$

b)

$\left(x+6\right)\left(x+4\right)$

c)

$x+6$

d)

$\frac{x+6}{x-5}$

34.

$\ Simplify\ \frac{25x^5y^4}{5x^8y^2}.$

a)

b)

c)

d)

35.

What is/are the non-permissible value(s) for this expression?

a)

x ≠ 0

b)

x ≠ 0 and y ≠ 0

c)

y ≠ 0

d)

x ≠ 0, x ≠ 0, and 5 ≠ 0

36.

What is/are the non-permissible value(s) for this expression?

a)

m ≠ -6

b)

m ≠ -6, 3

c)

m ≠ 3

d)

m ≠ 6, -3

37.

Simplify

a)

b)

c)

-8

d)

8

38.

Simplify the rational expression and identify the excluded values.
$\frac{xy^3}{x^2y}$

a)

$\frac{xy}{x};\ x\ne0$

b)

$\frac{y^2}{x};x\ne0$

c)

$xy^2;\ x\ne0$

d)

$\frac{y^2}{x};x\ne0;y\ne0$

39.

$\frac{x^2y}{xy}$ Simplify the rational expression and state the excluded values.

a)

$\frac{x}{y};\ x\ne0;y\ne0$

b)

$\frac{x}{y};y\ne0$

c)

$x;x\ne0;y\ne0$

d)

$x^2;y\ne0$

40.

$\frac{5ab^3}{10ab^4}$ Simplify the rational expression and state the excluded values.

a)

$\frac{1}{2b};a\ne0;b\ne0$

b)

$\frac{b}{2};b\ne0$

c)

$\frac{a}{2b};a\ne0;b\ne0$

d)

$\frac{a}{2};none$

41.

$\frac{12a^2b}{4a^3b}$ Simplify the rational expression and state the excluded values.

a)

$\frac{3b}{a};a\ne0$

b)

$\frac{3b}{a};a\ne0;b\ne0$

c)

$\frac{3}{a};a\ne0$

d)

$\frac{3}{a};a\ne0;b\ne0$

42.

$\frac{15xy^3z}{25x^2y^2z}$ Simplify the rational expression and state the excluded values.

a)

$\frac{y}{5x};x\ne0;y\ne0$

b)

$\frac{3yz}{5x};x\ne0$

c)

$\frac{3y}{5x};x\ne0;y\ne0;z\ne0$

d)

$\frac{3yz}{x};x\ne0;y\ne0;z\ne0$

43.

$\frac{8ab^2c^3}{36a^2bc^2}$ Simplify the rational expression and state the excluded values.

a)

$\frac{bc}{4a};a\ne0$

b)

$\frac{2bc}{9a};a\ne0;b\ne0;c\ne0$

c)

$\frac{2c}{6a};a\ne0$

d)

$\frac{2c}{9ab};a\ne0;b\ne0;c\ne0$

44.

$\frac{18\left(x-4\right)}{48\left(x-4\right)}$ Simplify the rational expression and state the excluded values.

a)

$\frac{18}{x-4};x\ne\left\{0,4\right\}$

b)

$\frac{3}{x-4};x\ne\left\{3,4\right\}$

c)

$\frac{3}{8};x\ne\left\{0,-4\right\}$

d)

$\frac{3}{8};x\ne4$

45.

$\frac{48\left(x+3\right)}{60\left(x+3\right)}$ Simplify the rational expression and state the excluded values.

a)

$\frac{12}{15};x\ne3$

b)

$\frac{12}{15};x\ne-3$

c)

$\frac{4}{5};x\ne3$

d)

$\frac{4}{5};x\ne-3$

46.

$\frac{\left(x-2\right)\left(x+1\right)}{\left(x-2\right)\left(x-1\right)}$ Simplify the rational expression and state the excluded values.

a)

$1;x\ne\left\{1,2\right\}$

b)

$\frac{x+1}{x-1};x\ne1$

c)

$\frac{1}{x-1};x\ne\left\{-1.-2\right\}$

d)

$\frac{x+1}{x-1};x\ne\left\{1,2\right\}$

47.

$\frac{\left(x+5\right)\left(x-3\right)}{\left(x-4\right)\left(x-3\right)}$ Simplify the rational expression and state the excluded values.

a)

$\frac{x+5}{x-4};x\ne4$

b)

$\frac{x+5}{x-4};x\ne-4$

c)

$\frac{x+5}{x-4};x\ne\left\{-4,-3\right\}$

d)

$\frac{x+5}{x-4};x\ne\left\{3,4\right\}$

48.

$\frac{x-2}{x^2-4}$ Simplify the rational expression and state the excluded values.

a)

$\frac{1}{x+2};x\ne2$

b)

$\frac{1}{x+2};x\ne\left\{-2,2\right\}$

c)

$\frac{1}{x-2};x\ne4$

d)

$\frac{1}{x+2};x\ne4$

49.

$\frac{a+3}{a^2-9}$ Simplify the rational expression and state the excluded values.

a)

$\frac{a+3}{a-3};a\ne9$

b)

$\frac{1}{a-3};a\ne\left\{3,-3\right\}$

c)

$\frac{1}{a+3};a\ne\left\{-3,3\right\}$

d)

$\frac{-1}{a-3};a\ne\left\{-3,3\right\}$

50.

$\frac{x-4}{16-x^2}$ Simplify the rational expression and state the excluded values.

a)

$\frac{-1}{4-x};x\ne16$

b)

$\frac{-1}{x+4};x\ne\left\{-4,4\right\}$

c)

$\frac{x-4}{\left(4-x\right)\left(4+x\right)};x\ne\left\{-4,4\right\}$

d)

$\frac{x-4}{4+x};x\ne\left\{-4,4\right\}$

51.

$\frac{x^3-8}{2-x}$ Simplify the rational expression and state the excluded values.

a)

$x+2;x\ne2$

b)

$x^2+2x+4;x\ne2$

c)

$\frac{x^2+4}{2-x};x\ne2$

d)

$-x^2-2x-4;x\ne2$

52.

Simplify the rational expression and state the excluded values.
$\frac{20-30x}{3x^2-2x}$

a)

$\frac{10\left(2-3x\right)}{x\left(3x-2\right)};x\ne-\frac{2}{3}$

b)

$\frac{10}{x};x\ne\frac{2}{3}$

c)

$\frac{-10}{x};x\ne\left\{\frac{2}{3},0\right\}$

d)

$\frac{10}{-x};x\ne0$

53.

$\frac{15-3x}{2x^2-10x}$ Simplify the rational expression and state the excluded values.

a)

$\frac{-3}{2x};x\ne\left\{-5,0\right\}$

b)

$\frac{3}{2x};x\ne\left\{-5,0\right\}$

c)

$\frac{-3}{2x};x\ne\left\{5,0\right\}$

d)

$\frac{3\left(5-x\right)}{2x\left(x-5\right)};\ x\ne\left\{0,5\right\}$

54.

$\frac{x^2-1}{2x^2+x-3}$ Simplify the rational expression and state the excluded values.

a)

$\frac{\left(x+1\right)}{\left(2x+3\right)};x\ne\left\{-\frac{3}{2},1\right\}$

b)

$\frac{1}{2x+3};x\ne\left\{-\frac{3}{2},1\right\}$

c)

$\frac{x-1}{2x+3};x\ne\left\{-\frac{2}{3},1\right\}$

d)

$\frac{1}{2x+3};x\ne-\frac{2}{3}$

55.

$\frac{x^2-4x+4}{x^2-4}$ Simplify the rational expression and state the excluded values.

a)

$x+4;x\ne4$

b)

$\frac{\left(x-2\right)}{\left(x+2\right)};x\ne\left\{-2,2\right\}$

c)

$\frac{x-2}{x+2};x\ne\left\{0,-2\right\}$

d)

$\frac{x+1}{x};x\ne\left\{0,4\right\}$

56.

Simplify the expression below

$\frac{6y\left(y+3\left(y-5\right)\right)}{y\left(y-5\right)\left(y-1\right)}$

a)

$\frac{6\left(y-5\right)}{y\left(y-1\right)}$

b)

$\frac{6y\left(y+3\right)}{y\left(y-1\right)}$

c)

$\frac{y\left(y-1\right)}{6\left(y+3\right)}$

d)

$\frac{y\left(y+3\right)}{6y\left(y-1\right)}$

57.

simplify the expression below:

$\frac{45}{10a-10}$

a)

$\frac{9}{2\left(a-1\right)}$

b)

$\frac{5}{10a}$

c)

$\frac{9}{2\left(1-a\right)}$

d)

$\frac{5}{2\left(a-1\right)}$

58.

For what values of x is $\frac{6x+4}{\left(x-4\right)\left(x+5\right)}$ undefined?

a)

x= 4 and x= 5

b)

x = 4 and x = -5

c)

x = -4 and x = 5

d)

x = 1 and x = -1

59.

Simplify the expression below:

$\frac{xy^2-4xy}{\left(y-4\right)\left(y+4\right)}$

a)

$\frac{x\left(y-4\right)}{\left(y+4\right)}$

b)

$\frac{xy\left(y-4\right)}{y+4}$

c)

$\frac{xy}{y+4}$

d)

$\frac{xy}{y-4}$

60.

Multiply the rational expressions

$\frac{3}{5}\times\frac{16}{3}$ =

a)

$\frac{6}{5}$

b)

$\frac{12}{5}$

c)

$\frac{4}{10}$

d)

$\frac{16}{5}$

61.

Divide the expression below:
$\frac{2}{9}\div\frac{4}{13}=$

a)

$\frac{8}{117}$

b)

$\frac{13}{18}$

c)

$\frac{6}{4}$

d)

$\frac{3}{5}$

62.

Multiply the following rational expression:
$\frac{8x}{3x^2y^2}\ \times\frac{9x^2y}{4a}=$

a)

$\frac{6x}{ay}$

b)

$\frac{6}{a}$

c)

$\frac{9x}{y}$

d)

$\frac{6x}{9y}$

63.

Divide the following rational expression:
$\frac{6xy^3}{8ab^2}\div\frac{3x^2y}{4ab^2}=$

a)

$y^2$

b)

$\frac{1}{x}$

c)

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

d)

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

64.

Simplify the expression:
$\frac{\left(x+10\right)}{3x\left(x+10\right)}=$

a)

$\frac{1}{3x}$

b)

$3x$

c)

$x+10$

d)

$3x^2+30x$

65.

Which property does this represent: $3(9+4)=3\cdot9+3\cdot4$

a)

Commutative Property of Addition

b)

Distributive Property

c)

Associative Property of Multiplication

d)

Addition Property of Equality

66.

Will the answer be positive or negative?
-2 × (-5) × (-1) × (-9)

a)

Positive

b)

Negative

67.

Which operation would you do first?
( 12 + 10) ÷ 10 · 14 - 6

a)

Division

b)

Multiplication

c)

Addition

d)

Subtraction

68.

Which of the following is undefined?

a)

7

b)

$\frac{1}{2}$

c)

$\frac{3}{4}$

d)

$\frac{9}{0}$

69.

Find the least common denominator of the expression

a)

18

b)

6x

c)

3xy

d)

6xy

70.

Simplify the expression

a)

$\frac{6x}{20xy}$

b)

$\frac{3}{10y}$

c)

$\frac{6x+1}{20xy}$

d)

$\frac{3}{20xy}$

71.

Simplify the expression

a)

$\frac{n}{2m}$

b)

$\frac{n}{3m}$

c)

$\frac{m^2+4n^2}{12m}$

d)

$\frac{n}{4m}$

72.

Simplify the expression

a)

$\frac{2a+4b}{12b^2}$

b)

$\frac{2a-4b}{12b^2}$

c)

$\frac{a-b}{6b^2}$

d)

$\frac{a+2b}{6b^2}$

73.

Simplify the expression

a)

(5x + 4y) / 9y

b)

(6y + 3x) / 3y

c)

(2y + x) / y

d)

(6y + 3x) / 9y

74.

Simplify the expression

a)

(-17x - 12y) / 15x

b)

(23x - 4y) / 15x

c)

(-17x - 4y) / 15x

d)

(-3x - 4y) / 8x

75.

Simplify the expression

a)

(30ab³ + 8a) / 10b³

b)

(15ab³ + 4a) / 5b³

c)

10a / 7b³

d)

(10a) / (5b³ + 2)

76.

Simplify the expression

a)

(4 - 2ab² + 3b³) / 4b²

b)

(4a - 2a²b² + 3ab³) / 4ab²

c)

(4 - 2ab² - 3b³) / 4b²

d)

(4a - 2a²b² - 3ab³) / 4ab²

77.

Simplify the expression

a)

(19k² -12k - 12) / 4k(5k-4)

b)

(19k² - 24k) / 4k(5k-4)

c)

(19k) / 4(5k-4)

d)

(19k - 24) / 4(5k-4)

78.

Simplify the expression

a)

(12n² + 28n + 4) / (2n-5)(n+2)

b)

(12n² - 28n + 4) / (2n-5)(n+2)

c)

(8n) / (3n + 3)

d)

(12n² + 2n -3) / (2n-5)(n+2)

79.

Solve for v.

a)

60

b)

-3

c)

15

d)

3

80.

solve for x.

a)

x= 9 1/3

b)

x = 21/4

c)

x = 5 1/4

d)

None of the above

81.

solve for k.

a)

7

b)

-16

c)

4

d)

-15

82.

Solve the equation for x.

a)

6

b)

12

c)

0

d)

3

83.

solve for x.

a)

6/10

b)

1

c)

0

d)

9/25

84.

solve for v

a)

24

b)

-4

c)

33

d)

15

85.

Solve for x.

a)

-11

b)

11

c)

0

d)

10

86.

solve for m.

a)

30

b)

43

c)

46

d)

54

87.

Clear the equation to solve.

a)

1

b)

2

c)

4.67

d)

12

88.

solve for x.

a)

-49

b)

153/5

c)

49

d)

85

89.

Solve for x.

a)

4 ¾

b)

3 ⅓

c)

5 ⅜

d)

3 ⅙

90.

Solve for a.

a)

-14/9

b)

-9/14

c)

-21/6

d)

6/21

91.

Solve for x.

a)

19

b)

-9

c)

-100

d)

-50

92.

Solve for k.

a)

1/7

b)

47/36

c)

7

d)

23

93.

Solve for m: 3/4(m-4)=9

a)

16

b)

-12

c)

-18

d)

24

94.

³/₄(6x + 2) = 15

a)

3

b)

6

c)

18

d)

20

95.

Solve: $\frac{1}{6x^2}=\frac{1}{3x^2}-\frac{1}{\ \ x\ }$

a)

$x=6$

b)

$x=\frac{1}{6}$

c)

$x=0$

d)

$Inconsistent$

96.

Solve: $\frac{1}{x}=\frac{6}{5x}+1$

a)

$x=-\frac{1}{5}$

b)

$x=\frac{1}{5}$

c)

$Identity$

d)

$x=0$

97.

Solve by cross-multiplying

a)

x = 6

b)

x = -6

c)

x = 6/7

d)

x = -6/7

98.

Solve by using the LCD.

a)

x = 4/3

b)

x = 2

c)

x = 3/4

d)

x = 2/3

99.

Solve by cross-multiplying.

a)

x = 2

b)

No Solution

c)

x = -10

d)

x = 10

100.

What do you want to say to me?

4 lines

Periodical Test

Total questions: 100

Worksheet time: 3hrs 20mins

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