Accelerated Coordinate Algebra/Analytic Geometry A Summer Work (14_15_ACA-AGA_SW)

Transcription

1 Name: Date: 1. Parallel lines m and n intersect line segment AC and ray CB. Use the information in the diagram to answer the questions. What are the degree measures of and Explain your answers. What is the measure of Show or explain how you got your answer. 1

2 2. Each of the graphs shown represents a different situation. Which graph shows the temperature of a pizza after it is put into an oven to bake? Explain your reasoning, including the label for each axis. Which graph shows the amount of gas in the tank of a truck driving at a constant speed on a level road? Explain your reasoning, including the label for each axis. Which graph shows the height of a ball from when it is thrown to the time is hits the ground? Explain your reasoning, including the label for each axis. Part D Write a situation that could be represented by the graph not used in Parts A, B, or C. Explain your reasoning. 2

3 3. A biology teacher gave three students in his class a different plant. He asked the students to record the heights of their plants, in centimeters (cm), everyday for one week. The students reported their results in different displays. Their results are shown in a graph, an equation, and a table. List the plants in order from the slowest rate of growth per day to the greatest rate of growth per day. Explain how you got your answer. If the growth rate for Plant 1 remains the same, on what day number will it be 24 cm tall? Explain how you got your answer. If the growth rate for each plant remains the same, when will Plant 2 and Plant 3 be the same height? Show work or give an explanation to justify your answer. 3

4 4. A right triangle has legs 5 units and 8 units in length and hypotenuse x units in length. What is the exact value of x? Leave your answer in terms of a square root. Between what two consecutive whole numbers is the value of x? Explain your answer. The side length of another right triangle is your work and explain your answer. units. Determine the length of this side to the nearest tenth. Show Create a right triangle with a side length of units and a hypotenuse length of whole number units. Label all three side lengths of the right triangle. Use algebra to prove that the sides you chose form a right triangle. 4

5 5. Parts A, B, and C each present a pair of linear equations. Without graphing the equations, determine whether the graphs of each pair of lines would intersect. Explain how you know whether the lines would intersect or not. Do the graphs of Line 1 and Line 2 intersect? Explain how you know without graphing the lines. Do the graphs of Line 3 and Line 4 intersect? Explain how you know without graphing the lines. Do the graphs of Line 5 and Line 6 intersect? Explain how you know without graphing the lines. 5

6 6. The coordinate grid shows the reading rates of Justin and Nadia during a reading program at school. Based on the graph, how long will it take Nadia to read 1 book? Explain your answer. If Justin s reading rate stays the same, how many books will Justin read in two weeks? Explain your answer. Based on the graph, what does the y -intercept for Nadia s reading rate represent? Using the graph, compare the y -intercept for Justin s reading rate to the y -intercept for Nadia s reading rate. Explain your answer. Part D Rafael is also in the reading program with Nadia and Justin. The table shows Rafael s reading rate over a period of six weeks. 6

7 Write a function to represent Rafael s reading rate as shown in the table. Show your work. Who has the greatest reading rate (Justin, Nadia, or Rafael)? Explain your answer. 7

8 7. The graph shows the relationship between the volume of Liquid 1 and its mass. Write the equation of the line that represents the graph of Liquid 1. Explain the meaning of the coefficient in the equation you wrote to the graph of Liquid 1. The equation is used to represent the relationship between the volume of Liquid 2 and its mass. Explain how the graph of Liquid 1 is similar to the graph of Liquid 2. How are the graphs different? Using the graph for Liquid 1, explain how you can use the point What is the value of g? to determine the value of g in the point 8

9 8. A given function is defined by the equation Does the equation define a linear function? Explain your answer. Two functions are considered parallel if their slopes are equivalent. Write the equation for a function that is parallel to the given function with a y -intercept of you wrote. Explain the equation Write the equation for a function that represents a proportional relationship and is also parallel to the given function. Explain the equation you wrote. 9

10 9. Triangle EGH is graphed on a coordinate grid. Using the Pythagorean theorem, determine the length of side Show your work. What is the slope of the line containing What is the slope of the line containing Explain the relationship between the slopes of and Write an equation to represent the line that passes through points E and G. If in the equation you wrote, what is the value of y? Show your work. 10

11 10. The scatter plot shows the relationship between the age of a reader and the time, in hours, the reader spends reading each month. What type of association (positive or negative) is shown between the age of the reader and the hours spent reading per month? Explain your answer. Does the data represented show a linear or nonlinear relationship? Explain your answer. Write an equation that would best represent the data shown in the scatter plot. Part D Explain what information the numbers you used in the equation for represents in the scatter plot. 11

12 11. Three packaging companies use the expressions shown to calculate the cost, in dollars, for shipping an item weighing x pounds. Company R: Company S: Company T: For what weight will the cost be the same for Company R and Company S? Show your work. For what weight will the cost be the same for Company S and Company T? Show your work. Which company has the highest rate? Explain your answer. Part D Avery says it is less expensive to ship an item using Company S than Company R. Is Avery correct? Explain your answer. 12

13 12. Jenn and Mara are playing a computer game in which a player receives x points for every correct decision and loses y points for every incorrect decision. Jenn made 18 correct and 12 incorrect decisions for a total of 39 points. Mara made 16 correct and 8 incorrect decisions for a total of 36 points. Write two linear equations in x and y to represent Jenn s and Mara s situation. Solve the system of linear equations from algebraically. Show your work. What are the coordinates of the point of intersection of the graphs of these two lines? Explain your answer. Part D Describe in words the significance of the point of intersection in this context. 13

14 13. Two squares and the lengths of their sides are shown in the diagram. If the area of the large square is what is the value of x? Explain how you got your answer. Is x a rational number? Explain how you know. If the area of the small square is what is the value of y? Explain how you got your answer. Is y a rational number? Explain how you know. 14

15 14. Water began leaking out of a hole in a storage tank. The hole was repaired, and the tank was refilled with water. The graph shows the relationship between the number of hours elapsed and the amount of water in the tank. What does the point mean in terms of the storage tank? Before the hole was repaired, what amount of water per hour leaked out of the tank? Explain your answer. During which interval(s) did the level of the water remain the same? Explain your answer. Part D If the hole had not been repaired and the water had continued to leak at the same rate, how many hours would have elapsed before the tank was empty? Explain your answer. 15

16 15. The three right triangles shown in the diagram are congruent. One base of each triangle lies on line segment CH. Line j intersects line segment BE at its midpoint, and line k intersects line segment FI at its midpoint. Using lines j and k, describe a sequence of transformations that maps onto Does the order of the transformations make a difference? Explain your answer. The distance between segment AB and segment DE is units. The distance between segment DE and segment GH is units. If the distance between lines j and k is 15 units, what is the value of x? Show your work. Describe a single transformation, without using lines j and k, which maps onto 16

17 16. A teacher asked students to draw a graph of a function with the following conditions: x-intercept at x-intercept at y-intercept at increasing for increasing for decreasing for decreasing for The graph shows one student s representation of the function. Does the student s graph represent a function? Explain your answer. Identify all conditions the student s graph did and did not meet. Draw a coordinate grid and sketch a graph of a function with all the teacher s conditions met. 17

18 17. Hector works 12.5 hours per week at a part-time job. His original pay rate was $8 per hour, but he received a raise of x dollars per hour. His new total weekly pay, y, is represented by the equation If what was the amount of Hector s raise per hour? Show your work. What are the slope and y -intercept of the equation Write the equation of a line, in than the graph of form, that has the same slope and a y -intercept that is 10 units more Explain your answers. Jamal s new weekly pay is given by the equation where y is the total pay in dollars. What is the solution to the system of equations and Show your work or explain your answer. 18

19 18. Parallel line segments and are graphed on the coordinate grid. Determine if these line segments are congruent. Show your work or explain your answer. Both line segments are reflected across the x -axis and then translated 4 units to the right, such that Explain how and are related. and Describe a transformation of that will result in a line segment that is perpendicular to in its current position. Justify your answer. 19

20 19. A line segment with endpoints and is graphed on the coordinate plane. Using the Pythagorean Theorem, determine the distance between the points X and Y. Explain how your work relates to the use of the Pythagorean Theorem. A reflection across the x -axis is applied to to obtain where X maps to and Y maps to What are the coordinates of and Explain your answer. 20

21 20. Two relations are given in different formats. Use these relations to answer the questions. Determine whether or not each relation represents a function. Justify your answers. Determine whether each function identified in is linear or nonlinear. Explain how you know. Write an equation for each linear function identified in. Explain what each part of your equation(s) represents. 21

22 21. Triangle GHJ is graphed on the coordinate plane. Triangle KLM is a reflection of is the image of J. Draw across the x -axis, such that K is the image of G, L is the image of H, and M on a 4-quadrant coordinate grid. Label the vertices appropriately. On the same coordinate grid, draw the reflection of across the y -axis. Use to label the corresponding vertices. What single transformation could be performed on to result in Explain your answer. Part D Explain whether or not and are congruent. 22

23 22. Tracey needs to convert to a fraction in lowest terms. Her work is shown. Tracey made at least one error. Explain any errors that Tracey made. What is the correct fraction in lowest terms? Show or explain your work. Explain whether is rational or irrational in terms of the decimal form and the fraction form of the number. 23

24 23. Jon is going to get a job as a delivery driver. He can choose between the two plans shown for his weekly salary. Let x represent the number of hours Jon works in a week and let y represent his weekly salary, in dollars. Which plan has a greater rate of change? Show or explain your work. Which plan has the greater pay for 15 hours worked in a week? Show or explain your work. For what number of hours worked in a week would Jon earn the same weekly salary under either plan? How much would Jon earn during this week? Show or explain your work. 24