algebra 1 secondary education mafs.912.a-apr.1.1 worksheet ... and... · alyssa emptied out her...

Algebra 1 Secondary Education

MAFS.912.A-APR.1.1 – Worksheet 1

Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education

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Name: _______________________________________________________ Date: ___/___/___

1. Find the difference. )15()832( 2 ggg

2. Find the product of 731 2 xxx .

3. Which polynomial represents the following?

1165 24 yyy

A. 11305 35 yy

B. yyy 55305 24

C. yyy 55305 35

D. 1156 24 yyy

4. What is the perimeter of a triangle whose side lengths are 42 x , 12 x , and x5 ?

A. 38 2 x

B. 372 xx

C. 1112 xx

D. xxxx 2040510 234

5. Below is Tania’s work for subtracting two polynomials, but she made a mistake. Identify the

step where Tania made her error and write out the remainder of the problem correctly.

61114178 23 xxxx

Step 1: 61114178 23 xxxx

Step 2: 61711814 23 xxxx

Step 3: 23314 23 xxx


MAFS.912.A-CED.1.1 – Worksheet 1


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Name: _______________________________________________________ Date: ___/___/___

1. Lacy and Sydney are making paper flowers for the junior homecoming float. Lacy makes 6

flowers every minute and Sydney makes 4 flowers every minute. Both girls start at the same

time.

Write and solve an equation to find the number of minutes, m, it takes Lacy and Sydney to make

a total of 600 flowers.

2. Kegan wants to buy a new skateboard that will cost $140. So far, Kegan has saved $30 toward

the purchase of the skateboard. To raise the remaining money needed, Kegan mows his

neighbor’s lawn and charges $10 each time he completes the job.

Write an equation to find x, the number of times Kegan mows his neighbor’s lawn. How many

times will Kegan need to mow his neighbor’s lawn to have enough money to buy the

skateboard?

3. Tina scored 94, 68, and 88 on her first 3 Algebra 1 tests. Her next test is her final which counts

double. Write and solve an equation that Tina could use to determine the minimum grade she

must score on her final to have a mean score of 80.




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4. Rene used a $4 off coupon to buy bows which cost $2 each. Write an inequality Rene could use

to determine the number of bows she can buy if she plans to spend more than $8. Then graph

the solution set.

5. Palm Beach South Middle School’s cafeteria can produce 12 pizzas in one hour, and the cafeteria

needs to produce at least 30 pizzas to feed the 6th grade students at the school. In order to

make sure that all pizzas are cooked in time for lunch, what is the least amount of time the

cafeteria must allow for cooking the pizzas?

A. 2 hours

B. 2 ½ hours

C. 3 hours

D. 3 ¼ hours




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Name: _______________________________________________________ Date: ___/___/___

1. Jordan signed up for the Annual Cross Florida bike ride which is a 170 mile bike ride. After

weeks of training he rides at an average of 15 miles per hour. Write and graph an equation that

can be used to show Jordan’s progress in miles (y) after a number of hours (x).

Draw Graph Below

2. Lisette is saving money to buy a car. She has $972 already and adds $20 per week from her part

time job. Which of the following equations represents this situation if y represents the total

amount of money that Lisette has saved?

A. 97220 xy

B. 97220 xy

C. 97220 xy

D. 97220 xy

3. Noah has 144 hot dogs to sell at the football game. On average, he sells 31 hot dogs per hour.

Write an equation to model this situation.




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4. The glee club is selling cupcakes at a local fair. They must pay $20 to rent a booth and they are

selling the cupcakes for $2 each. Graph their profit or loss, in dollars, against the number of

cupcakes they sell.




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Name: _______________________________________________________ Date: ___/___/___

1. Janice has final exams in Algebra 1 and Biology on Friday. She has up to 12 hours to study for the

exams and her mom said she must spend more time on Algebra (a) than Biology (b). Which of the

following constraints can be used to represent this situation?

A.

ba

ba 12

B.

ba

ba 12

C.

ba

ba 12

D.

ba

ba 12

2. Alyssa emptied out her change jar to buy a new binder for school. She found 147 coins consisting

of dimes (d) and nickels (n) that totaled $11.65. Write one of the constraints that would be used

to determine how many dimes and how many nickels Alyssa had in her change jar.

3. A company is repaving their parking lot and trying to decide how many parking spaces they can

make when painting the new lines. The lot has 3200 square feet of room for the parking spaces.

A standard car’s parking space is 162 square feet and a compact car’s parking space is 120 square

feet. Select all of the following that are viable solutions to this parking lot situation.

A. 13 standard cars and 10 compact cars

B. 10 standard cars and 13 compact cars

C. 18 standard cars and 6 compact cars

D. 6 standard cars and 18 compact cars

E. 19 standard cars 26 compact cars




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4. Annalise realized she needed two part-time jobs after school to raise enough money to buy a car

within a month after getting her driver’s license. She works the same number of hours at each job

in one week and receives $10 per hour to babysit and $8 per hour to bag groceries. She also

spends $11 per week on lunch at school. Which of the following equations represents the amount

of money Annalise earns (y) in a week based on the number of hours (x) she works?

A. 1118 xy

B. 1118 xy

C. 810 xy

D. 310 xy

5. Johnnie likes to buy slices of pizza in the cafeteria for lunch for $1.75. Amy prefers to buy

hamburgers for lunch, which cost $2.50 each. Between the two of them, Johnnie and Amy have

$15.50. How many hamburgers and slices of pizza can they buy? Sort the following solutions into

their appropriate category.

Categories

Viable Solution Non-Viable Solution

Solutions

3 slices and 2 hamburgers




5 slices and 1 hamburger

1 slice and 5 hamburgers




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Name: _______________________________________________________ Date: ___/___/___

1. Mr. Dominguez wrote the formula below to calculate a, the acceleration of his motor.

bt

sva

Solve Mr. Dominguez’s formula for t, the final time.

2. The movement of moving particles is described in the equation cvtht

r 222

2

. Solve the

equation for v.

3. Solve the equation below for x.

2

cxbxa

4. Raymond was asked to come to the board and solve the equation rabh for a. What

should be Raymond’s first step?

A. Multiply each side of the equation by b.

B. Subtract r from both sides of the equation.

C. Divide each side of the equation by a.

D. Add h to each side of the equation.

5. Solve the equation y – b = m(x – a) for a.


MAFS.912.A-REI.1.1 – Worksheet 1

The School District of Palm Beach County


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Name: _______________________________________________________ Date: ___/___/___

1. Using the table below, explain the process used for each step in solving the equation.

352124 ccc

Steps Solution Steps Process

1 352124 ccc Given

2. Erica solved the equation below.

352)5(3 aa

Step 1 3a + 15 = 2a + 35

Step 2 5a + 15 = 35

Step 3 5a = 20

Step 4 a = 4

Which step is the first incorrect step in Erica’s solution shown above?

A. Step 1

B. Step 2

C. Step 3

D. Step 4





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3. Ken solved the linear equation 18)15(2 y using the following steps.

Step 1 2(5y – 1) = 18

Step 2 10y – 1 = 18

Step 3 10y = 19

Step 4 y = 1.9

Which statement is true about Ken’s method?

A. Ken made a mistake between Steps 1 and 2.

B. Ken made a mistake between Steps 2 and 3.

C. Ken made a mistake between Steps 3 and 4

D. Ken solved the equation correctly.

4. List the steps in solving the equation .4)84(216 d

Step 1: _________________________________________

Step 2: _________________________________________

Step 3: _________________________________________

Step 4: _________________________________________

5. Explain Mia’s mistake in solving the equation below.

yy 22)5(2

yy 115

1152 y

162 y

8y

_____________________________________________

_____________________________________________

_____________________________________________

_____________________________________________

____________________________________________.




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Name: _______________________________________________________ Date: ___/___/___

1. Which of the following inequalities is equivalent to 1945 a ?

A. 3a

B. 5a

C. 3a

D. 10a

2. Graph the solution set on a number line for each inequality listed below.

I 124 y

II 8)2(2 y

III yy 225

3. Solve bab 38 for b.

4. Solve the equation below for f.

4

3

6

523

ff




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5. Which of the following is the graph of 352 c ?

A.

B.

C.

D.




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Name: _______________________________________________________ Date: ___/___/___

1. Rewrite the quadratic equation yxx 1122 2 in vertex form by completing the square.

2. Select all of the solutions to the equation 0532 2 xx .

A. 2

5

B. 1

C. 5

2

D. 1

E. 2

5




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3. Fill in the missing step of the derivation of the quadratic formula.

02 cbxax

cbxax 2

cxa

bxa

2

ca

b

a

bx

a

bxa

42

22

2

a

acb

a

bxa

4

4

2

22

2

22

4

4

2 a

acb

a

bx

2

2

4

4

2 a

acb

a

bx

a

acbbx

2

42




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4. Select all of the following ordered pairs that are solutions of the equation 1825 2 xx .

(–1, 0)

0,

5

1

0,

5

7

0,

5

461

0,

5

461

5. Find the solution(s) of the equation 020)2(5 2 x .

Algebra 1

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1. Mr. Xavier took his 18 students and 9 other chaperones to an amusement park. He paid $882 for admission. Mrs. Yadira took her 11 students and 4 other cheperones to the same amusement park. She paid $489 for admission. Which equation should be added to the equation 18s + 10c = 882 to determine s, the amount the amusement park charges for student admission?

A. 22s + 10c = 978 B. 11s + 5c = 489 C. 9s + 5c = 441 D. 11s + 4c = 489

2. Fawn bought a total of 70 cakes for a tea party. She spent $3,025. Fawn bought vanilla cakes for $22 each and a fruit filled cake for $55 each. The system of equations below can be used to find the number of vanilla cakes, v, and the number of fruit filled cakes, f, Fawn purchased. Which system of equations has the same solution as the system below.

{𝑣 + 𝑓 = 70

22𝑣 + 55𝑓 = 3,025

A. {22𝑣 + 𝑓 = 70

22𝑣 + 55𝑓 = 3,025

B. {𝑣 + 55𝑓 = 3,85022𝑣 + 55𝑓 = 3,025

C. {𝑣 + 𝑓 = 70

22𝑣 + 55𝑓 = 3,025

D. {22𝑣 + 22𝑓 = 1,54022𝑣 + 55𝑓 = 3,025

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3. A school treasurer purchased jackets for the school store. She used the system of equations below to determine the price for each student jacket, x, and the price for each adult ticket, y. Write a system of equations that has the same solution as the system of equations below.

{84𝑥 + 12𝑦 = 9,612126𝑥 + 21𝑦 = 13,643

A:

B:

4. Rachel is solving the system of equations {7𝑥 − 21𝑦 = 142𝑥 + 3𝑦 = 11

using the

elimination method. Which of the following steps could she use?

A. Divide the first equation by 2 and then add the result to the second equation.

B. Multiply the first equation by 21 then add the result to the second equation.

C. Multiply the second equation by 3 then add the result to the first equation. D. Divide the first equation by 7 then add the result to the second equation.

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5. Mr. Nigma is solving the system of equations 4x – 3y = 9 and 2x + 6y = 5. Which system of equations has the same solution?

A. {4𝑥 − 3𝑦 = 9−15𝑦 = −1

B. {4𝑥 − 3𝑦 = 99𝑦 = 19

C. {2𝑥 + 6𝑦 = 56𝑥 = 23

D. {2𝑥 + 6𝑦 = 510𝑥 = 23




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Name: _______________________________________________________ Date: ___/___/___

1. Julio wants to make a small scale soccer field in his backyard for his daughter to practice. He has

painted off lines to create a perimeter of 270 feet. He has also measured the length of the field

to be 35 feet longer than the width of the field. Write and graph the system of equations which

could be used to find the length and width of the field.

2. While analyzing the landing procedures of airplanes, George recorded one plane at an altitude

of 5,000 feet descending at a rate of 300 feet per minute and one at an altitude of 14,000 feet

descending at a rate of 1,200 feet per minute. Which of the following solutions represents

when the two airplanes will reach the same altitude?

A. (6, 3200)

B. (10, 2000)

C. (12.7, 1190)

D. (21, 1300)

Len

gth

Width




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3. Three times a number is subtracted from another number and the difference is 3. The sum of

the two numbers is 31. What is the smaller of the two numbers?

4. Solve the system of equations below.

yx

yx

332

21

5. Solve the system of equations below.

1772

1785

yx

yx

Algebra 1

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1. Which of the following is a solution of the function graphed below?

A. (-2, 6) B. (1, -2) C. (6, -2) D. (2, 1)

2. Select all the points that are in the solution set graphed below.

A. (5, 3) B. (2, 4) C. (4, 2) D. (7, 1) E. (0, 6)

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3. Which graph represents the solution to the equation x – 3y = – 9 ?

A.

C.

B.

D.

Algebra 1

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Standard 4. Ravi graphed the solution set of an equation below.

Which equation did Ravi solve?

A. x + 4y = -3 B. x – 4y = -3 C. x + 4y = 3 D. x – 4y = 3

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5. Which of the following is a solution of the equation graphed below?

A. (1, 9) B. (-1, 0) C. (0, 0) D. (9, 1)




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Name: _______________________________________________________ Date: ___/___/___

1. What is the solution to f(x) = g(x), if f(x) = – x and g(x) = x.

2. The graphs of )(xf and )(xg are shown below. Which of the following is closest to the

solution of )()( xgxf ?

A. (–1.6, 0.2)

B. (0, –1)

C. (0.2, –1.6)

D. (0.5, –2)

3. The table below shows the results of evaluating two functions, )(xf and )(xg , for

different values of x. Using this information, give an approximate solution to the

nearest hundredth for )()( xgxf .

x )(xf )(xg

1.2 2.4 1.7

1.3 2.7 2.2

1.4 3.0 2.7

1.5 3.3 3.4

1.6 3.6 4.1

1.7 3.9 4.9




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4. The graphs of )(xf and )(xg are shown below. Which of the following is the solution

of )()( xgxf .

A. (1, 0)

B. (1, 3)

C. (1.6, 5.8)

D. (2, 7)

5. Complete the table of successive approximations to find the x-value of the solution of

)()( xgxf to the nearest hundredth.

x 2)( 2 xxf 1)( xxg

0 –2 -1

1 –1 0

2 6 1

1.5 0.25 0.5



Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education - Updated 08/13/15

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Name: _______________________________________________________ Date: ___/___/___

1. Graph the inequality 14 yx .

2. Which of the following graphs represents the inequality 72 xy ?

A.

C.

B.

D.



Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education - Updated 08/13/15

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3. Which of the following represents the solution set to the system of inequalities?

23

4

xy

xy

A.

C.

B.

D.

4. Select all of the ordered pairs that are in the solution set of the system of inequalities given.

35

126

xy

yx

A. (–3, 1) D. (–7, 4)

B. (0, –3) E. (1, 1)

C. (3, 3) F. (4, –2)

5. Graph the system of inequalities:

63

46

yx

xy


MAFS.912.A-SSE.1.1 – Worksheet 1


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Name: _______________________________________________________ Date: ___/___/___

1. Eli needs to place buoys at specific points in the inlet. He used the expression 814 x to find

the location for each buoy. Which expression is equivalent to Eli’s expression?

A. 22 9x

B. 33 xx

C. 3392 xxx

D. 3392 xxx

2. Andre wrote the expression below in his mathematics notes. Write an equivalent expression

that shows the greatest common factor of each term in Andre’s expression.

2x7 – 10x6y + 7x5y2 – 9x4y3

3. The area of a rectangular field is represented by 2x2 + 13x + 21. What are the length and width

of the field?




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4. Select all of the expressions that are NOT equivalent to bcacbxax .

□ cbaxba )()( □ bcax

□ )()( cxbcxa □ (a + b) (x + c)

□ ))(( xcab □ )( cxab

5. Niara is writing a computer program for three-dimensional graphics. Part of her program applies

the expression33 827 yx . Which expression is equivalent to

33 827 yx .

A. )23(2323 yxyxyx

B. 22 46923 yxyxyx

C. 22323 yxyx

D. 323 yx




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Name: _______________________________________________________ Date: ___/___/___

1. Which expression is equivalent to 4x2 – 49?

A. (2x + 7)2

B. (2x – 7)2

C. (x + 7)(4x – 7)

D. (2x + 7)(2x – 7)

2. Select all of the factors of the expression 5x2 – 45.

A. 5

B. 9

C. x + 9

D. x – 9

E. 5x – 9

3. Match each expression with an equivalent expression.

(x – 3)(x + 3) (x – 3)(x – 3) (x + 3)(x + 3)

x2 – 6x + 9

x2 + 6x + 9

(x2 – 9)




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4. Use factoring to write an expression that is equivalent to 25b16 – 64c2.

5. Write the expression 7x3 – 28xy2 as the product of 3 factors.




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Name: _______________________________________________________ Date: ___/___/___

1. Monique has been tracking the jumps of frogs in her backyard to collect data for a project. She

found that the height of a frog’s jump in inches can be modeled by the expression 2

4

14 tt ,

where t is the time in seconds. Write an equivalent expression to easily show the times at

which the frog is on the ground.

2. Claudio is clearing out a field for the neighborhood kids to play. The area of the field can be

represented by the expression 1100282 ww , where w is the width of the field. Use the

options below to identify an equivalent expression that reveals the width of the field.

A. 1296)14( 2 w

B. 1100)28( ww

C. )22)(50( ww

D. )22)(50( ww

3. Sonja has decided to try out for the track and field team at her high school and would like to be

able to jump the hurdles. She did some research to find that if her jump models the expression

2242 2 xx , she can clear a 68cm hurdle without any problem. Write an equivalent

expression to easily show the maximum height Sonja must be able to jump.




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4. Anna received a gift of $5,000 from her grandmother and decided to invest it. The expression t12)0005.1(5000 represents the amount of money Anna is earning on her investment. Select all

of the following that are equivalent expressions so that Anna can better understand how her

money is invested.

A. t)0005.1(5000 12

B. t12)5.25000(

C. t12)0005.1(5000

D. t12

12

06.15000

E. 12)0005.1(5000 t

F. t125025

5. A function for a popular amusement park ride in Ohio is defined by the expression

606416 2 ss , where s is the time in seconds. Which of the following is an equivalent

expression that reveals the zeros of the function?

A. 2)2(16 s

B. )32)(52( ss

C. )10)(6(4 ss

D. )32)(52(4 ss

algebra 1 secondary education mafs.912.a-apr.1.1 worksheet ... and... · alyssa emptied out her...

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