Five-Minute Check (over Chapter 7)

CCSS

Then/Now

New Vocabulary

Example 1: Simplify a Rational Expression

Example 2: Standardized Test Example: Undefined Values

Example 3: Simplify Using –1

Key Concept: Multiplying Rational Expressions

Example 4: Multiply and Divide Rational Expressions

Example 5: Polynomials in the Numerator and Denominator

Example 6: Simplify Complex Fractions

Over Chapter 7

A. 2.4849

B. 1.9459

C. 0.7831

D. 0.5389

Evaluate log12 7.

Over Chapter 7

A.

B.

C.

D.

Over Chapter 7

A. 6

B. 7

C. 8

D. 9

Solve log3 (x2 – 12) = log3 4x.

Over Chapter 7

A. –0.5108

B. –0.2197

C. 0.2197

D. 0.4979

Solve 5ex – 3 = 0.

Over Chapter 7

A. about 42 years ago

B. about 34 years ago

C. exactly 29 years ago

D. about 24 years ago

Suppose $200 was deposited in a bank account and it is now worth $1100. If the annual interest rate was 5% compounded continuously, how long ago was the account started? Use the formula A = Pert.

Over Chapter 7

A. y = 19.3e(0.003)t; about 20.1 million

B. y = 19.3e(0.03)t; about 29.4 million

C. y = 19.3e(1.003)t; about 52.6 million

D. y = 19.3e(1.3)t; about 70.8 million

Suppose the population of New York State grows at a rate of 0.3% compounded continuously. In 2006, the population was 19.3 million. Write an equation that represents the population and predict the population in after t years 2020.

Content Standards

A.APR.7 Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

Mathematical Practices

8 Look for and express regularity in repeated reasoning.

You factored polynomials.

• Simplify rational expressions.

• Simplify complex fractions.

• rational expression

• complex fraction

Simplify a Rational Expression

Look for common factors.

A. Simplify .

Answer:

Simplify.

Eliminate common factors.

●

Simplify a Rational Expression

Just as with a fraction, a rational expression is undefined if the denominator equals zero.

Answer: The values that would make the denominator equal to 0 are –7, 3, and –3. So the expression is undefined at y = –7, y = 3, and y = –3.

The original factored denominator is (y + 7)(y – 3)(y + 3).

B. Under what conditions is the expression

undefined?

A. Simplify .

A.

B.

C.

D.

A. x = 4 or x = –4

B. x = –5 or x = 4

C. x = –5, x = 4, or x = –4

D. x = –5

B. Under what conditions is the expression

undefined?

Read the Test Item

You want to determine which values of p make the denominator equal to 0.

For what value(s) of p is undefined?

A 5 B –3, 5

C 3, –5 D 5, 1, –3

Undefined Values

Solve the Test Item

Look at the possible answers. Notice that the p term and the constant term are both negative, so there will be one positive solution and one negative solution. Therefore, you can eliminate choices A and D. Factor the denominator.

Answer: B

p2 – 2p –15 = (p – 5)(p + 3) Factor the denominator.

p – 5 = 0 or p + 3 = 0 Zero Product Property

p = 5 p = –3 Solve each equation.

Undefined Values

A. –5, –3, –2

B. –5

C. 5

D. –5, –3

For what value(s) of p is undefined?

Simplify Using –1

Factor the numerator and the denominator.

Answer: –a

Simplify .

b – 2 = –(–b + 2) or –1(2 – b)

Simplify.

A. y – x

B. y

C. x

D. –x

Simplify .

Multiply and Divide Rational Expressions

Answer:

A. Simplify .

Simplify.

Simplify.

Multiply and Divide Rational Expressions

B. Simplify

Multiply by the reciprocal of the divisor.

Simplify.

Multiply and Divide Rational Expressions

Answer:

Simplify.

A. Simplify .

A.

B.

C.

D.

B. Simplify .

A. AnsA

B. AnsB

C. AnsC

D. AnsD

Polynomials in the Numerator and Denominator

= –1Simplify.

A. Simplify .

Factor.

1 + k = k + 1,1 – k = –1(k – 1)

Answer: –1

Polynomials in the Numerator and Denominator

Multiply by the reciprocal of the divisor.

B. Simplify .

Factor.

Polynomials in the Numerator and Denominator

Answer:

Simplify.

A. Simplify .

A.

B.

C. 1

D. –1

A.

B.

C.

D.

Simplify Complex Fractions

Simplify .

Multiply by the reciprocal of the divisor.

Express as a division expression.

Simplify Complex Fractions

Simplify.

Answer:

Factor.

–1

Simplify .

A. e B.

C. e D.