algebra class cumulative test: units 1-3 solving … equations/cumm te… · cu mulative test:...

Cumulative Test: Units 1-3

Algebra Class


Solving Equations, Graphing

Equations & Writing Equations


Algebra 1 Exam – Answer Sheet

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Part 1: Multiple Choice - Questions are worth 1 point each.

Multiple Choice - Total Correct:

___________________ (out of 15 points total)


Algebra 1 Answer Sheet - Continued

Part 2: Fill in the blank. Answers are worth 2 points each.

16.

17. 18.


19.

20.

21.

Fill In the Blank - Total Correct:



Part 3: Short Answer - 3 points each

22.

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23.

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24.

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Short Answer - Total Correct:


Cumulative Test- Total Correct: (Add the total points for all 3 sections)


33-36 – A 22-25 - D

29-32 – B 21 and below - E

26-28 -C


Algebra Class Part 1 – Cumulative Test

Solving Equations, Graphing Equations, & Writing Equations

Part 1: Multiple Choice. Choose the best answer for each problem. (1 point each)

1. Which equation is represented on the graph?

A. y = -3/4x + 6

B. y = 4/3x + 7

C. y = -4/3x + 6

D. y = 4/3x + 6

2. Which line on the graph has a slope of ½?

A. Line A

B. Line B

C. Line C

D. Line D


3. Which of the following steps would you use first to solve the following equation?

3(x-7) + 4 = 20

A. Subtract 4 from both sides.

B. Add 4 to both sides.

C. Divide by 3 on both sides.

D. Distribute the 3 throughout the parenthesis.

4. Solve for x: ½(2x-4) + 5 = -1

A. x = -4

B. x = -3/2

C. x = -7/2

D. x = 4

5. Write the following equation in standard form: y = ¼x – ¾

A. x – 4y = -3

B. x – 4y = 3

C. ¼x – y = ¾

D. –x + 4y = -3


6. Find the slope of the line that passes through the points (5,2) & (-9, 10)

A. 2

B. -2

C. -4/7

D. 4/7

7. Which equation represents the line that passes through the points (-6, 4) & (5,4)

A. y = 4x

B. y = 4

C. y = x + 4

D. y = 11x + 4

8. Which description best represents the graph for the equation: y = -9

A. A horizontal line through the point (0, -9)

B. A vertical line through the point (0, -9)

C. A vertical line through the point (-9, 0)

D. A line with a rise of -9 and a run of 1 that passes through the origin.


9. Solve for y: 6y + 4 = 4(y-2) + 16

A. y = 10

B. y = -2

C. y = -10

D. y = 2

10. The relation between the sides of a rectangle are shown below. The perimeter of the rectangle

is 32 cm. What is the length of the longest side of the rectangle.

x + 2

2x + 2

A. 4cm

B. 6 cm

C. 10 cm

D. 20 cm

11. What is the x intercept for the equation: 4x – 8y = -40

A. x-intercept = -5 (-5,0)

B. x-intercept = 5 (5,0)

C. x-intercept = -10 (-10,0)

D. x-intercept = 10 (10,0)


12. Which equation is equivalent to: 4x + 3y = 6

A. y = -4/3x + 2

B. y = 4/3x + 2

C. y = -4x + 6

D. y = -3/4x + 6

13. A landscaping company charges $7.50 per yard of mulch plus a $15 delivery fee. Which

equation could you use to find the cost of having a yard of mulch delivered?

A. 7.50x + y = 15

B. y = 7.50x + 15

C. 15x + y = 7.50

D. y = 15x + 7.50

14. Theresa is selling candy bars for $1.50 a piece and candles for $5 apiece. She has made a

total of $145.00 in sales. Which equation could be used to determine the amount of candy bars and

candles sold? Let x represent the number of candy bars and y represent the number of candles.

A. y = 1.5x + 5

B. x + y = 145

C. 5x + 1.50y = 145

D. 1.50x + 5y = 145

15. Adam found a job that offered him an average pay raise of $1500 per year. After 8 years on the

job, Adam’s salary was $72000. What was the starting salary that Adam was offered when he took

the job?

A. $12,000

B. $60,000

C $70,500

D. $65,000


Part 2: Fill in the blank. Solve each problem on your answer sheet. Show all of your work.

(2 points each)

16. Solve for x: ¼x – 8 = ⅔(x – 19.5)

17. Graph the following equation on the grid: 8x – 2y = -16

18. Graph the following equation on the grid: y = -4/5x + 8

19. In the year 2003, the average cost of a trip to Disney World for a family of four was $2300. In

2010, the average cost of a trip to Disney for a family of four is $4,200. Write an equation that can

be used to predict the cost of a trip to Disney for any year after 2000. Let x = 0 represent the year

2000.

(Round all decimals to the hundredths place)

20. The ticket prices for attending a Yankees baseball game increase by $2.75 per year. In the

year 2009, the ticket price for a premium terrace seat was $80. Write an equation that could be

used to determine the price of a premium terrace seat for any year after 2000. Let x = 0 represent

the year 2000.

21. A local banquet room charges $35 an hour for use of facilities plus a $30 clean up fee. How

many hours can Joseph rent the hall for $240?


Part 3: Short answer. Respond to each problem on your answer sheet. Make sure you

answer all parts of each problem. (3 points each)

22. Laurie knits sweaters for dogs, babies, and children. She sells them at craft shows. She sold 3

times as many baby sweaters than dog sweaters. She sold 5 more children sweaters than dog

sweaters. The prices for each sweater are shown below:

Dog - $7.50 Baby - $10.25 Children - $ 14.75

• Write an expression to represent the number of baby sweaters sold and an expression to

represent the number of children’s sweaters sold. Let x represent the number of dog

sweaters sold.

• The total sales for Laurie’s sweaters was $391.75. Write an equation to represent the total

sales of Laurie’s sweaters.

• How many baby sweaters did Laurie sell? Explain how you determined your answer.

23. The cost of tuition at a private school in the year 2002 was $12,100. In the year 2009 the cost

was $16,900. Let x = 0 represent the year 2000.

• Write an equation that could be used to predict the tuition for any year after 2000.

• Predict the tuition for the year 2015.


24. Carl has been tracking the price of round trip airfare between Baltimore and Orlando for 10

weeks. The results are show in the graph below.

• What is the y-intercept in this problem? What does it mean in the context of this problem?

• What is the rate of change between weeks 4 and 6?

Copyright© 2009 Algebra-class.com

Unit Unit Unit Unit 3333: : : : WritingWritingWritingWriting EquationsEquationsEquationsEquations

Algebra Class Part 1 – Cumulative Test – Answer Key

Solving Equations, Graphing Equations, & Writing Equations

Part 1: Multiple Choice. Choose the best answer for each problem. (1 point each)

1. Which equation is represented on the graph?

A. y = -3/4x + 6

B. y = 4/3x + 7

C. y = -4/3x + 6

D. y = 4/3x + 6

2. Which line on the graph has a slope of ½?

A. Line A

B. Line B

C. Line C

D. Line D

Y-intercept = 6 The line is falling from left to right,

so you know that the slope is

negative. Therefore, you can

eliminate answers B & D since they

have positive slopes.

The slope of this line is -4/3 (count

down 4 and right 3). The y-

intercept is 6. The correct answer

choice is C.

Line A is the only line that has a rise

of 1 and a run of 2. Count up 1

and right 2.

You can eliminate answer choices

B and C since they are falling from

left to right. This means they have

a negative slope.



3. Which of the following steps would you use first to solve the following equation?

3(x-7) + 4 = 20

A. Subtract 4 from both sides.

B. Add 4 to both sides.

C. Divide by 3 on both sides.

D. Distribute the 3 throughout the parenthesis.

4. Solve for x: ½(2x-4) + 5 = -1

A. x = -4

B. x = -3/2

C. x = -7/2

D. x = 4

5. Write the following equation in standard form: y = ¼x – ¾

A. x – 4y = -3

B. x – 4y = 3

C. ¼x – y = ¾

D. –x + 4y = -3

If the distributive property is present, you must

distribute first to remove the parenthesis.

2[½(2x-4) + 5] = -1(2) Multiply by 2 to get rid of

the fraction.

1(2x-4) + 10 = -2 Result after multiplying by 2

2x -4 + 10 = -2

2x + 6 = -2 Combine like terms (-4 + 10)

2x + 6 – 6 = -2 – 6 Subtract 6 from both sides.

2x = -8 Simplify: (-2 -6= -8)

2x/2 = -8/2 Divide by 2 on both sides.

x = -4

(4)y = 4[¼x – ¾] Multiply by 4 to remove the fraction.

4y = x – 3 Result after multiplying by 4

-x + 4y = x –x – 3 Subtract x on both sides.

-x + 4y = -3 Simplify

-1[-x +4y] = -3(-1) Multiply by -1 to make the lead coefficient

positive.

x – 4y = 3



6. Find the slope of the line that passes through the points (5,2) & (-9, 10)

A. 2

B. -2

C. -4/7

D. 4/7

7. Which equation represents the line that passes through the points (-6, 4) & (5,4)

A. y = 4x

B. y = 4

C. y = x + 4

D. y = 11x + 4

8. Which description best represents the graph for the equation: y = -9

A. A horizontal line through the point (0, -9)

B. A vertical line through the point (0, -9)

C. A vertical line through the point (-9, 0)

D. A line with a rise of -9 and a run of 1 that passes through the origin.

Use the formula to find the slope of two points:

y2- y1 = 10 – 2 = 8 = 4

x2 – x1 -9 – 5 -14 -7

Simplify to lowest terms

The slope of the line is -4/7

Step 1: First find the slope of the line by using the formula:

y2- y1 = 4 – 4 = 0 Slope = 0

x2 – x1 5 –(-6) 11

Step 2: Find the y-intercept using the slope, and 1 point.

y = mx + b

4 = 0(5) + b

4 = b

Y = 0x + 4 should be written as: y = 4

**You may also have realized that both

points given had a y-coordinate of 4.

Therefore this is a horizontal line with a y-

intercept of 4.

All points have a y-coordinate of 9. Therefore, the

result is a horizontal line through the point (0,-9).

**A vertical line would start with x =



9. Solve for y: 6y + 4 = 4(y-2) + 16

A. y = 10

B. y = -2

C. y = -10

D. y = 2

10. The relation between the sides of a rectangle is shown below. The perimeter of the rectangle is

32 cm. What is the length of the longest side of the rectangle.

x + 2

2x + 2

A. 4cm

B. 6 cm

C. 10 cm

D. 20 cm

11. What is the x intercept for the equation: 4x – 8y = -40

A. x-intercept = -5 (-5,0)

B. x-intercept = 5 (5,0)

C. x-intercept = -10 (-10,0)

D. x-intercept = 10 (10,0)

6y + 4 = 4y – 8 + 16 Distribute 4 throughout the parenthesis

6y + 4 = 4y + 8 Combine like terms (-8+16 = 8)

6y – 4y + 4 = 4y – 4y + 8 Subtract 4y from both sides.

2y +4 = 8 Combine like terms (6y – 4y = 2y)

2y + 4 -4 = 8- 4 Subtract 4 from both sides

2y = 4 Simplify: (8 – 4 = 4)

2y/2 = 4/2 Divide by 2 on both sides.

y = 2

P = 2L + 2w The perimeter formula

32 = 2(2x+2) + 2(x+2) Substitute for P, L & W.

32 = 4x + 4 + 2x + 4 Distribute: (2 sets that involve the distributive

property.)

32 = 6x + 8 Combine like terms.

32 – 8 = 6x + 8 -8 Subtract 8 form both sides.

24 = 6x Simplify: 32-8 = 24

24/6 = 6x/6 Divide by 6 on both sides

4 = x

If x = 4, then the longest side is 2x+2

2(4) +2 = 10 cm

To find the x-intercept, let y = 0

4x – 8(0) = -40 Substitute 0 for y.

4x = -40

4x/4 = -40/4 Divide by 4 on both sides.

x = -10

The x-intercept is -10 or (-10,0)



12. Which equation is equivalent to: 4x + 3y = 6

A. y = -4/3x + 2

B. y = 4/3x + 2

C. y = -4x + 6

D. y = -3/4x + 6

13. A landscaping company charges $7.50 per yard of mulch plus a $15 delivery fee. Which

equation could you use to find the cost of having a yard of mulch delivered?

A. 7.50x + y = 15

B. y = 7.50x + 15

C. 15x + y = 7.50

D. y = 15x + 7.50

14. Theresa is selling candy bars for $1.50 a piece and candles for $5 apiece. She has made a

total of $145.00 in sales. Which equation could be used to determine the amount of candy bars and

candles sold? Let x represent the number of candy bars and y represent the number of candles.

A. y = 1.5x + 5

B. x + y = 145

C. 5x + 1.50y = 145

D. 1.50x + 5y = 145

15. Adam found a job that offered him an average pay raise of $1500 per year. After 8 years on the

job, Adam’s salary was $72000. What was the starting salary that Adam was offered when he took

the job?

A. $12,000

B. $60,000

C $70,500

D. $65,000

Rewrite the equation in slope intercept form:

4x -4x + 3y = -4x + 6 Subtract 4x from both sides.

3y = -4x + 6

3y/3 = -4x/3 + 6/3 Divide all terms by 3.

y = -4/3x + 2

7.50 per yard is the rate or slope in the problem. “Per” is your keyword for slope.

15 is a delivery or set fee. This is the y-intercept.

Since you know the slope and y-intercept, this equation can be written in slope

intercept form:

Y = mx + b m = 7.50 b = 15

Y = 7.50x + 15

Since we know the total (145) and we can add the sales of candy bars + candles to

get this total, we can write the equation in standard form.

Price of candy• # of candy + Price of candles • number of candles = total sales

1.50x + 5y = 145

We know the rate of change or slope (1500 per year). We also know a point (8, 72000)

In order to find the starting salary (when year = 0 or x = 0), we need to find the y-intercept.

Let’s substitute:

Y = mx + b m = 1500 x = 8 y = 72000

72000 = 1500(8) + b

72000 = 12000+ b

72000 – 12000 = 12000-12000 + b Subtract 12000 from both sides.

60000 = b Therefore, his starting salary is 600000.



Part 2: Fill in the blank. Solve each problem on your answer sheet. Show all of your work.

(2 points each)

16. Solve for x: ¼x – 8 = ⅔(x – 19.5)

17. Graph the following equation on the grid: 8x – 2y = -16

12[¼x – 8] = 12[⅔(x – 19.5)] Multiply both sides by the LCM, 12.

3x – 96 = 8(x – 19.5) Result after multiplying by 12.

3x – 96 = 8x – 156 Distribute the 8 throughout the parenthesis

3x -8x – 96 = 8x -8x – 156 Subtract 8x from both sides.

-5x -96 = -156 Simplify: 3x -8x = -5x

-5x -96 + 96 = -156 + 96 Add 96 to both sides.

-5x = -60 Simplify: -156+96 = -60

-5x/-5 = -60/-5 Divide both sides by -5

X = 12

Answer: x = 12

Step 1: Find the x-intercept.

8x -2(0) = -16 Let y = 0

8x = -16

X = -2 x-intercept = -2

Step 2: Find the y-intercept.

8(0) – 2y = -16

-2y = -16

Y = 8 y-intercept = 8



18. Graph the following equation on the grid: y = -4/5x + 8

19. In the year 2003, the average cost of a trip to Disney World for a family of four was $2300. In

2010, the average cost of a trip to Disney for a family of four is $4,200. Write an equation that can

be used to predict the cost of a trip to Disney for any year after 2000. Let x = 0 represent the year

2000.

(Round all decimals to the hundredths place)

Y = mx + b

Y = -4/5x + 8

Slope y-intercept

Step 1: Plot the point (0,8) this is the y-

intercept.

Step 2: From this point count down 4 and right

5. The slope is -4/5. Plot this point and draw a

line through your two points.

Step 1: We can write two ordered pairs from this problem: (3, 2300) (10, 4200)

Step 2: Use the formula to find the slope.

y2- y1 = 4200 – 2300 = 1900 = 271.43 The slope is 271.43

x2 – x1 10 -3 7

Step 3: Choose 1 point to substitute into the slope intercept form equation. I chose (3, 2300)

Y = mx + b

2300 = 271.43(3) + b

2300 = 814.29 + b Simplify: 271.43(3) = 814.29

2300 – 814.29 = 814.29 – 814.29 + b Subtract 814.29 from both sides

1485.71 = b Simplify: 2300- 814.29 = 1485.71

Now that we know the slope and y-intercept we can write the equation.

Y = 271.43x + 1485.71



20. The ticket prices for attending a Yankees baseball game increase by $2.75 per year. In the

year 2009, the ticket price for a premium terrace seat was $80. Write an equation that could be

used to determine the price of a premium terrace seat for any year after 2000. Let x = 0 represent

the year 2000.

21. A local banquet room charges $35 an hour for use of facilities plus a $30 clean up fee. How

many hours can Joseph rent the hall for $240?

In this problem, we know the rate (slope) is 2.75 per year. (Per year are your key words for slope)

We also know a point (9, 80) (In the year 2009, the price was 80)

We can use the slope and a point and substitute into y = mx + b to find b (the y-intercept)

Y = mx + b m = 2.75 (9, 80)

80 = 2.75 (9) + b Substitute

80 = 24.75 + b Simplify: 2.75 • 9 = 24.75

80 – 24.75 = 24.75 – 24.75 + b Subtract 24.75 from both sides.

55.25 = b Simplify: 80-24.75 = 55.25

Y = mx + b m = 2.75 b = 55.25

Y = 2.75x + 55.25 The equation written in slope intercept form.

Step 1: In this problem we know the rate (slope) is $35 an hour. The fee is $30 flat, so this is the y-

intercept.

Since we know the slope and y-intercept we can write the equation in slope intercept form.

Y = mx + b m = 35 b = 30

Y = 35x + 30 y = total cost & x= the number of hours

Step 2: We know the total amount spent is $240, therefore this represents y in the equation.

Y = 35x + 30

240 = 35x + 30 Substitute 240 for y.

240 – 30 = 35x + 30 -30 Subtract 30 from both sides.

210 = 35x Simplify: 240-30 = 210

210/35 = 35x/35 Divide by 35 on both sides.

6 = x x = 6 Joseph could rent the hall for 6 hours for $240.



Part 3: Short answer. Respond to each problem on your answer sheet. Make sure you

answer all parts of each problem. (3 points each)

22. Laurie knits sweaters for dogs, babies, and children. She sells them at craft shows. She sold 3

times as many baby sweaters than dog sweaters. She sold 5 more children sweaters than dog

sweaters. The prices for each sweater are shown below:

Dog - $7.50 Baby - $10.25 Children - $ 14.75

• Write an expression to represent the number of baby sweaters sold and an expression to

represent the number of children’s sweaters sold. Let x represent the number of dog

sweaters sold.

• The total sales for Laurie’s sweaters was $391.75. Write an equation to represent the total

sales of Laurie’s sweaters.

• How many baby sweaters did Laurie sell? Explain how you determined your answer.

x = dog sweaters

3x = baby sweaters

x + 5 = children’s sweaters

Price (dog) • # of dog + Price (baby) • # of baby + Price (children’s) • # of children’s = total sales

7.50x + 10.25(3x) + 14.75(x+5) = 391.75

7.50x + 10.25(3x) + 14.75(x+5) = 391.75 Equation

7.50x + 30.75x + 14.75x + 73.75 = 391.75 Distribute

53x + 73.75 = 391.75 Combine like terms (x terms)

53x + 73.75 – 73.75 = 391.75 – 73.75 Subtract 73.75

53x = 318 Simplify (391.75-73.75 = 318)

53x/53 = 318/53 Divide by 53 on both sides

X = 6

Baby sweaters = 3x

3 • 6 = 18

Laurie sold 18 baby sweaters. I solved the equation

for x. I found that x = 6 which meant that she had

sold 6 dog sweaters. Since she sold 3 times as many

baby sweaters as dog sweaters, I multiplied 3 times 6

to get 18.



23. The cost of tuition at a private school in the year 2002 was $12,100. In the year 2009 the cost

was $16,900. Let x = 0 represent the year 2000.

• Write an equation that could be used to predict the tuition for any year after 2000.

• Predict the tuition for the year 2015.

I can write two ordered pairs: (2, 12100) & (9, 16900)

Step 1: Find the slope using the formula.

y2- y1 = 16900 – 12100 = 4800 = 685.71 The slope (m) is 685.71

x2 – x1 9-2 7

Step 2: Substitute the slope and 1 point into the slope intercept form equation to find b.

Y = mx + b m = 685.71 x = 2 y = 12100

12100 = 685.71(2) + b Substitute

12100 = 1371.42 + b Simplify: 685.71(2) = 1371.42

12100 – 1371.42 = 1371.42 -1371.42 + b Subtract 1371.42 from both sides

10728.58 = b

M = 685.71 b = 10728.58

• Y = 685.71x + 10728.58 is the equation that can be used to predict the tuition for any year

after 2000.

Step 3: To predict the tuition for the year 2015, substitute 15 for x into the equation.

Y = 685.71x + 10728.58

Y = 685.71(15) + 10728.58

Y = 21014.23

• The cost of tuition for the year 2015 is predicted to be 21014.23.



Umm

24. Carl has been tracking the price of round trip airfare between Baltimore and Orlando for 10

weeks. The results are show in the graph below.

• What is the y-intercept in this problem? What does it mean in the context of this problem?

• What is the rate of change between weeks 4 and 6?

• The y-intercept in this problem is 250. This means that when Carl first started tracking

the airfares, the cost of roundtrip airfare to Orlando was $250.

In order to find the rate of change between weeks 4 and 6, we will need to write two points and

use the slope formula.

(4, 350) (6, 150)

y2- y1 = 150 – 350 = -200 = -100

x2 – x1 6-4 2

The rate of change between weeks 4 and 6 is -100. This means that the cost of the airfare

dropped about $100 per week during this 2 week time span.



Cumulative Test Part 1: Analysis Sheet

Directions: For any problems, that you got wrong on the answer sheet, circle the

number of the problem in the first column. When you are finished, you will be able to

see which Algebra units you need to review before moving on. (If you have more

than 2 circles for any unit, you should go back and review the examples and practice

problems for that particular unit.)

Problem Number

Algebra Unit

3, 4, 9, 10, 16, 21, 22 Solving Equations Unit

2, 6, 8, 11, 12, 17, 18, 24 Graphing Equations Unit

1, 5, 7, 13, 14, 15, 19, 20, 23 Writing Equations Unit

Please take the time to go back and review the problems that you got incorrect. All of

the skills that you learned in these three units, will be needed to solve problems in the

upcoming units.

algebra class cumulative test: units 1-3 solving … equations/cumm te… · cu mulative test:...

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