Cumulative Test: Units 1-3. Algebra Class Cumulative Test: Units 1-3 Solving Equations, Graphing Equations & Writing Equations

Transcription

1 Algebra Class Cumulative Test: Units 1-3 Solving Equations, Graphing Equations & Writing Equations

2 Algebra 1 Exam Answer Sheet Part 1: Multiple Choice - Questions are worth 1 point each.. Multiple Choice - Total Correct: (out of 15 points total)

3 Algebra 1 Answer Sheet - Continued Part 2: Fill in the blank. Answers are worth 2 points each

4 Fill In the Blank - Total Correct: (out of 12 points total)

5 Part 3: Short Answer - 3 points each

6 24. Short Answer - Total Correct: (out of 9 points total) Cumulative Test- Total Correct: (Add the total points for all 3 sections) (out of 36 points total) A D B 21 and below - E C

7 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 Which line on the graph has a slope of ½? A. Line A B. Line B C. Line C D. Line D

8 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

9 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 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.

10 9. Solve for y: 6y + 4 = 4(y-2) + 16 A. y = 10 B. y = -2 C. y = -10 D. y = 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)

11 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 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 Theresa is selling candy bars for $1.50 a piece and candles for $5 apiece. She has made a total of $ 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 y = 145 D. 1.50x + 5y = 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 $ 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

12 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 = Graph the following equation on the grid: y = -4/5x 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 Let x = 0 represent the year (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 Let x = 0 represent the year 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?

13 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 - $ 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 $ 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 Write an equation that could be used to predict the tuition for any year after Predict the tuition for the year 2015.

14 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?

15 Unit 3: Writing Equations 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 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. Y-intercept = 6 2. Which line on the graph has a slope of ½? A. Line A B. Line B C. Line C D. Line D 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. Copyright 2009 Algebra-class.com

16 Unit 3: Writing Equations 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. If the distributive property is present, you must distribute first to remove the parenthesis. 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 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 = -2 2x + 6 = -2 Combine like terms ( ) 2x = -2 6 Subtract 6 from both sides. 2x = -8 Simplify: (-2-6= -8) 2x/2 = -8/2 Divide by 2 on both sides. x = 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 (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 Copyright 2009 Algebra-class.com

17 Unit 3: Writing Equations 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 Use the formula to find the slope of two points: y 2 - y 1 = 10 2 = 8 = 4 x 2 x Simplify to lowest terms The slope of the line is -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 Step 1: First find the slope of the line by using the formula: y 2 - y 1 = 4 4 = 0 Slope = 0 x 2 x 1 5 (-6) 11 Step 2: Find the y-intercept using the slope, and 1 point. y = mx + b 4 = 0(5) + b 4 = b **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. Y = 0x + 4 should be written as: y = 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) 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 = 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. Copyright 2009 Algebra-class.com

18 Unit 3: Writing Equations 9. Solve for y: 6y + 4 = 4(y-2) y + 4 = 4y Distribute 4 throughout the parenthesis A. y = 10 6y + 4 = 4y + 8 Combine like terms (-8+16 = 8) B. y = -2 6y 4y + 4 = 4y 4y + 8 Subtract 4y from both sides. C. y = -10 D. y = 2 2y +4 = 8 Combine like terms (6y 4y = 2y) 2y = 8-4 Subtract 4 from both sides 2y = 4 Simplify: (8 4 = 4) 2y/2 = 4/2 Divide by 2 on both sides. y = 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 P = 2L + 2w The perimeter formula A. 4cm B. 6 cm C. 10 cm D. 20 cm 32 = 2(2x+2) + 2(x+2) Substitute for P, L & W. 32 = 4x x + 4 Distribute: (2 sets that involve the distributive property.) 32 = 6x + 8 Combine like terms = 6x 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 11. What is the x intercept for the equation: 4x 8y = -40 To find the x-intercept, let y = 0 A. x-intercept = -5 (-5,0) B. x-intercept = 5 (5,0) C. x-intercept = -10 (-10,0) D. x-intercept = 10 (10,0) Copyright 2009 Algebra-class.com 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)

19 Unit 3: Writing Equations 12. Which equation is equivalent to: 4x + 3y = 6 Rewrite the equation in slope intercept form: A. y = -4/3x + 2 B. y = 4/3x + 2 C. y = -4x + 6 D. y = -3/4x + 6 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 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 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 Theresa is selling candy bars for $1.50 a piece and candles for $5 apiece. She has made a total of $ 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 y = 145 D. 1.50x + 5y = 145 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 = 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 $ What was the starting salary that Adam was offered when he took the job? A. $12,000 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 = B. $60, = 1500(8) + b C $70, = b = b Subtract from both sides. D. $65, = b Therefore, his starting salary is Copyright 2009 Algebra-class.com

20 Unit 3: Writing Equations 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) 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 = Add 96 to both sides. -5x = -60 Simplify: = -60-5x/-5 = -60/-5 Divide both sides by -5 X = 12 Answer: x = Graph the following equation on the grid: 8x 2y = -16 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 Copyright 2009 Algebra-class.com

21 Unit 3: Writing Equations 18. Graph the following equation on the grid: y = -4/5x + 8 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. 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 Let x = 0 represent the year (Round all decimals to the hundredths place) Step 1: We can write two ordered pairs from this problem: (3, 2300) (10, 4200) Step 2: Use the formula to find the slope. y 2 - y 1 = = 1900 = The slope is x 2 x Step 3: Choose 1 point to substitute into the slope intercept form equation. I chose (3, 2300) Y = mx + b 2300 = (3) + b 2300 = b Simplify: (3) = = b Subtract from both sides = b Simplify: = Now that we know the slope and y-intercept we can write the equation. Y = x Copyright 2009 Algebra-class.com

22 Unit 3: Writing Equations 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 Let x = 0 represent the year 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 = b Simplify: = = b Subtract from both sides = b Simplify: = Y = mx + b m = 2.75 b = Y = 2.75x The equation written in slope intercept form. 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? 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 = 35x + 30 Substitute 240 for y = 35x Subtract 30 from both sides. 210 = 35x Simplify: = /35 = 35x/35 Divide by 35 on both sides. 6 = x x = 6 Joseph could rent the hall for 6 hours for $240. Copyright 2009 Algebra-class.com

23 Unit 3: Writing Equations 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 - $ 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. x = dog sweaters 3x = baby sweaters x + 5 = children s sweaters The total sales for Laurie s sweaters was $ Write an equation to represent the total sales of Laurie s sweaters. Price (dog) # of dog + Price (baby) # of baby + Price (children s) # of children s = total sales 7.50x (3x) (x+5) = How many baby sweaters did Laurie sell? Explain how you determined your answer. 7.50x (3x) (x+5) = Equation 7.50x x x = Distribute 53x = Combine like terms (x terms) 53x = Subtract x = 318 Simplify ( = 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. Copyright 2009 Algebra-class.com

24 Unit 3: Writing Equations 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 Write an equation that could be used to predict the tuition for any year after Predict the tuition for the year I can write two ordered pairs: (2, 12100) & (9, 16900) Step 1: Find the slope using the formula. y 2 - y 1 = = 4800 = The slope (m) is x 2 x Step 2: Substitute the slope and 1 point into the slope intercept form equation to find b. Y = mx + b m = x = 2 y = = (2) + b Substitute = b Simplify: (2) = = b Subtract from both sides = b M = b = Y = x is the equation that can be used to predict the tuition for any year after Step 3: To predict the tuition for the year 2015, substitute 15 for x into the equation. Y = x Y = (15) Y = The cost of tuition for the year 2015 is predicted to be Copyright 2009 Algebra-class.com

25 Unit 3: Writing Equations 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) y 2 - y 1 = = -200 = -100 x 2 x The rate of change between weeks 4 and 6 is This means that the cost of the airfare dropped about $100 per week during this 2 week time span. Copyright 2009 Algebra-class.com

26 Unit 3: Writing Equations 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. Copyright 2009 Algebra-class.com