Coordinate Algebra Practice EOCT Answers Unit 1. #1 Unit 1 A rectangle has a length of 12 m and a...

Coordinate AlgebraPractice

EOCT AnswersUnit 1

#1 Unit 1A rectangle has a length of 12 m and a width of 400 cm. What is the perimeterof the rectangle?

Step 1: Change 12 meters to centimeters

× 100 cm 1 m

= 1200 cm12 m1

Step 2: Find perimeter using formula P = 2L + 2W

400 cm

1200 cm P = 2(1200 cm) + 2(400 cm)

P = 2400 cm + 800 cm

P = 3200 cm

A. 824 cm

B. 1600 cm

C. 2000 cm

D. 3200 cm

#2 Unit 1

The tension caused by a wave moving along a string is found

using the formula T = . If m is the mass of the string in

grams, L is the length of the string in centimeters, and v is the velocity of the wave in centimeters per second, what is the unit of the tension of the string, T ?

2mv

L

2 22

2

( )

( )

sec (sec)

( )

m grams g

cm cmv

L cm

2mvT

L

2

2

( )( )

(sec)( )

cmg

cm

#2 Unit 1

(cm)

1

2

2

( )( )

(sec)( )

cmg

Tcm

2

2

( )(sec)( )

g cm

cm

2

2

( ) ( )

(sec) 1

g cm cm

2

2 1

( ) 1

(sec) ( )

g cmT

cm

1

2

( ) 1

(sec) 1

g cm 2

( )

(sec)

g cm

A. gram-centimeters per second squaredB. centimeters per second squaredC. grams per centimeter-second squaredD. centimeters squared per second

#3 Unit 1

The distance a car travels can be found using the formula d = rt, where d is the distance, r is the rateof speed, and t is time. How many miles does the car travel, if it drives at a speed of 70 miles per hour for ½ hour?

d = r t1

270 miles hour

hour 1d

70 miles 0.5 hour

hour 1d = 35 miles

A. 35 miles

B. 70 miles

C. 105 miles

D. 140 miles

#4

Unit 1 A certain population of bacteria has an average growth rate of 0.02 bacteria per hour. The formula for the growth of the bacteria’s population is A= P (2.71828)0.02t, where P0 is the original population, and t is the time in hours.

If you begin with 200 bacteria, about how many bacteria will there be after 100 hours?

A= 200(2.71828)0.02100

A= 200(2.71828)2

A= 200(7.389046)

A= P(2.71828)0.02t

= 1477.81

Answer

1478

#5 Unit 1

The sum of the angle measures in a triangle is 180°. Two angles of a triangle measure 20° and 50°. What is the measure of the third angle?

Third Angle = x

x + 20° + 50° = 180°

x + 70° = 180°–70° –70°

x = 110°

A. 30°B. 70°C. 110°D. 160°

#6 Unit 1Which equation shows P = 2l + 2w when solved for w ?

–2l –2lP = 2l + 2w

P – 2l = 2w

P – 2l 2w 2 2

P – 2l2

=

= w

A.

B.

C.

D.

P

lw

2

2

2 Plw

22

Plw

2

2lPw

#7 Bruce owns a business that produces widgets. He must bring in more in revenue than he paysout in costs in order to turn a profit.

It costs $10 in labor and materials to make each of his widgets. His rent each month for his factory is $4000. He sells each widget for $25.

How many widgets does Bruce need to sell monthly to make a profit?

A. 160B. 260C. 267D. 400

C = 10x + 4000R = 25x

Cost to make x widgetsRevenue (in dollars)from selling x widgets

Unit 1

Note: A profit occurs when enough widgets are made and sold to break even. (i.e. R = C)

R = C25x = 10x + 4000(Set up equation)

#7 Bruce owns a business that produces widgets. He must bring in more in revenue than he paysout in costs in order to turn a profit.

It costs $10 in labor and materials to make each of his widgets. His rent each month for his factory is $4000. He sells each widget for $25.

How many widgets does Bruce need to sell monthly to make a profit?

A. 160B. 260C. 267D. 400

Unit 1

25x = 10x + 4000(Set up equation)

–10x –10x

15x = 4000

15x 400015 15=

x = 267

Note: A minimum of 267 widgets must be sold in order to make a profit.

Coordinate AlgebraPractice

EOCT AnswersUnit 2

#1 Unit 2Which equation shows ax – w = 3 solved for w ?

–axax – w = 3

–w = 3 – ax–ax

=–1–w 3 – ax

–1w = –3 + axw = ax – 3

A. w = ax – 3B. w = ax + 3C. w = 3 – axD. w = 3 + ax

#2 Unit 2Which equation is equivalent to

118

3

4

7

xx?

A. 17x = 88

B. 11x = 88

C. 4x = 44

D. 2x = 44

Least Common Denominator

8

7 311

4 8

x x

8 8

1 1

7 3 11

4 8

x x

56 24 88

4 8

x x

14x – 3x = 88

11x = 88

#3 Unit 2Which equation shows 4n = 2(t – 3) solved for t ?

4n = 2(t – 3)

2n = t – 3

24n 2(t – 3)

2=

+3+32n + 3 = t

4n = 2(t – 3)

4n = 2t – 6+6+6

4n + 6 = 2t

2n + 3 = t

Method #1 Method #2

4n + 6 2t22 =

#4 Unit 2Which equation shows 6(x + 4) = 2(y + 5) solved for y ?

6(x + 4) = 2(y + 5)

–106x + 24 = 2y + 10

–106x + 14 = 2y

3x + 7 = y

6x + 14 2y22

=

A. y = x + 3

B. y = x + 5

C. y = 3x + 7

D. y = 3x + 17

#5 Unit 2This equation can be used to find h, the number of hours it takes Flo and Bryan to mow their lawn.How many hours will it take them to mow their lawn?

A. 6

B. 3

C. 2

D. 1


6

2h + h = 6

13 6

h h

6 6

1 1

13 6

h h

6 6 6

3 6

h h

3h = 6h = 2

3h 63 3

=

#6 Unit 2This equation can be used to determine how many miles apart the two communities are. What is m, the distance between the two communities?

A. 0.5 miles

B. 5 miles

C. 10 miles

D. 15 miles


20

2m = m + 10

5.0515515

mm

0.510 20

m m

20 20

1 1

–m –m

m = 10

0.510 20

m m

20 20 10

10 20

m m

#7 Unit 2For what values of x is the inequality true?

A. x < 1

B. x > 1

C. x < 5

D. x > 5


3

2 + x > 3–2 –2

2 1

3 3

x

2 1

3 3

x

3 3

1 1

6 3 3

3 3

x

x > 1

#8

Unit 2 A manager is comparing the cost of buying ball capswith the company emblem from two different companies.

A. 10 capsB. 20 capsC. 40 capsD. 100 caps

•Company X charges a $50 fee plus $7 per cap.•Company Y charges a $30 fee plus $9 per cap.

For what number of ball caps (b) will themanager’s cost be the same for both companies?

Cost Formula: Company X

CX = 7b + 50Cost Formula: Company Y

CY = 9b + 30CX = CY

7b + 50 = 9b + 30 (Subtract 7b on both sides)

50 = 2b + 30 (Subtract 30 on both sides)

20 = 2b (Divide 2 on both sides)

10 = b

#9Unit 2A shop sells one-pound bags of peanuts for $2 and

three-pound bags of peanuts for $5. If 9 bags are purchased for a total cost of $36, how many three-pound bags were purchased?

Let x = # of one-pound bagsLet y = # of three-pound bags

Method #1Substitution

(Total number of bags)x + y = 9Equation #1:(Total value of bags)2x + 5y = 36Equation #2:

Solve Equation #1 for x

x + y = 9–y –y

x = 9 – y

Substitute x = 9 – y into Equation #2

2(9 – y) + 5y = 3618 – 2y + 5y = 36

18 + 3y = 363y = 18y = 6

6 three-poundbags

#9Unit 2A shop sells one-pound bags of peanuts for $2 and

three-pound bags of peanuts for $5. If 9 bags are purchased for a total cost of $36, how many three-pound bags were purchased?

Let x = # of one-pound bagsLet y = # of three-pound bags

Method #2Elimination

(Total number of bags)x + y = 9Equation #1:(Total value of bags)2x + 5y = 36Equation #2:

Multiply Equation #1 by –2

–2(x + y) = –2(9)

Add New Equation #1 and Equation #2

3y = 18

y = 66 three-pound

bags

–2x – 2y = –18

–2x – 2y = –182x + 5y = 36

(New Equation #1)

#10 Unit 2Which graph represents a system of linear equations that has multiple common coordinate pairs?

A.

C. D.

Has onecommon

coordinatepair

Has onecommon

coordinatepair

Has nocommon

coordinatepairs

Multiplecommon

coordinatepairs

(Two linesoverlap)

B.

#11 Unit 2Which graph represents x > 3 ?

A.

B.

C.

D.

x > 3

x > 3

x < 3

x < 3

#12 Unit 2Which pair of inequalities is shown in the graph?

A. y > –x + 1 and y > x – 5

B. y > x + 1 and y > x – 5

Line 1Line 2

Both given inequalities haveslopes equal to positive one.This is a contradiction to theslope of Line 1 being negative.

NoteLine 1 graph has a negative slope.Line 2 graph has a positive slope.


C. y > –x + 1 and y > –x – 5

D. y > x + 1 and y > –x – 5

Line 1Line 2


Both given inequalities haveslopes equal to negative one.This is a contradiction to theslope of Line 2 being positive.

Line 2 has a positive slopewith a negative y-intercept.However, the line y > x + 1has a positive slope, but they-intercept is positive.


A. y > –x + 1 and y > x – 5

B. y > x + 1 and y > x – 5

Line 1Line 2

Both given inequalities haveslopes equal to positive one.This is a contradiction to theslope of Line 1 being negative.


Coordinate Algebra Practice EOCT Answers Unit 1. #1 Unit 1 A rectangle has a length of 12 m and a...

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