algebra 2 unit 1 print - edl€¦ · 11/29/2016 algebra 2 unit 1 - print 2/23

11/29/2016 Algebra 2 Unit 1 - Print

https://academyca.springboardonline.org/ebook/assessment/teacher/print/6BF85F4E5BD311E5A0BA1299BFC1B123/assessment 1/23

Algebra 2 Unit 1 Print

Question 1

Bentano spends $170 to order 30 pounds of nuts from an online company. The company charges$3.50 per pound for peanuts and $7.50 per pound for almonds. It also charges a flat fee of $13 forshipping and handling.

Which equation can be used to find p, the number of pounds of peanuts Bentano buys?

3.5p + 7.5 (p − 30) − 13 = 170

3.5p + 7.5 (p − 30) + 13 = 170

3.5p + 7.5 (30 − p) − 13 = 170

3.5p + 7.5 (30 − p) + 13 = 170



Question 2

The cost of a taxi ride, in dollars, is $2 for the first quarter mile plus $0.40 for each quarter mile afterthat. Jameel cannot afford to spend more than $20 on a taxi ride.

The equation can be used to find m, the distance, in miles, that Jameelcan travel for $20. What is the maximum distance?

2 + 0.4 (4m − 1) = 20

A 11.5 miles

B 13.5 miles

C 14.0 miles

D 16.0 miles



Question 3

Isaac shoveled 9 of his neighbors' driveways after a snow storm. He charged $25 for a shortdriveway and $45 for a long driveway.

Which equation can be used to find y, the total amount that Isaac charged when x of the drivewaysare short?

A y = 25x + 45 (9 − x)

B y = 45x + 25 (9 − x)

C y = 25x + 45 (9 + x)

D y = 45x + 25 (9 + x)



Question 4



Penn is using Shipping World's international shipping rates to calculate the shipping cost for herpackages. The company charges $30 plus $8 per pound for each package.

Which graph models the cost, y, of shipping a package that weighs x pounds?



Question 5

Melissa plans to run her first marathon. Her sponsors have pledged to donate a total of $45 plus $5per mile that she runs.

Graph the equation that models the amount that her sponsors will donate, y, if she runs x miles.



Question 6

Question 7

An architect measures a beam to be 96.55 centimeters long, with an accuracy of plus or minus 0.02centimeter. Which equation can be used to find the limits of the actual length of the beam?

A |x − 96.55| = 0.02

B |x + 96.55| = 0.02

C |96.55 − 0.02| = x

D |96.55 + 0.02| = x

Which number line shows the solution to the inequality ?3|2x + 4| − 5 > 13

A

B

C

D



Question 8

Akiva has an international calling card worth $50. Each call to India costs $2.20 per minute.

Which function represents the amount of money that Akiva has left on her card after speaking for mminutes?

A C (m) = −2.2m + 50

B C (m) = 2.2m − 50

C C (m) = −50m + 2.2

D C (m) = 50m − 2.2



Question 9

Dino has $1,000 in a savings account that was started for him when he was born. He has a parttimejob where he earns $60 each week, and he puts $20 of that into his account each week. An equationcould be used to model the amount in his account, y, after x weeks.

Which statements are true about a graph of the equation that will show his account balance during ayear? Check all that apply.

The xaxis should be labeled from 0 to 12 months since you want to see the change overa year.

The xaxis should be labeled from 0 to 52 weeks since you want to see the change over ayear.

The yaxis should be labeled from $0 to $1,000 since the money in the account will not goabove $1,000.

The yaxis should be labeled from $0 to $1,300 since the money in the account will not goabove $1,300.

The yaxis should be labeled from $750 to $1,000 since that is the approximate range ofy values for the year.

The yaxis should be labeled from $1,000 to $2,100 since that is the approximate rangeof y values for the year.



Question 10

Mike can take the city bus to school, or he can ride his bicycle. One bus ride costs him $1.75. Hecan bring his lunch to school or buy it there. Buying lunch in school costs $2.50. He tries to spend nomore than $30 on these options each month. Let x represent the number of lunches that Mike buysin school. Let y represent the number of bus rides that he takes.

Which inequality represents all ordered pairs (x, y) that are possible options for Mike?

A for and 2.5x + 1.75y ≤ 30 x ≥ 0 y ≥ 0

B for and 2.5x + 1.75y ≥ 30 x ≤ 0 y ≤ 0

C for and 30 − 1.75y ≤ 2.5x x ≥ 0 y ≤ 0

D for and 30 − 2.5x ≤ 1.75y x ≤ 0 y ≥ 0



Question 11

The graph shows this system of inequalities, with their shaded solution region.

Which ordered pairs satisfy all three inequalities? Check all that apply.

y ≤ − x + 513

y ≥ 2x − 2

y ≥ −2x − 3

(–3, 0)

(–2, 5)

(0, 0)

(2, 2)

(3, 4)

(6, 3)



Question 12

Which shows the solution to this system of equations?

−3y + 12 = x − 2

2y + 10 = 9x

A (2, 2)

B (2, 4)

C (4, 2)

D (4, 4)



Question 13

A child care company charges $435 per month for children who attend full time and $275 per monthfor children who attend part time. This month, they have 35 children registered for a total fee of$12,985.

Let x represent the number of children who attend full time and y represent the number of childrenwho attend parttime. Which system of equations could be used to model this situation?

A ; x + y = 35 275x + 435y = 12, 985

B ; x + y = 275 35x + 35y = 435

C ; x + y = 435 35x + 35y = 12, 985

D ;

x + y = 12, 985 435x + 275y = 35



Question 14

Beniah sells hats and umbrellas. He charges $7.75 per hat and $9.50 per umbrella. Last week hesold 90 items for a total of $757.

Let x represent the number of hats that Beniah sold and y represent the number of umbrellas that hesold. Which system of equations could be used to model this situation?

A ; x + y = 7.75 9.5x + 9.5y = 90

B ; x + y = 9.5 7.75x + 7.75y = 757

C ; x + y = 90 7.75x + 9.5y = 757

D ; x + y = 757 9.5x + 7.75y = 90



Question 15

Graph the piecewisedefined function that is given by when and by when .

y = x + 5 x < 0 y = 5x ≥ 0



Question 16

Question 17

Graph the function .y = |2x + 3|

The graph of can be obtained from the graph of by what transformation? .

Consider the functions and .f (x) = |x + 3| g (x) = − |x + 3|

g f



Question 18

Let and .

What is ?

f (x) = 3x + 2 g (x) = 4x

(f ⋅ g) (3)

A 23

B 38

C 116

D 132



Question 19

Wayne's Windows charges a $40 flat fee to cover travel and expenses plus $25 per hour to washwindows at one building. A function c(h) can relate the cost of washing a building's windows and thenumber of hours, h, that it takes to wash them.

Wayne's Windows can wash one window pane every 3 minutes. A function h(p) can relate the hoursthat are needed to wash windows and the number of panes, p, in the windows.

Which composition of functions describes the cost, c(h(p)), of washing p panes at one building?

A c (h (p)) = 40 + 0.05p

B c (h (p)) = 40 + 1.25p

C c (h (p)) = 40 + 28p

D c (h (p)) = 40 + 115p



Question 20

Mr. Franklin has a furnace that burns 0.8 gallon of oil per hour in the winter. He pays $1.15 pergallon for oil.

Which functions and composition of functions could be used to determine the cost of heating hishouse for 12 hours?

A gives the gallons used in h hours; gives the cost ofusing g gallons; gives the cost of using the furnace for 12hours.

g (h) = 0.8h c (g) = 1.15gc (g (12)) = 0.92 (12)

B gives the gallons used in h hours; gives the cost ofusing g gallons; gives the cost of using the furnace for 12hours.

g (h) = 0.8h c (g) = 1.15gc (g (12)) = 1.95 (12)

C gives the gallons used in h hours; gives thecost of using g gallons; gives the cost of using thefurnace for 12 hours.

g (h) = 0.8 + h c (g) = 1.15 + gc (g (12)) = 0.92 + 12

D gives the gallons used in h hours ; gives thecost of using g gallons; gives the cost of using thefurnace for 12 hours.

g (h) = 0.8 + h c (g) = 1.15 + gc (g (12)) = 1.95 + 12



Question 21

Question 22

Let and .

What is the composition ?

f (x) = 3x + 1 g (x) = − 1x2

(f ∘ g)(x)

A 3 + − 3x − 1x3 x2

B 3 − 2x2

C + 3xx2

D 9 + 6xx2

Let and .

What is ?

f (x) = 2x − 1 g (x) = 4 − f (x)

(g ∘ f)(4)

A −9

B −7

C −3

D 7



Question 23

Question 24

Let .

What is the inverse of this function in slopeintercept form?

y = 3x+24

A y = x − 243

B y = x −43

23

C y = 4x − 23

D y = x +34

24

Let .

What is ?

f (x) = (3x + 15)

f −1

A (x) = − 5f −1 x3

B (x) = + 5f −1 x3

C (x) = −f −1 x15

15

D (x) = +f −1 x15

15



Question 25

Let . Suppose there is a function such that and .

What is ?

f (x) = 4x − 3 g f (g (x)) = x g (f (x)) = x

g (x)

A g (x) = 4x − 3

B g (x) = x−34

C g (x) = −4x + 3

D g (x) = x+34

algebra 2 unit 1 print - edl€¦ · 11/29/2016 algebra 2 unit 1 - print 2/23

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