Section 2.1 Review KEY.pdf

(1)

SDUHSD Math B Honors Module #2 – TEACHER EDITION 2016-2017

₃₈

Section 2.1: Review

Name: Period:

1. A proportional constant of relates the number of inches a flower grows to the number of weeks since being planted.

a. State the independent and dependent variables.

independent variable: weeks dependent variable: height b. Complete the table.

c. Write an equation that represents this relationship and use the equation to predict how tall the flower will be after 8 weeks.

The flower will be 2 inches tall after 8 weeks. d. Can the flower continue to grow in this manner forever?

No, the flower will eventually die or stop growing; otherwise it would get too big to support its weight.

e. Is this situation proportional? Explain why or why not using your table of values and equation. This situation is proportional because every x-value can be multiplied by to get the corresponding

y-value. The constant of proportionality is . The equation relates x-values to y-values through multiplication only.

2. Laura has a job delivering newspapers. Laura gets paid $100 dollars for delivering 200 papers. a. State the independent and dependent variables.

independent: # of papers delivered dependent: dollars earned

b. Find the unit rate. State what it describes.

the unit rate is 0.5; Laura earns $0.50 per paper delivered

c. Complete the table of values and graph for this situation. Label each axis and label your line Laura. Should your points be connected? Explain why or why not.

x: # of papers y: dollars earned

100 50

200 100

300 150

d. Write an equation for this situation.

3. Kali also has a job delivering newspapers. She gets paid $20 for expenses and then $140 for delivering 350 papers.

a. Find the unit rate for this situation. State what it describes. the unit rate is 0.4; Kali earns $0.40 per paper delivered

b. Graph this situation on the same coordinate plane used above. Label your line Kali.

x: weeks 1 3 6 9 30

y: height 1 2 3 10

Laura

Kali

40 80 120 160 200 240 280 20

40 60 80 100 120 140 160 180

0

# of papers delivered

d

o

llar

s e

a

rn

ed

(2)

₃₉

Stage 1 Stage 2 Stage 3 c. Write an equation for this situation.

d. Which situation, Laura or Kali, represents a non-proportional relationship? Justify using your graph and equations.

e. What does the point (200, 100) represent in the context? When 200 papers are delivered, both Laura and Kali earn $100.

4. Nayala bought 5 pounds of mangos for $6.25.

a. What is the price per pound for the mangos that she bought? The mangos cost $1.25 per pound.

b. Which line on the graph, A, B, or C, represents Nayala’s situation?

Line B represents Nayala’s situation.

5. Emma is putting together an order for sugar, flour, and salt for her restaurant pantry. The graph shows the cost to buy pounds of sugar and flour. One line shows the cost of buying pounds of flour and the other line shows the cost of buying pounds of sugar.

a. From the graph, which ingredient costs more to buy per pound? Justify your answer.

Sugar costs more per pound because the line for sugar is steeper. It has a higher unit rate.

b. The cost to buy salt by the pound is less than sugar and flour. Draw a possible line that could represent the cost to buy x pounds of salt. Answers will vary. Draw any line that is below the line for flour.

6. Write two different rules that describe the pattern where is the stage number and is the total number of blocks. Explain how your rules connect to the pattern.

Rule 1:

This rule shows s groups of 4 plus 2.

Rule 2:

This rule shows the stage number plus 2 groups of the stage number plus one plus the stage number again.

Sugar

Flour

Stage 2

s groups of 4

+2

Stage 2

s

s+1

(3)

₄₀

Stage 1 Stage 2 Stage 3 Stage 4

a. Simplify both rules. What do you notice? Both rules simplify to b = 4s + 2

b. How many blocks are in stage 0? How is this value represented in the simplified rule? There are 2 blocks in stage 0. This value is the constant in the rule.

c. Use your rule to find the number of blocks in the 50th stage. There will be 202 blocks in the 50th_stage.

d. Which stage has 582 blocks? Stage 145

7. Use the pattern to complete the following. a. Draw stage 4.

b. How many new blocks are added to the pattern from one stage to the next?

4 blocks

c.

first difference: 4 unit rate: 4

d. Create a graph of this data. Show the unit rate on your graph.

e. What is the simplified form of the equation that gives the number of blocks, for any stage Where do you see the different parts of the equation in the geometric model, table, and graph?

Equation:

Model

4 blocks added from one stage to the next

2 is the number of blocks at stage 0

Table 4 is the first difference

4 is the constant difference in the y-values

When x = 0, y = 2

Graph 4 is the unit rate

2 is the number at which the line intersects the y-axis (y-intercept) Stage (s) # of Blocks (b)

1

6

2

10

3

14

4

18 +4

+4

+1

(4)

₄₁

f. If the equation changed to , how would your geometric model change? How would your

table change? How would your graph change? Model

2 blocks would be added from one stage to the next

There is -1 block in stage 0

Table 2 is the first difference

When x = 0, y = -1

Graph

2 is the unit rate, so the graph would be less steep

-1 is the y-intercept

8.

For each of the representations given below, identify the unit rate and initial value or y-intercept.

e.

a. The local community center charges a monthly fee of $15 to use their facilities plus $2 per visit.

unit rate: $2 per visit initial value: $15

b. unit rate:5 blocks per stage

initial value:0 blocks

x y

2 10

3 5

4 0

c. unit rate:

y-intercept:20

d. unit rate:

y-intercept: -3 Stage 1 Stage 2 Stage 3

unit rate:

(5)

₄₂

Directions: Complete the remaining representations that are not given. When needed, label the columns in

the table and axes on the graph. 9.

Context

The number of students currently enrolled at Discovery Place Preschool is 24. Enrollment is increasing by 6 students each year. Consider the relationship between the number of years from now and the number of students enrolled.

Table

independent variable: time (years) dependent variable: # of students

x: Time (years) y: # of students

2 36

4 48

6 60

Graph

Should your points be connected on your graph? Explain why or why not. No. Fractional parts of students cannot be enrolled.

Equation

Is this situation proportional? Explain why or why not using the context.

No. At 0 years, there were 24 students enrolled which represents the point (0,24). The graph does not pass through the origin.

What is the unit rate? What does the unit rate represent in the context?

+6; the increase in enrollment each year

a. What is the y-intercept of your graph? How is the y-intercept shown in the equation? (0, 24); 24 is the constant in the equation

b. What does the y-intercept represent in the context? the number of students currently enrolled

c. How would you change the context so that the relationship between number of years and number of students enrolled is ?

The number of students currently enrolled is 40.

d. What would happen to the graph if the maximum enrollment at the school was 72?

The graph would stop increasing at the point (8, 72). In 8 years, the school will reach its maximum capacity of 72 students.

e. How would the graph of the line change if enrollment increased to 10 students each year? The line would be steeper because the unit rate increased.

2 4 6 8 10 12 14

12 24 36 48 60 72 84

0

Time (years)

#

of S

tud

Section 2.1 Review KEY.pdf

38