Free Printable Summative Test in Mathematics 8

1.

What is the area of a rectangle if the length is equal to 2x + 3 and width is x + 3?

a)

$2x^2+2x+9$

b)

$2x^2+4x+9$

c)

$2x^2+9x+9$

d)

$2x^2+7x+9$

2.

Which of the following statements are not true about factoring?

a)

Factoring is a process of changing variables.

b)

Factoring is a reverse process of multiplication.

c)

A polynomial is factored completely when it has been written as the product consisting only prime numbers.

d)

Factoring a polynomial means writing it as a product of two polynomials.

3.

Which of the following factoring method is being used when you factored out a monomial in a given polynomial?

a)

Factoring by grouping

b)

Factoring the Difference of Two Squares

c)

Common Monomial Factoring

d)

Factoring by Grouping

4.

Which of the following are the factors of 20x – 10?

a)

2x (10x – 5)

b)

10 (2x – 1)

c)

4 (2x – 5)

d)

x (x – 10)

5.

What are the factors of 5mn + 25m + 3n³ + 15n²?

a)

(5m + 3n)(n + 5)

b)

(3m + 5n)(n + 5)

c)

(5m + 3n²)(n + 5)

d)

(3m² + 5n)(n + 5)

6.

What are the factors of p² – 81?

a)

(p + 9) (p – 9)

b)

(p – 9) (p – 9)

c)

(p + 9) (p + 9)

d)

(9 + p) (9)

7.

Find the missing term so that ______ - 48m + 64 forms a perfect square trinomial.

a)

3m²

b)

6m²

c)

9m²

d)

12m²

8.

Which of the following are the factors of –5x³ + 5x?

a)

5x (x² – 1)

b)

–5x (x² + 1)

c)

5x (- x² + 1)

d)

–5x (x + 1) (x – 1)

9.

How do we determine if a polynomial is a perfect square trinomial?

a)

When the first and last terms are perfect squares and both positive.

b)

When the only the first term is perfect square and positive.

c)

When the only the last term is perfect square and positive.

d)

When the first and last terms are not perfect squares and both negative.

10.

Which of the following is not true about difference of two squares?

a)

It consists of three terms.

b)

The operation involved is subtraction.

c)

There is a minus sign between the two terms.

d)

It is binomial and each term is a square.

11.

Does 9x² – 24x + 16 a perfect square trinomial?

a)

Yes, because the factor of the polynomial is (3x + 4) (3x – 4).

b)

Yes, because the factor of the polynomial is (3x – 4)²

c)

No, because it doesn’t have a perfect square term

d)

No, because it doesn’t have any factor

12.

Factor the polynomial y² – 20y +100.

a)

(y + 10) (y+ 10)

b)

(y + 20) ( y + 5)

c)

(y – 10) (y – 10)

d)

(y – 20) (y – 5)

13.

The factors of a polynomial is equal to (m + 11)(m +1). What is the polynomial?

a)

m² + 12m + 11

b)

m² – 12m – 11

c)

m² + 12m – 11

d)

m² – 12m + 11

14.

The factors of a polynomial is equal to (3y + 2)(y – 5). What is the polynomial?

a)

3y² – 10y + 11

b)

3y² + 13y – 11

c)

3y² + 12y – 10

d)

3y² – 13y – 10

15.

The area of a square table top is 16x² – 8x + 1. Find the length of its side.

a)

4x – 2

b)

4x – 3

c)

4x – 1

d)

4x – 4

16.

The volume of a rectangular box is x³ + 1000. If x = 12 cm, find the volume of the box.

a)

2,728 cm³

b)

1,618 cm³

c)

1,036 cm³

d)

2,748 cm³

17.

Factor the expression r² – 9r + 14.

a)

(r + 14)( r + 1)

b)

(r – 14) (r – 1)

c)

(r + 7)(r + 2)

d)

(r – 7) (r – 2)

18.

What is the side of square whose area is 4x² – 44x + 121?

a)

4x + 11

b)

4x – 11

c)

2x + 11

d)

2x – 11

19.

Which of the following is a sum of two cubes?

a)

m⁹ + 8

b)

m⁶ + 9

c)

m³ - 27

d)

m³ + 9

20.

Which of the following is a difference of two cubes?

a)

m³ + 9

b)

m³ – 27

c)

m⁶ + 9

d)

m⁹ + 8

21.

When the denominator of a rational expression is equal to 0, what will happen to the expression?

a)

The expression is simplified.

b)

The expression is undefined.

c)

The expression is equal to 0.

d)

The expression is equal to 1.

22.

What will be the value of x that will make the expression $\frac{3x}{2x-8}$ undefined?

a)

2

b)

3

c)

4

d)

5

23.

What will be the value of x that will make the expression $\frac{x^2+4x+5}{x^2-6x+5}$ undefined?

a)

1

b)

3

c)

5

d)

7

24.

If x= 2, what will be the value of the expression $\frac{3x}{x-5}$ ?

a)

– 2

b)

– 3

c)

– 4

d)

– 5

25.

When do we say that a fraction or rational expression is in simplest form?

a)

When both numerator and denominator are 0.

b)

When the numerator is negative and the denominator is positive.

c)

When both numerator and denominator have no other common factor except 1.

d)

When the denominator is equal to 0.

26.

Simplify the expression $\frac{-9x^4y^6}{15y^6z}$ .

a)

$\frac{-9y^6}{15z}$

b)

$\frac{9x^4}{15y^6}$

c)

$\frac{-3x^4}{5z}$

d)

$\frac{-3x^4}{5}$

27.

Which of the following is the simplified form of the expression $\frac{4x+8}{12x-24}$

a)

$\frac{(x+2)}{3(x-2)}$

b)

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

c)

$\frac{(x+2)(x-2)}{3}$

d)

$\frac{3}{(x+2)(x-2)}$

28.

Which of the following is the simplified form of the expression $\frac{6x-36}{x^2-36}$ .

a)

$\frac{6}{(x+6)(x-6)}$

b)

$\frac{6}{(x+6)}$

c)

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

d)

$(x+6)(x-6)$

29.

Which of the following is the simplified form of the expression $\frac{6x^2+24x}{x^2+8x+16}$

a)

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

b)

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

c)

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

d)

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

30.

Find the sum of the expressions $\frac{5x}{x+2}+\frac{10}{x+2}$ .

a)

$\frac{5}{x+2}$

b)

x+2

c)

5

d)

$\frac{1}{5}$

31.

Find the sum of the expressions $\frac{r-1}{2r+1}+\frac{r-1}{2r+1}$

a)

$\frac{2(r-1)}{2r+1}$

b)

2r + 1

c)

2 (r - 2)

d)

2

32.

Find the sum of the expressions $\frac{1}{3x}+\ \frac{2}{3x}$

a)

$\frac{1}{x}$

b)

x

c)

-1

d)

1

33.

Find the sum of the expressions $\frac{6p-3}{2p+1}+\frac{2p+7}{2p+1}$

a)

1/4

b)

4

c)

2p +1

d)

4(2p-1)

34.

Find the sum of the expressions $\frac{3}{x+1}+\frac{10}{x+1}$

a)

$\frac{10}{x+1}$

b)

$\frac{11}{x+1}$

c)

$\frac{12}{x+1}$

d)

$\frac{13}{x+1}$

35.

Subtract $4-\ \frac{2}{x+4}$ .

a)

$\frac{2}{x+4}$

b)

$\frac{4x+10}{x+4}$

c)

$\frac{2x+7}{x+4}$

d)

$\frac{4x+14}{x+4}$

36.

Subtract $\frac{x+9}{x+3}-\ \frac{-4x-6}{x+3}$ .

a)

$\frac{5x-3}{x+3}$

b)

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

c)

5

d)

$\frac{5x+3}{x+3}$

37.

Which of the following is the LCD of $\frac{3}{8x^2y^5}$ and $\frac{5}{24xy^6}$ ?

a)

$24x^2y^6$

b)

$24xy^5$

c)

$8x^3y^3$

d)

$8x^2y^6$

38.

Find the product of $\frac{x^2-1}{x}$ and $\frac{2x}{x+1}$ .

a)

2x (x – 1)

b)

2 (x – 1)

c)

(x – 1)(x + 1)

d)

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

39.

Find the product of $\frac{n+5}{3n}$ and $\frac{3n}{n+5}$ .

a)

0

b)

- 1

c)

1

d)

Undefined

40.

Simplify the expression $\frac{(4x)^0}{(2xy)^2}$ using the laws of exponent.

a)

$\frac{x}{2xy}$

b)

$\frac{1}{4x^2y^2}$

c)

$\frac{1}{2xy}$

d)

$\frac{1}{4xy}$

41.

Simplify the expression $\frac{(a+b)^2(a-b)^4}{(a+b)(a-b)^3}$ using the laws of exponent.

a)

(a + b) (a – b)

b)

$\frac{1}{(a+b)(a-b)}$

c)

a + b

d)

(a – b)

42.

Find the quotient of $\frac{5x^3}{4}\div\frac{15x}{8}$ .

a)

2x²

b)

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

c)

$\frac{2x^2}{3}$

d)

$\frac{x^3}{6}$

43.

Divide $\frac{(n-4)^2}{3n}\div\frac{n^2-16}{n+4}$ .

a)

$\frac{1}{3n}$

b)

$\frac{3n}{(n-4)(n+4)}$

c)

$\frac{3(n-4)}{(n+4)}$

d)

$\frac{n-4}{3n}$

44.

A 5-foot tall woman casts a shadow of 6 feet. At the same time, a tree casts a shadow of 30 feet. How tall is the tree?

a)

22 feet

b)

23 feet

c)

24 feet

d)

25 feet

45.

Joel can do a job in 3 hours. Peter can do the same job in 6 hours. How long would it take if they worked together on the same job?

a)

2 hours

b)

2.5 hours

c)

3 hours

d)

3.5 hours

46.

A number is increased by 6 times its reciprocal is equal to 5. Find the number.

a)

2

b)

3

c)

4

d)

5

47.

Gas consumption is proportional to driving time. If 10 gallons of gas is used in 2.6 hours at a certain speed, If a tank holds 30 gallons, how long can you travel at that speed before needing gas?

a)

4.8 hours

b)

5.8 hours

c)

6.8 hours

d)

7.8 hours

48.

The sum of a number and fifteen times its reciprocal is 8. Find the number.

a)

5

b)

6

c)

7

d)

8

49.

Angel takes 3 hours to drive a distance of 150 km. at this rate, how long will it take her to drive a distance of 275 km?

a)

8.5 hours

b)

5.5 hours

c)

7.5 hours

d)

6.5 hours

50.

What do you call the expression that represents a quotient of two expressions?

a)

Rational Expression

b)

Rational Equation

c)

Rational Inequality

d)

Real Numbers

Summative Test in Mathematics 8

Total questions: 50

Worksheet time: 1hrs 25mins

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