Quiz about First Periodical Test Grade 8 SY 2023-2024

Question 1

A polynomial is an expression consisting of

Accepted Answer

Variables, constants, and exponents

Answer

Variables and constants only

Answer

Variables, constants, and radicals

Answer

Variables, constants, and logarithms

Question 2

Which of the following is an example of a monomial polynomial?

Accepted Answer

$$5xy$$

Answer

$$3x^2+2x-1$$

Answer

$$x^3+2x^2-x+4$$

Answer

$$2x^2y^2-3xy$$

Question 3

How many terms does a binomial polynomial have?

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 4

What is a trinomial polynomial?

Accepted Answer

A polynomial with three terms

Answer

A polynomial with four terms

Answer

A polynomial with two terms

Answer

A polynomial with one term

Question 5

1. How many terms does the polynomial $$5x^4-3x^2+2x-7$$

have?

Accepted Answer

4

Answer

1

Answer

2

Answer

3

Question 6

What must ALWAYS be done before factoring polynomials?

Accepted Answer

Look for the Greatest Common Factor (GCF)

Answer

Find the values of a, b and c

Answer

Look for the value of the variables

Answer

Factor the difference of two squares

Question 7

1. What is the prime factorization of the monomial $$6x^2$$ ?

Accepted Answer

$$2∙3∙x∙x$$

Answer

$$2x^2$$

Answer

$$3x^2$$

Answer

$$2^2∙3∙x$$

Question 8

What is the greatest common factor of $$12x^3$$ and $$18x^2$$

Accepted Answer

$$6x^2$$

Answer

$$6x$$

Answer

$$6x^3$$

Answer

$$12x^2$$

Question 9

What is the factored form of the expression ? $$16x^3-24x^2$$

Accepted Answer

$$4x^2(4x-6)$$

Answer

$$8x^2(2x-3)$$

Answer

$$8x^2(2x^2-3)$$

Answer

$$4x^2(4x^2-6)$$

Question 10

What is the factored form of the monomial $$20x^2y^3z^4$$ ?

Accepted Answer

$$2*2*5*x*x*y*y*y*z*z*z*z$$

Answer

$$2*10*x*x*y*y*y*z*z*z*z$$

Answer

$$2*2*5*x^2*y^3*z^4$$

Answer

$$10x^2y^3z^4$$

Question 11

What is the factored form of the binomial $$x^2-9$$ ?

Accepted Answer

$$(x-3)(x+3)$$

Answer

$$(x+3)(x+3)$$

Answer

$$(x-3)(x-3)$$

Answer

$$(x-9)(x-9)$$

Question 12

What is the factored form of the binomial $$8x^3-1$$ ?

Accepted Answer

$$(2x-1)(4x^2+2x+1)$$

Answer

$$(2x+1)(4x^2+2x+1)$$

Answer

$$(2x-1)(2x^2+2x+1)$$

Answer

a) $$(2x-1)(4x^4+2x^2+1)$$

Question 13

1. What is the factored form of the binomial $$y^3+64$$ ?

Accepted Answer

$$(y+4)(y^2-4y+16)$$

Answer

$$(y-4)(y^2-4y+16)$$

Answer

$$(y+4)(y^2+4y+16)$$

Answer

$$(y+4)(y^3-4)$$

Question 14

Which factoring method is typically used for binomials of the form $$a^2-b^2$$ ?

Accepted Answer

Factoring a sum and difference of squares

Answer

Factoring by grouping

Answer

Factoring a sum of cubes

Answer

Factoring a trinomial

Question 15

1. What is the factored form for the sum of two cubes $$a^3+b^3$$ ?

Accepted Answer

$$(a+b)(a^2-ab+b^2)$$

Answer

$$(a-b)(a^2+ab+b^2)$$

Answer

$$(a^3+b^3)$$

Answer

$$(a^2-b^2)$$

Question 16

1. For the binomial $$8x^3-1$$ , which factoring method is applied?

Accepted Answer

Factoring a difference of cubes

Answer

Factoring a trinomial

Answer

Factoring by grouping

Answer

Factoring a sum and difference of squares

Question 17

What type of trinomial is $$x^2+5x+6$$ ?

Accepted Answer

General Trinomial with "a" equal to 1

Answer

Imperfect square trinomial

Answer

Perfect square trinomial

Answer

General Trinomial with "a" greater than 1

Question 18

Which of the following pattern is used in factoring sum of perfect square trinomials?

Accepted Answer

$$a^2+2ab+b^2=(a+b)(a+b)$$

Answer

$$a^2-2ab+b^2=(a-b)(a-b)$$

Answer

$$a^2+2ab+b^2=(a-b)(a+b)$$

Answer

$$a^2-2ab+b^2=(a+b)(a-b)$$

Question 19

Which of the following pattern is used in factoring difference of perfect square trinomials?

Accepted Answer

$$a^2-2ab+b^2=(a-b)(a-b)$$

Answer

$$a^2+2ab+b^2=(a+b)(a+b)$$

Answer

$$a^2+2ab+b^2=(a-b)(a+b)$$

Answer

$$a^2-2ab+b^2=(a+b)(a-b)$$

Question 20

Which of the following is a perfect square trinomial?

Accepted Answer

$$x^2-4x+4$$

Answer

$$x^2+5x+6$$

Answer

$$2x^2+5x+3$$

Answer

$$x^2+5x+4$$

Question 21

Factor the perfect square trinomial: $$4x^2+12x+9$$

Accepted Answer

$$(2x+3)(2x+3)$$

Answer

$$(4x+6)(4x+6)$$

Answer

$$(2x+4)(2x+4)$$

Answer

$$(2x-3)(2x-3)$$

Question 22

Factor the trinomial: $$2x^2-5x-3$$

Accepted Answer

$$(2x+1)(x-3)$$

Answer

$$(2x-3)(x+1)$$

Answer

$$(2x-1)(x+3)$$

Answer

$$(2x+1)(x+3)$$

Question 23

Factor the trinomial: $$:x+5x+6$$

Accepted Answer

$$(x+2)(x+3)$$

Answer

$$(x+1)(x+6)$$

Answer

$$(x-1)(x-6)$$

Answer

$$(x+1)(x-6)$$

Question 24

In the process of factoring by grouping, what is the next step after creating two groups of terms?

Accepted Answer

Factor each group separately.

Answer

Combine like terms within each group.

Answer

Rearrange the terms to create a single expression.

Answer

None of the above.

Question 25

Which of the following expressions below is factorable by grouping?

Accepted Answer

$$2x^3+x^2+6x+3$$

Answer

$$12xy$$

Answer

$$x^2+3x+2$$

Answer

$$x^2-9$$

Question 26

Factor the multinomial $$2x^3+x^2+6x+3.$$

Accepted Answer

$$(x^2+3)(2x+1)$$

Answer

$$(2x^2+3)(x+1)$$

Answer

$$(x+3)(2x^2+1)$$

Answer

$$(2x^2-1)(x-3)$$

Question 27

What is the result of factoring the expression $$3ab+6a-2b-4$$ using the grouping method?

Accepted Answer

$$(3a+6)(b-1)$$

Answer

$$(3a-6)(b-1)$$

Answer

$$(3a-6)(b+1)$$

Answer

$$(3a+6)(b+1)$$

Question 28

Which of the following is a rational expression?

Accepted Answer

$$2x-3$$

Answer

$$\sqrt{x}$$

Answer

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

Answer

$$|x|$$

Question 29

A rational algebraic expression is one that can be expressed as a ratio of:

Accepted Answer

Two polynomials

Answer

Two integers

Answer

Two algebraic expressions

Answer

Two square roots

Question 30

In the rational expression $$\frac{2x-1}{3x^2+5}$$ , which part is the numerator?

Accepted Answer

$$2x-1$$

Answer

$$3x^2+5$$

Answer

$$2x$$

Answer

$$5$$

Question 31

In the rational expression $$\frac{2x-1}{3x^2+5}$$ , which part is the denominator?

Accepted Answer

$$3x^2+5$$

Answer

$$2x-1$$

Answer

$$2x$$

Answer

$$5$$

Question 32

For the rational algebraic expression $$\frac{x^2-3}{5x-5}$$ , what value of "x" makes the expression undefined?

Accepted Answer

1

Answer

-1

Answer

0

Answer

5

Question 33

In a rational algebraic expression, what is the term that must be excluded from the domain to avoid division by zero?

Accepted Answer

The denominator

Answer

The numerator

Answer

The constant term

Answer

The coefficient of the highest degree variable

Question 34

What is the value of $$x^0$$ , where x is any nonzero real number?

Accepted Answer

1

Answer

0

Answer

x

Answer

Undefined

Question 35

According to the zero exponent rule, any nonzero number raised to the power of 0 is equal to:

Accepted Answer

1

Answer

0

Answer

-1

Answer

The original number

Question 36

What is the value of $$x^{-3}$$ , where x is a nonzero real number?

Accepted Answer

$$\frac{1}{x^3}$$

Answer

$$-3$$

Answer

$$x^3$$

Answer

Undefined

Question 37

According to the negative exponent rule, a nonzero number raised to a negative exponent is equal to:

Accepted Answer

The reciprocal of that number raised to the positive exponent

Answer

The square of that number

Answer

Zero

Answer

Undefined

Question 38

When simplifying a rational expression, what do you look for to factor out common terms in the numerator and denominator?

Accepted Answer

Common factors

Answer

Least common multiples

Answer

The largest coefficient

Answer

Square roots

Question 39

Simplify the expression:

$$\frac{3^{-3}a^4}{9^{-2}a^2}$$

Accepted Answer

$$3a^2$$

Answer

$$\frac{1a^2}{3}$$

Answer

$$\frac{1}{3a^2}$$

Answer

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

Question 40

What is the process of making a rational algebraic expression simpler by eliminating common terms in the numerator and denominator called?

Accepted Answer

Simplification

Answer

Expansion

Answer

Fractionation

Answer

None of the above

Question 41

Simplify the expression $$\frac{100x^2y}{20xy}$$

Accepted Answer

$$5x$$

Answer

$$\frac{x}{5}$$

Answer

$$\frac{xy}{5}$$

Answer

$$5xy$$

Question 42

Simplify the expression $$\frac{4x+20}{x^2-25}$$

Accepted Answer

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

Answer

$$\frac{4}{x+5}$$

Answer

$$\frac{4}{x+25}$$

Answer

$$\frac{4}{x-25}$$

Question 43

Simplify the expression $$\frac{x^2+5x+6}{x^2+4x+4}$$

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 44

Add the similar rational algebraic expressions: $$\frac{3x}{x^2-9}+\frac{9}{x^2-9}$$

Accepted Answer

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

Answer

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

Answer

$$\frac{3}{x+9}$$

Answer

$$\frac{3}{x-9}$$

Question 45

Add the similar rational algebraic expressions: $$\frac{2x^2-8}{x^2+4x+4}+\frac{4-x^2}{x^2+4x+4}$$

Accepted Answer

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

Answer

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

Answer

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

Answer

$$\frac{x-2}{x-2}$$

Question 46

Add the similar rational algebraic expressions: $$\frac{2x^2+8x+2}{x^2+3x+2}+\frac{2-4x-x^2}{x^2+3x+2}$$

Accepted Answer

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

Answer

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

Answer

$$\frac{x-1}{x+2}$$

Answer

$$\frac{x+2}{x-1}$$

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