Quiz about Lesson #1 – Algebra II

Question 1

Which of the following are monomials?

Accepted Answer

$$3xy^0$$

Accepted Answer

$$-7a^3b^2$$

Accepted Answer

$$5x^2$$

Answer

1/x

Answer

4x + 3

Question 2

For the monomial $$-6x^4y^3$$ , what is the: coefficient? degree of the term? power of x? power of y?

Accepted Answer

coefficient: -6, degree of the term: 7, power of x: 4, power of y: 3

Answer

coefficient: -6, degree of the term: 12, power of x: 3, power of y: 4

Answer

coefficient: 6, degree of the term: 7, power of x: 4, power of y: 3

Answer

coefficient: -6, degree of the term: 12, power of x: 4, power of y: 3

Question 3

Simplify each of the following using exponent rules: $$x^3 · x^5$$ = ___

Accepted Answer

$$x^8$$

Answer

$$x^{15}$$

Answer

$$x^2$$

Answer

$$x^{35}$$

Question 4

Simplify each of the following using exponent rules: $$y^7 / y^2$$ = ___

Accepted Answer

$$y^5$$

Answer

$$y^9$$

Answer

$$y^2$$

Answer

$$y^3$$

Question 5

Simplify each of the following using exponent rules: $$(a^2)^4$$ = ___

Accepted Answer

$$a^8$$

Answer

$$a^6$$

Answer

$$a^4$$

Answer

$$a^{16}$$

Question 6

Simplify each of the following using exponent rules: $$(3x^2y)(-2x^3y^4)$$ = ___

Accepted Answer

$$-6x^5y^5$$

Answer

$$6x^6y^4$$

Answer

$$-5x^5y^4$$

Answer

$$-6x^4y^6$$

Question 7

Rewrite with positive exponents: $$x^{-4}$$ = ___

Accepted Answer

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

Answer

$$x^4$$

Answer

$$-x^4$$

Answer

$$-1/x^4$$

Question 8

Rewrite with positive exponents: $$1/a^{-2}$$ = ___

Accepted Answer

$$a^2$$

Answer

$$a^{-2}$$

Answer

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

Answer

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

Question 9

Rewrite with positive exponents: $$(2/x)^{-3}$$ = ___

Accepted Answer

$$x^3/8$$

Answer

$$8/x^3$$

Answer

$$2^3/x^3$$

Answer

$$x^{3/2}$$

Question 10

Convert to scientific notation: 0.00052 = ___

Accepted Answer

$$5.2 imes 10^{-4}$$

Answer

$$5.2 imes 10^{-3}$$

Answer

$$5.2 imes 10^{-5}$$

Answer

$$0.52 imes 10^{-4}$$

Question 11

For the monomial $$9x^2y^5$$ , what is the coefficient?

Accepted Answer

9

Answer

2

Answer

5

Answer

7

Question 12

For the monomial $$9x^2y^5$$ , what is the degree of the term?

Accepted Answer

7

Answer

6

Answer

5

Answer

8

Question 13

For the monomial $$9x^2y^5$$ , what is the power of x?

Accepted Answer

2

Answer

5

Answer

9

Answer

1

Question 14

For the monomial $$9x^2y^5$$ , what is the power of y?

Accepted Answer

5

Answer

2

Answer

9

Answer

7

Question 15

Simplify the following using exponent rules: $$x^6 · x^2$$

Accepted Answer

$$x^8$$

Answer

$$x^{12}$$

Answer

$$x^4$$

Answer

$$x^3$$

Question 16

Simplify the following using exponent rules: $$z^9 / z^4$$

Accepted Answer

$$z^5$$

Answer

$$z^{13}$$

Answer

$$z^4$$

Answer

$$z^{36}$$

Question 17

Simplify the following using exponent rules: $$(b^3)^3$$

Accepted Answer

$$b^9$$

Answer

$$b^6$$

Answer

$$b^3$$

Answer

$$b^0$$

Question 18

Simplify the following using exponent rules: $$(−5a^2b)(2a^3b^4)$$

Accepted Answer

$$-10a^5b^5$$

Answer

$$-7a^6b^3$$

Answer

$$10a^6b^4$$

Answer

$$-10a^4b^6$$

Question 19

Rewrite with positive exponents: $$y^{-5}$$

Accepted Answer

$$\frac{1}{y^5}$$

Answer

$$y^5$$

Answer

$$-y^5$$

Answer

$$-1/y^5$$

Question 20

Rewrite with positive exponents: $$1/m^{-3}$$

Accepted Answer

$$m^3$$

Answer

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

Answer

$$-m^3$$

Answer

$$m^{-3}$$

Question 21

Rewrite with positive exponents: $$\left(\frac{3}{w}\right)^{-2}$$

Accepted Answer

$$w^2/9$$

Answer

$$3w^2$$

Answer

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

Answer

$$3w^{-2}$$

Question 22

Convert 0.0000061 to scientific notation:

Accepted Answer

$$6.1 imes 10^{-6}$$

Answer

$$6.1 imes 10^6$$

Answer

$$0.61 imes 10^{-5}$$

Answer

$$61 imes 10^{-7}$$

Question 23

Multiply and write the answer in scientific notation: $$(8 imes 10^6) / (2 imes 10^3)$$

Accepted Answer

$$4 imes 10^3$$

Answer

$$4 imes 10^9$$

Answer

$$16 imes 10^3$$

Answer

$$6 imes 10^2$$

Question 24

Which of the following is a monomial?

Accepted Answer

$$7x^2y$$

Answer

3x + 1

Answer

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

Answer

$$\sqrt{x} + 5$$

Question 25

Which of the following is equal to 0.00052 in scientific notation?

Accepted Answer

$$5.2 imes 10^{-4}$$

Answer

$$5.2 imes 10^4$$

Answer

$$5.2 imes 10^{-3}$$

Answer

$$5.2 imes 10^3$$

Question 26

Simplify $$(3x^2)(-4x^3)$$

Accepted Answer

$$-12x^5$$

Answer

$$-12x^6$$

Answer

$$-7x^5$$

Answer

$$-12x^3$$

Question 27

Simplify $$(3 imes 10^5)(2 imes 10^3)$$

Accepted Answer

$$6 imes 10^8$$

Answer

$$6 imes 10^{15}$$

Answer

$$5 imes 10^8$$

Answer

$$6 imes 10^2$$

Question 28

Simplify $$\frac{6x^5}{2x^2}$$

Accepted Answer

$$3x^3$$

Answer

$$12x^7$$

Answer

$$3x^2$$

Answer

$$3x^7$$

Question 29

Simplify $$\frac{9 imes10^6}{3 imes10^2}$$

Accepted Answer

$$3 imes 10^4$$

Answer

$$3 imes 10^8$$

Answer

$$6 imes 10^4$$

Answer

$$3 imes 10^5$$

Question 30

What is the simplified form of $$x^3·x^5$$ ?

Accepted Answer

$$x^8$$

Answer

$$x^{-8}$$

Answer

$$x^{-2}$$

Answer

$$x^2$$

Question 31

Simplify $$(2x^3y^2)^2$$

Accepted Answer

$$4x^6y^4$$

Answer

$$4x^5y^2$$

Answer

$$2x^6y^4$$

Answer

$$4x^3y^2$$

Question 32

What is the value of $$(4x^3)^0$$ ?

Accepted Answer

1

Answer

0

Answer

x

Answer

3

Question 33

Which expression is not a monomial?

Accepted Answer

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

Answer

$$-7x^2y$$

Answer

$$6x^4y^2$$

Answer

$$3a^2b^3$$

Question 34

Simplify the following: $$\frac{-4x^6}{2x^2}$$

Accepted Answer

$$-2x^4$$

Answer

$$2x^4$$

Answer

$$-2x^8$$

Answer

$$-8x^3$$

Question 35

An architect is designing a rectangular prism-shaped water tank. The length is $$5x^2$$ meters, the width is $$2x$$ meters, and the height is $$3x^3$$ meters. What is the volume of the tank as a monomial?

Accepted Answer

$$30x^6$$

Answer

$$10x^5$$

Answer

$$15x^7$$

Answer

$$6x^8$$

Question 36

The kinetic energy of a moving object is given by $$KE = \frac{1}{2} mv^2$$ . Suppose the mass $$m = 4x^3$$ kilograms and velocity $$v = 3x$$ meters/second. Write the expression for kinetic energy as a monomial. Simplify and identify the coefficient.

Accepted Answer

KE = $$18x^5$$ ; Coefficient: 18

Answer

KE = $$12x^4$$ ; Coefficient: 12

Answer

KE = $$6x^6$$ ; Coefficient: 6

Answer

KE = $$36x^3$$ ; Coefficient: 36

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