MTH 005 Unit 4 Review

Exponents & Their Properties

100

State whether the following equation is an example of the product rule, the quotient rule, the power rule, raising a product to a power, or raising a quotient to a power. 

(a^6)^4

What is the power rule?

200

State whether the following equation is an example of the product rule, the quotient rule, the power rule, raising a product to a power, or raising a quotient to a power.

What is raising a product to a power rule?

300

Simplify.

(x + y)^5/((x + y)^2

What is (x + y)³?

400

3⁵x¹⁰  / 2⁵y¹⁰

or

243x¹⁰ / 32y¹⁰

500

Simplify.

(3x^ay^bz^c)(y^fz^g)

3x^ay^b+fz^c+g

Negative Exponents & Scientific Notation

100

Express 4^-3 using a positive exponent.

What is 

1/4^3

200

A thumb drive can contain about 600 million pieces of information. How many sound files, each needing 40,000 pieces of information, can a CD-ROM hold? Write the answer in scientific notation.

What is 1.5 x 10^{4 files?}

300

(2.4 *10^5)(5.4 * 10^16)

Using appropriate significant digits.

What is 1.3 * 10²²?

400

 

Express answer using positive exponents only.

What is a⁷ / b⁸ ?

500

  Answer using positive exponents only.

What is x¹⁶y²² ?

Polynomials

100

Is the polynomial linear or quadratic   y = 4x  +  15 ?

What is linear?

200

Which of the following are monomials?  (There will be more than one answer.)

A.  3x                          D. -67x⁴y²z⁴ 

B.   2                           E.  -4x + y³

C.  3x  +  5                   F. d    

You must get all of them correct to get points.

                      

What are A, B, D, AND F?

300

-2y³  +  6y⁴  - 18y +  4y⁵

1. How many terms are in the polynomial above?

2. Write the polynomial in Standard Form (descending order).
3. What is the degree of the polynomial?

4. What is the lead coefficient?                         You must answer all correct to get points!

1. 4

2. 4y⁵ +6y⁴ - 2y³ -18y

3. 5th degree

4. 4

400

Is the polynomial linear or quadratic   

y = x²   +  3x  -  2 ?

What is quadratic?

500

Find P(-5) for the polynomial function given by 

P(x)= 2x³ - x² + 5x +2

What is -298?

Adding and Subtracting Polynomials

100

Add.

(6x² + 2y – 3xy + 5) + (4x² – 5y + 3xy – 8)

What is 10x² - 3y - 3?

200

(2x³ + 11x + 2) – (x³ – 2x + 7)      

What is x³ + 13x - 5?

300

(7x³ – 2 + x² + 13x) – (4x³ + 10)

Write in descending order.

What is 3x³+ x² + 13x - 12?

400

(12x³ – 5x² – 70x + 1) - (-17x³ + 22x – 1)

Write in descending order.

What is 29x³ - 5x² - 92x + 2?

500

Bob mowed (2x² + 5x – 3) yards on Monday, (4x –7) yards on Tuesday, and he mowed (3x² + 10) yards on Wednesday.  How many yards did he mow in the three days?

What is (5x² + 9x) yards?

Multiplying Polynomials

100

What property is used when multiplying a monomial and a polynomial?

What is the distributive property?

200

What rule is used when multiplying monomials containing variables with exponents?

What is the product rule?

300

Multiply.

2x(4x³ + 3x – 8)

What is 8x⁴ + 6x² - 16x?

400

Multiply.

(x + 4)(2x² + 5x - 1)

What is 2x³ + 13x² + 19x - 4?

500

Multiply.

(8x² + 2x)(2x² - 2x + 5)

What is 16x⁴ - 12x³ + 36x² + 10x ?

Polynomials in Several Variables

100

True or false?

x²y³ and x³y² are like terms

What is false?

200

What is the degree of of the polynomial?

5x⁵y² - 3x³y⁸ + 11x²y³

What is 11th degree?

300

Evaluate the polynomial 3x²y³ - 2x³y³ + 11x - 15y when x = -2 and y = 3.

What is 689?

400

Given f(x)= x² - 4x + 2, 

find f(a+3).

What is f(a + 3) = a² + 2a - 1?

500

Simplify.

(8x³ - 4y²)(x² - 2y² + 2xy)

What is 8x⁵ -16x³y² + 16x⁴y - 4x²y² + 8y⁴ - 8xy^{3 ?}