Show all work on separate grid and lined paper. Number each question clearly.

Transcription

1 Algebra summer homework 2015 In addition to the practice problems below, students are to work in IXL.com in the 8 th grade content. Students must know all of the perfect squares from 1 to 625 for automatic recall. They must also know divisibility rules for 2, 3, 4, 5, 6, 8, 9. Students must know the area formula for basic shapes such as square, rectangle, triangle, trapezoid. Students must be able to fluently perform operations with fractions and have mastery of factoring numbers. Show all work on separate grid and lined paper. Number each question clearly. 1. Jamal and Alisha played a round of miniature golf. They made some notes of the time it took to play. Their data are shown in the next table: Hole Number Time Since Start (minutes) a. On grid paper, graph the (hole number, time) data. Be sure to give the graph a title, to label the graph axes, and to indicate the scale on each axis. b. Describe the pattern of change you see in the graph and the table. c. Draw a graph model. d. Write an equation for the graph model. e. Use your equation or graph model to estimate the time it took Jamal and Alisha to play the first 7 holes. Explain how you arrived at your estimate. f. Use your equation or graph model to estimate the time it would take Jamal and Alisha to play 27 holes. Explain how you arrived at your estimate. Write an equation and sketch a graph for the line that meets the given conditions. 2. A line that passes through the points (2, 7) and (6, 15) 3. A line that passes through the points (2, 9) and ( 2, 3)

2 Write an equation for the line shown. Identify the slope and the y-intercept For parts (a) (c), write an equation and sketch a graph for the line that meets the given conditions. Use one set of axes for all three graphs. 6. a. A line with slope 2 and y-intercept (0, 0) b. A line with slope 2 that passes through the point (3, 3) c. A line with slope 2 that passes through the point (3, 9) d. What do you notice about the equations and graphs of the three lines? 7. Arrange the following numbers on a number line.,,,, 1.5, 8. What is the length of the line segment that connects points (0, 0) and (4, 2)?

3 9. a. On Grid 1, sketch and label graphs and. On Grid 2, sketch and label graphs of and. b. On Grid 1, which equation represents the faster rate of growth? c. On Grid 2, which equation represents the faster rate of decay? d. How do the graphs help you to answer parts (b) and (c)? e. How do the equations help you to answer parts (b) and (c)? 10. Study the pattern in the table. Tell whether the relationship between x and y is linear, exponential, or neither, and explain your answer. If the relationship is linear or exponential, write an equation for it. x y x y x y ,156 10, a. There are 6 students going to a tennis tournament. How many different ways can they form doubles teams? b. There are 6 students in the chess club. How many different ways can they play against one another? c. There are 6 students planning a school dance. How many different two-person committees can they form? d. What do you notice about your answers to parts (a) (c)? Explain why this occurs.

4 14.Find the measure of each angle in the diagram below. 15. The figure below represents a section of a school. a. Write an expression for the area of the gym. b. Write an expression for the area of the cafeteria. c. Write an expression for the total area of the gym and the cafeteria. d. Write an expression for the total perimeter of the gym and the cafeteria. Evaluate the expression for the given value of x x + 9 when x = x 2 when x = x 2 + x 11 when x = 2

5 19. 42(x + 1) when x = 4 Austin is participating in a 30K race. He runs at an average speed of 10 kilometers per hour and walks at an average speed of 6 kilometers per hour. He wants to complete the race in 4 hours. Let y represent the number of hours he walks. 20. a. What equation relates x and y to the goal of covering 30 kilometers? b. What equation relates x and y to the goal of completing the course in exactly 4 hours? 21. Solve each inequality. Then graph the solution on a number line. Show your work. a. b. Solve the following inequalities. Then, create number line graphs for each solution x + 20 < 32 Solve the following inequality. Then, create a number line graph for the solution x + 12 > 36

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