solving equations unit 2 warm-up a - ms. ferguson

Solving Equations UNIT 2 Warm-Up A

(2-A)

Representations of Rational Numbers (Fractions, Decimals, Percents)

Daily Graph

Proportions

Factoring

Current Unit Problem Sets (Since we haven't gotten started yet…review from unit 1.)

x y

A -2 2

B -1 0

C 0 -2

D 1 -4

E 2 -6

Reduce each fraction to simplest form.

1)

= ______ 2)

= ______ 3)

= ______ 4)

= ______ 5)

= ______

6)

= ______ 7)

= ______ 8)

= ______ 9)

= ______ 10)

= ______

Solve each of the following proportions.

12)

13)

Find the prime factors, and then write all factor pairs for each number. prime factorization factor pairs

14) 29 ________________ ____________________________________________________________________________________ 15) 30 ________________ ____________________________________________________________________________________

16) Simplify the following expressions.

a) 2(6) +

b) c)

17) Fill in the square with the correct inequality symbol.

a) b)

18) Evaluate the following expressions for

a.

b.

19) Evaluate the following expressions for

a. – b.

11) Plot and label the points recorded in the table. Describe the pattern in the x-column. _____________________________________________________________ Describe the pattern in the y-column. _____________________________________________________________

Solving Equations UNIT 2 Warm-Up B

(2-B)


Daily Graph

Proportions

Factoring

Current Unit Problem Sets

x y

A

B

C

D

E

Reduce each fraction to simplest form.

1)

= ______ 2)

= ______ 3)

= ______ 4)

= ______ 5)

= ______

6)

= ______ 7)

= ______ 8)

= ______ 9)

= ______ 10)

= ______

Solve each of the following proportions.

12)

13)


14) 31 ________________ ____________________________________________________________________________________ 15) 32 ________________ ____________________________________________________________________________________

16) Solve. 17) Solve.

18) Solve.

19) Solve.

11) Record the points in the table from the graph. Describe the pattern in the x-column. _____________________________________________________________ Describe the pattern in the y-column. _____________________________________________________________

Solving Equations UNIT 2 Warm-Up C

(2-C)


Daily Graph

Proportions

Factoring


x y

A

B

C

D

E

Convert to a fraction in simplest form.

1) = ______ 2) = ______ 3) = ______ 4) = ______ 5) = ______

6) = ______ 7) = ______ 8) = ______ 9) = ______ 10) = ______

Write a proportion and solve each problem. Include units in your solution.


14) 33 ________________ ____________________________________________________________________________________ 15) 34 ________________ ____________________________________________________________________________________


18) Solve.

19) Solve.


12) A baseball team has won 14 games. The ratio of

games won to games played is 7 to 12. How many

games has the team played?

13) In 3 hours, 225 cases of candy can be produced. At

this rate, how much candy can be produced in 8 hours?

Solving Equations UNIT 2 Warm-Up D

(2-D)


Daily Graph

Proportions

Factoring


x y

A

B

C

D

E


1) = ______ 2) = ______ 3) = ______ 4) = ______ 5) = ______

6) = ______ 7) = ______ 8) = ______ 9) = ______ 10) = ______


14) 35 ________________ ____________________________________________________________________________________ 15) 36 ________________ ____________________________________________________________________________________

16) Solve.

17) Solve.

18) Solve.

19) Solve.


Write a proportion and solve each problem. Include units in your solution. 12) A duplicating machine can produce 50 copies in 2

minutes. At this rate, how long will it take to produce

150 copies?

13) A recipe for making 12 cupcakes calls for 2 cups of

flour. How much flour would be needed to make 18

cupcakes?

Solving Equations UNIT 2 Warm-Up E

(2-E)


Daily Graph

Proportions

Factoring


x y

-2

-1

0

1

2


1) = ______ 2) = ______ 3) = ______ 4) = ______ 5) = ______

6) = ______ 7) = ______ 8) = ______ 9) = ______ 10) = ______


14) 37 ________________ ____________________________________________________________________________________ 15) 38 ________________ ____________________________________________________________________________________

16) Solve.

17) Solve.

18) Solve.

19) Solve.

11) Use the following equation to evaluate for the y-values: Plot the points and sketch the graph.

Write a proportion and solve each problem. Include units in your solution. 12) A baseball player is hitting 2 home runs in every

25 times at bat. How many home runs would you

expect him to hit in 550 times at bat?

13) The average heart beats 96 times in 60 seconds.

How many times does it beat in 10 seconds?

Solving Equations UNIT 2 Warm-Up F

(2-F)


Daily Graph

Proportions

Factoring


x y

-2

-1

0

1

2


1) = ______ 2) = ______ 3) = ______ 4) 40 = ______ 5) = ______

6) = ______ 7) = ______ 8) = ______ 9) = ______ 10) = ______

Write a proportion and solve. Include units in your solution.


14) 39 ________________ ____________________________________________________________________________________ 15) 40 ________________ ____________________________________________________________________________________

16) Solve.

17) Solve.

18) Solve.

19) Solve.

11) Use the following equation to evaluate for the y-values:

– Plot the points and sketch the graph.

12) A recipe for making two dozen muffins calls for 4

eggs. How many eggs would you need for 18 muffins?

13) Kelly can type 4 pages in 20 minutes. How many

pages can she type in 3 hours?

Solving Equations UNIT 2 Warm-Up G

(2-G)


Daily Graph

Proportions

Factoring


x y

-2

-1

0

1

2

Convert to a decimal.

1)

= ______ 2) = ______ 3) = ______ 4)

= ______ 5)

= ______

6)

= ______ 7)

= ______ 8) 35 = ______ 9) = ______ 10) = ______



14) 41 ________________ ____________________________________________________________________________________ 15) 42 ________________ ____________________________________________________________________________________

16) Solve.

17) Solve.

18) Solve.

19) Solve.


Plot the points and sketch the graph.

12) 64 feet of rope weighs 20 lbs. 28 feet of rope

weighs n lbs.

13) Two liters of apple juice at $3.80. Five liters of

apples juice at m dollars.

Solving Equations UNIT 2 Warm-Up H

(2-H)


Daily Graph Proportions

Factoring


x y

-2

-1

0

1

2


1) = ______ 2)

= ______ 3)

= ______ 4)

= ______ 5) = ______

6) = ______ 7) = ______ 8)

= ______ 9)

= ______ 10)

= ______



Write a proportion and solve. Include units in your solution. The distance on a map is given. Find the actual distance, if the scale on the map is 1 in. : 40 mi.

12) 5 in. 13) 4

3in.


14) 43 ________________ ____________________________________________________________________________________ 15) 44 ________________ ____________________________________________________________________________________

16) Simplify by combining like terms. a) ________________ b) ________________

17) Simplify by using the distributive property. a) ________________ b) ________________

18) Simplify by using the distributive property and

then combining like terms.

________________

________________

19) Show checking the solution into the

equation:

Was a correct solution?

Solving Equations UNIT 2 Warm-Up I

(2-I)



Factoring


x y

0

1

2

3

4


1)

= ______ 2) = ______ 3) 33 = ______ 4)

= ______ 5)

= ______

6)

= ______ 7)

= ______ 8) 300 = ______ 9) 67 = ______ 10) = ______

11) Use the following equation to evaluate for the y-values: Note: 24 is off the grid, just don't plot the last point. Plot the points and sketch the graph.

Write a proportion and solve. Include units in your solution. The distance on a map is given. Find the actual distance, if the scale on the map is 1 cm. : 20 mi.

12) cm 13)

cm.


14) 45 ________________ ____________________________________________________________________________________ 15) 46 ________________ ____________________________________________________________________________________



________________

________________

17) Solve.

18) Solve.


equation:


Solving Equations UNIT 2 Warm-Up J

(2-J)



Factoring


x y

-1

0

1

2

3


1)

= ______ 2) = ______ 3) = ______ 4)

= ______ 5)

= ______

6)

= ______ 7)

= ______ 8) 35 = ______ 9) = ______ 10) = ______


Write a proportion and solve. Include units in your solution. 12) 13)


14) 47 ________________ ____________________________________________________________________________________ 15) 48 ________________ ____________________________________________________________________________________



________________

________________

17) Solve.

18) Solve.


equation:


Solving Equations UNIT 2 Warm-Up K

(2-K)



Factoring


x y

-2

-1

0

1

2


1)

= ______ 2)

= ______ 3)

= ______ 4)

= ______ 5)

= ______

6)

= ______ 7)

= ______ 8)

= ______ 9)

= ______ 10)

= ______




14) 49 ________________ ____________________________________________________________________________________ 15) 50 ________________ ____________________________________________________________________________________



________________

________________

17) Solve.

18) Solve.


equation:


Solving Equations UNIT 2 Warm-Up L

(2-L)



Factoring


x y

-2

-1

0

1

2


1)

= ______ 2)

= ______ 3)

= ______ 4)

= ______ 5)

= ______

6)

= ______ 7)

= ______ 8)

= ______ 9)

= ______ 10)

= ______




14) 51 ________________ ____________________________________________________________________________________ 15) 52 ________________ ____________________________________________________________________________________



________________

________________

17. Solve.

18) Solve.

19) Show checking the solution

into the

equation:

Was

a correct solution?

12) At 3:00 P.M. a tree 20 meters tall casts a shadow of 30 meters. A utility pole next to the tree casts a shadow of 12 meters. How tall is the pole?

13) A flagpole casts a shadow 9 feet long at the same time that a 72-foot building casts a shadow of 18 feet. How tall is the flagpole?

Solving Equations UNIT 2 Warm-Up M

(2-M)



Factoring


x y

-2

-1

0

1

2


1)

= ______ 2)

= ______ 3)

= ______ 4)

= ______ 5)

= ______

6)

= ______ 7)

= ______ 8)

= ______ 9)

= ______ 10)

= ______





14) 53 ________________ ____________________________________________________________________________________ 15) 54 ________________ ____________________________________________________________________________________


18) Solve.


equation:


Solving Equations UNIT 2 Warm-Up N

(2-N)



Factoring


x y

-5

-3

0

3

5


1)

= ______ 2)

= ______ 3)

= ______ 4)

= ______ 5)

= ______

6)

= ______ 7)

= ______ 8)

= ______ 9)

= ______ 10)

= ______





14) 55 ________________ ____________________________________________________________________________________ 15) 56 ________________ ____________________________________________________________________________________

16) Graph the inequalities on the number lines. a) b)

17) Write an equation for the following sentence. _______________________________________________

18) Solve.

19) Solve. – –

12) If 3 apples cost $6, how much would 12 apples cost?

13) 3 pounds of coffee cost $15. How many pounds can you buy for $45?

Solving Equations UNIT 2 Warm-Up O

(2-O)



Factoring


x y

-4

-3

-2

-1

0

Convert to a percent.

1)

= ______ 2) = ______ 3) = ______ 4) = ______ 5)

= ______

6)

= ______ 7)

= ______ 8)

= ______ 9) = ______ 10) = ______





15) 57 ________________ ____________________________________________________________________________________ 16) 58 ________________ ____________________________________________________________________________________


17) Write an equation for the following sentence.

_______________________________________________

18) Solve and then graph the solution set.

19) Solve. – –

12) Three tea bags are needed to make a gallon of iced tea. How many tea bags are needed to make four gallons?

13) If 5 pencils cost 20 cents, how much would 15 pencils cost?

Solving Equations UNIT 2 Warm-Up P

(2-P)



Factoring


x y

-2

-1

0

1

2


1) = ______ 2)

= ______ 3) = ______ 4)

= ______ 5) = ______

6) = ______ 7)

= ______ 8) = ______ 9)

= ______ 10)

= ______





14) 59 ________________ ____________________________________________________________________________________ 15) 60 ________________ ____________________________________________________________________________________


17) Write an equation for the following sentence.

_______________________________________________


19) Solve. – –

12) If 3 twinkies cost $1, how much is it for 15 twinkies?

13) You can buy 2 hot dogs for $3. How much would it be for 4 hot dogs?

Solving Equations UNIT 2 Warm-Up Q

(2-Q)



Factoring


x y

-5

-3

0

3

5


1)

= ______ 2) = ______ 3)

= ______ 4)

= ______ 5) = ______

6) = ______ 7)

= ______ 8)

= ______ 9) = ______ 10)

= ______





15) 61 ________________ ____________________________________________________________________________________ 16) 62 ________________ ____________________________________________________________________________________

16) Solve.

17) Solve.


19) Solve. – – –

12) The ratio of teachers to students needs to be 1:30. If there were 120 students, how many teachers would be needed?

13) The ratio of seventh graders to eighth graders participating in the science fair is 4:3. There are 18 eight graders participating in the science fair. How many 7th graders are there?

Solving Equations UNIT 2 Warm-Up R

(2-R)



Factoring


x y

-4

-2

0

2

4


1)

= ______ 2) = ______ 3) = ______ 4)

= ______ 5) = ______

6) = ______ 7)

= ______ 8)

= ______ 9) = ______ 10)

= ______





15) 63 ________________ ____________________________________________________________________________________ 16) 64 ________________ ____________________________________________________________________________________

16) Solve.

17) Solve.


19) Solve. – –

12) To make lemonade, you need 6 lemons and 8 cups of water. How many lemons do you need if you have 24 cups of water?

13) Darrell drove 187 miles in 3 hours. What was Darrell’s average rate of speed in miles per hour?

Solving Equations UNIT 2 Warm-Up S

(2-S)



Factoring


x y

-3

-1

0

1

3


1)

= ______ 2) = ______ 3) = ______ 4) = ______ 5)

= ______

6)

= ______ 7)

= ______ 8)

= ______ 9) = ______ 10) = ______





15) 65 ________________ ____________________________________________________________________________________ 16) 66 ________________ ____________________________________________________________________________________

16) Solve.

17) Solve.


19) Solve. – –

12) If three bakers can prepare 15 cakes in 60 minutes, how long will it take six bakers working at the same rate to prepare 20 cakes?

13) At Discount Copy, 12 copies cost $0.66. Melissa needs 56 copies. How much should they cost?

Solving Equations UNIT 2 Warm-Up T

(2-T)



Factoring


x y

-3

-1

0

1

3


1)

= ______ 2) = ______ 3)

= ______ 4) = ______ 5)

= ______

6) = ______ 7)

= ______ 8)

= ______ 9)

= ______ 10)

= ______





15) 67 ________________ ____________________________________________________________________________________ 16) 68 ________________ ____________________________________________________________________________________

16) Solve.

17) Solve.


19) Solve.

12) Two 100-W light bulbs used a total of 400 Wh of energy. For how many hours did the light bulbs use power?

13) An amusement park line is moving about 4 feet every 15 minutes. At this rate, approximately how long will it take for a person at the back of the 50- foot line to reach the front of the line?

solving equations unit 2 warm-up a - ms. ferguson

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