Five-Minute Check (over Chapter 8)

Then/Now

New Vocabulary

Example 1: Write Expressions Using Exponents

Example 2: Write Expressions Using Exponents

Concept Summary: Order of Operations

Example 3: Real-World Example: Evaluate Expressions

Example 4: Evaluate Algebraic Expressions

Over Chapter 8

A. Yes; there are 4 points.

B. Yes; the y-values are different.

C. No; 0 is paired with –1 and 2.

D. No; there are not enough points.

Determine whether the relation {(–2, –2), (0, –1), (–2, 1), (0, 2)} is a function.

Over Chapter 8

A. x-int = 3; y-int = 3

B. x-int = 3; y-int = 6

C. x-int = 2; y-int = 6

D. x-int = 2; y-int = 3

Find the x-intercept and y-intercept for the graph 2x + y = 6.

Over Chapter 8

Find the slope of the line that passes through the pair of points A(4, 2) and B(–4, –4).

A.

B.

C.

D.

Over Chapter 8

State the slope and y-intercept for the graph of the equation x + 2y = –8.

A.

B.

C.

D.

Over Chapter 8

A. r = 2s, r = s – 17

B. s = 2r, s = r + 17

C. r = 2s, r = s + 17

D. s = 2r, s = r – 17

Sarah collected twice as many canned goods for the food bank as Ryan. Ryan collected 17 cans less than Sarah. Which system of equations can be used to find the number of canned goods each friend collected?

You evaluated expressions without exponents. (Lesson 2–4)

• Write expressions using exponents.

• Evaluate expressions containing exponents.

• exponent

• power

• base

Write Expressions Using Exponents

A. Write 9 ● 9 ● 9 ● 9 using exponents.

The base 9 is a factor 4 times. So, the exponent is 4.

Answer: 9 ● 9 ● 9 ● 9 = 94

Write Expressions Using Exponents

B. Write (–1)(–1) using exponents.

The base –1 is a factor 2 times. So, the exponent is 2.

Answer: (–1) ● (–1) = (–1)2

A. 88

B. 58

C. 48

D. 85

A. Which expression is the same as 8 ● 8 ● 8 ● 8 ● 8?

A. (–2)3

B. 28

C. (–3)2

D. (3)–2

B. Which expression is the same as (–2)(–2)(–2)?

Write Expressions Using Exponents

A. Write w ● w ● w ● w ● w using exponents.

The base w is a factor 5 times. So, the exponent is 5.

Answer: w ● w ● w ● w ● w = w5

Write Expressions Using Exponents

B. Write (5x + 1)(5x + 1) using exponents.

Answer: (5x + 1)(5x + 1) = (5x + 1)2

The base is 5x + 1. It is a factor 2 times, so the exponent is 2.

Write Expressions Using Exponents

First, group the factors with like bases. Then write using exponents.

C. Write using exponents.

Answer:

x ● x ● x ● x = x4 and y ● y ● y = y3

A. bb

B. –4b

C. 4b

D. b4

A. Which expression is the same as b ● b ● b ● b?

A. (4 – 2x)2

B. 4 – 2x2

C. 2(4 – 2x)

D. 42 – 2x2

B. Write the expression using exponents. (4 – 2x)(4 – 2x)

A. 9ab5

B. 9a3b5

C. (9ab)8

D. 9a8b8

C. Write the expression using exponents. 9 ● a ● a ● a ● b ● b ● b ● b ● b.

Evaluate Expressions

A. HOCKEY North American hockey rinks are built according to National Hockey League specifications. The distance from the goal line to the closest blue line is 26 feet. Evaluate the expression to find this dimension.

26 = 2 ● 2 ● 2 ● 2 ● 2 ● 2 2 is a factor 6 times.

= 64 Simplify.

Answer: The distance from the goal line to the closest blue line is 64 feet.

Evaluate Expressions

B. HOCKEY North American hockey rinks are built according to National Hockey League specifications. The length of the rink is 23 ● 52 feet. Evaluate the expression to find this dimension.

23 ● 52 = 2 ● 2 ● 2 ● 5 ● 5 Evaluate powers.

= 200 Simplify.

Answer: The length of the rink is 200 feet.

A. 7 ft

B. 12 ft

C. 64 ft

D. 81 ft

A. The distance between two houses is 43 feet. Evaluate 43 to find the distance.

A. 135 ft

B. 150 ft

C. 1125 ft

D. 1250 ft

B. The distance from the parking lot to the front door is 32 ● 53 feet. Evaluate 32 ● 53 to find the distance.

Evaluate Algebraic Expressions

Evaluate x2 – y3 if x = –5 and y = 2.

x2 – y3 = (–5)2 – 23 Replace x with –5 and y with 2.

= 25 – 8 Evaluate powers; (–5)2 = 25 and 23 = 8.

= 17 Subtract.Answer: 17

A. 11

B. 15

C. 121

D. 129

Evaluate x3 – y2 if x = 5 and y = –2.