8 th Grade Math STAAR Review

Transcription

1 8 th Grade Math STAAR Review 1. Five students are each trying to raise the same amount of money for a fundraiser. The table below shows how much of each student s goal has been met. Write the numbers in order from least to greatest. 3. Point M is located at (-3, 2) on a coordinate grid. Point M is translated 6 units left and 4 units down to create point M. Determine the distance between point M and point M. Student Part of Goal Met Chelsea 0.6 Devon 2 3 Marcela 63% Joshua 37 Louis Amadeus invested $13,500 in an account that pays 3.5% annual simple interest. Amadeus will not make any additional deposits or withdrawals. How much interest will Amadeus earn on his investment at the end of 3 years? 2. Does the graph below show a proportional relationship? Explain your reasoning. 5. An aquarium is being filled with water. The graph shows the height of the water over time as the aquarium is being filled. Describe the rate of change for this situation.

2 6. In the diagram, a person who is 6 ft tall is standing on the ground 3 ft away from point P. A line segment drawn from the top corner of the building to point P creates two similar triangles. Write a proportion the find h, the height of the building in feet. Determine the height of the building. 9. The value of y varies directly with x. When y = 100, x =!!. What is the value of y when x is 4!!? 10. A triangular prism and its dimensions are shown in the diagram. What is the lateral surface area of this triangular prism in square centimeters? 7. Carnival A charges an entrance fee of $7.00 and $0.75 per ticket for the rides. Carnival B charges an entrance fee of $12.00 and $0.65 per ticket for the rides. How many tickets must be purchased in order for the total cost at Carnival A to be less than Carnival B. 8. The coordinate grid shows parallelogram PQRS. Parallelogram PQRS is rotated 270ᵒ counterclockwise about the origin to create parallelogram P Q R S. Write a rule to describe this transformation. 11. Jordyn made 25 international long-distance phone calls to Edinburgh last year. The scatterplot below shows the length and cost of each phone call she made. Describe the relationship between the length of the call and the cost of the call.

3 12. Determine the slope and y-intercept of the linear function shown on the grid. 15. The set designer for a play painted some background scenery on a large piece of plywood. He used a 13- foot-long pole to hold the piece of plywood upright, as shown in the diagram below. What is h, the total height in feet of the piece of plywood? 13. An elementary school has a rectangular field and a rectangular playground that are similar in shape. Each dimension of the field is 2.4 times the corresponding dimension of the playground. Which statement is true? A The area of the field is 4.8 times the area of the playground. B The area of the field is 5.76 times the area of the playground. C The perimeter of the field is 4.8 times the perimeter of the playground. D The perimeter of the field is 5.76 times the perimeter of the playground. 16. Which table contains only corresponding x-values and y-values where the value of y is 5 more than the quotient of x and 2? A x y C x y Write the equation of the graph of the linear function in slope-intercept form. B x y D x y A globe shaped like a sphere has a radius of 10.4 centimeters. Determine the volume of the globe in cubic centimeters. Round to the nearest hundredth.

4 18. Taylor and her family are discussing how to pay for her college education. The cost of tuition at the college that Taylor wants to attend is $12,000 per year. Taylor s parents will pay 75% of the tuition cost every year, and she will pay the rest. Taylor has one year to save enough money to attend her first year of college. What is the minimum amount of money she should save every month in order to reach her goal? 21. Jadyn used a microscope to measure the diameter of a hair. She found that the diameter of the hair was centimeters. How is this number written in scientific notation? The coordinates of the vertices of a quadrilateral are P (1, 6), R (2, 3), S (3, 3), and T (4, 6). Quadrilateral PRST is reflected across the y-axis to create quadrilateral P R S T. Write a rule to describe this transformation. 23. The scatterplot shows the average number of hours each of 13 people spends at work every week and the average number of hours each of them spends on recreational activities every week. Based on the scatterplot, predict the average number of hours a person spends at work every week if that person spends an average of 30 hours on recreational activities every week? 20. Which situation represents a proportional relationship? Circle all that apply. A The cost of purchasing strawberries for $4 per pound, plus a $0.50 service charge B The cost of purchasing peaches for $7 per box of peaches with a coupon of $1.00 off per box C The cost of purchasing apples for $2.25 per pound plus a shipping fee of $0.25 per pound D The cost of purchasing a basket of grapefruit for $1.50 per pound plus $5 for the basket

5 24. Four triangles are shown. Based on these triangles, determine the measure of w. Explain your reasoning. 27. The manager of a restaurant recorded how many people were in different groups of customers and how much those groups spent on food and beverages. The scatterplot below shows the data she recorded. Based on this scatterplot, about how much money would a group of 12 people be expected to spend on food and beverages at this restaurant? 25. Which set(s) of ordered pairs represents y as a function of x? Circle all that apply. A {(1, -5), (1, -6), (5, -2), (5, -7)} B {(0, 0), (1, 1), (2, 2), (3, 3)} C {(2, 2), (2, 3), (3, 3), (3, 4)} D {(3, -5), (4, -5), (5, -5), (6, -5)} E {(0, 0), (0, 1), (0, 2), (0, 3)} F {(4, 1), (5, 1), (6, 1), (7, 1)} 28. Which statement describes the mapping? 26. Circle II was dilated with the origin as the center of dilation to create Circle I. Write a rule in algebraic notation to describe the dilation applied to Circle II to create Circle I. A The mapping represents y as a function of x, because each y-value corresponds to exactly one x-value. B The mapping does not represent y as a function of x, because two of the x-values correspond to the same y-value. C The mapping represents y as a function of x, because each x-value corresponds to exactly one y-value. D The mapping does not represent y as a function of x, because there are more x-values than different corresponding y-values.

6 29. A cylinder has a diameter of 14.2 cm and a height of 5.1 cm. One equation for calculating the volume of a cylinder is V=Bh, where B represents the area of the base of the cylinder. Which expression can be used to find the value of B, in square centimeters, for this cylinder? A π (14.2) 2 B 2 π (14.2) C π (3.8) 2 D π (7.1) Which representation of a transformation does not preserve congruence? 34. A (x,y) (x + 2, y 3) B (x,y) (2x, 2y) C (x,y) (- x, - y) D (x,y) (- y, x) 30. Three groups of students used different methods to estimate the diagonal length of a patio in feet. Their results were: 5 17 ft ft 20!! ft Order the diagonal lengths from greatest to least. 31. The model represents an equation. What value of x makes the equation true? = 35. A landscaping company is laying grass in three square fields joined at their vertices, as shown in the figure below. Each region will be covered in squares of sod without any gaps or overlaps. Based on this information, which statement is true? 32. The diagram shows the side view of a ramp used to help load and unload a moving van. Determine the measurement of the length of the ramp to the nearest tenth of a foot. 2 ft 8 ft A The number of squares of sod needed to cover Region X is the same as the number of squares of sod needed to cover both Region Y and Region Z. B The number of squares of sod needed to cover Region Y is the same as the number of squares of sod needed to cover both Region X and Region Z. C The number of squares of sod needed to cover Region Z is the same as the number of squares of sod needed to cover both Region X and Region Y. D None of these

7 36. Mr. Myers is renting a car for one day. The table below shows the total amount he will be charged based on the number of miles he drives. Write an equation to represent c, the number of dollars Mr. Myers should be charged for m miles. 40. Quadrilateral WXYZ was translated 4 units to the left and 2 units up. Write a rule to describe the translation that was applied to Quadrilateral WXYZ to create Quadrilateral W X Y Z. Number of Miles, m Total Amount Charged, c 5 $ $ $ $ Order the numbers from least to greatest. -2.4, 24%, 2.42, -!!! 41. Lilly has $1000 to deposit into two different savings accounts. Lilly will deposit $600 into Account I, which earns 4.25% annual simple interest. She will deposit $400 into Account II, which earns 7! % interest compounded annually.! Lilly will not make any additional deposits or withdrawals. Determine the total balance of the two accounts at the end of 4 years. 38. A container used for storing wheat after a harvest is in the shape of a cylinder with a diameter of 16 ft and a height of 21 ft. Determine the volume of the storage container to the nearest cubic foot. 42. On a field trip, there are three adults for every 45 students. Which graph models a relationship with the same unit rate? 39. Write an equation in slope-intercept form for the linear function shown on the coordinate grid.

8 43. The measures of two angles are (7x 10) and (4x + 14). What is the value of x if these angles are congruent? What is the value of x if these angles are supplementary? 44. Which point on the number line represents the location of 79? 47. Mauricio bought a new car. He made an initial payment of $1,000 to a dealership, and he will pay $300 each month until the car is paid off. Which equation represents the relationship m, the number of monthly payments Mauricio has made, and t, the total amount that Mauricio has paid. A t = 1000m B t = 300m 1000 C t = 1000m 300 D t = 300m The dimensions of an ice cream cone are shown below. What is the volume of the cone to the nearest cubic inch? 45. The list shows the number of times the five students listened to a song last week. What is the mean absolute deviation of the numbers in the list? 47, 12, 32, 21, 38, Which graph represents y as a function of x? A C 46. Does the scatterplot below suggest a linear relationship between x and y? B D

9 The graph of a linear function is shown on the coordinate grid. What is the y-intercept of the graph of the linear function? Practice filling in your answer on the grid. 51. Are all real numbers whole numbers? Explain your reasoning. Draw a Venn diagram to show the relationship between real numbers and whole numbers. 54. Which representation does not show y as a function of x? 52. The areas of three circles are shown. Put the circles in order from greatest to least area. 55. Write an equation that can be used to describe the relationship between x and y shown in the graph below. Circle A Circle B Circle C A = 3.5π cm 2 A =!"! cm2 A = 11 cm 2

10 56. Sierra has a bucket that originally contained 360 fl oz of water and is being filled at a rate of 5 fl oz per minute. Kara has a bucket that originally contained 620 fl oz of water and is being drained at a rate of 8 fl oz per minute. What is x, the number of minutes that need to pass in order for the two buckets to contain the same amount of water? Write an equation to represent the situation and solve. 59. Figure I and Figure II are similar polygons. Which proportion must be true? I II 57. What value of x makes this equation true? 0.7x 5 = 0.2x + 8 A B C D! =!!!! =!!!!.! =!!!! =!!! 60. Quadrilateral ABCD was dilated with the origin as the center of dilation to created quadrilateral A B C D. Write a rule to represent the dilation that was applied to quadrilateral ABCD to create quadrilateral A B C D. 58. The two lines graphed on the coordinate grid each represent an equation. Determine the ordered pair that represents a solution to both equations. 61. Madisen planted a flower in a container shaped like a cylinder. The dimensions of the container are shown below. Determine the volume of soil the container could hold in cubic centimeters. Round to the nearest centimeter.

11 62. Mr. Melendez wants to paint his storage shed. He needs to calculate the lateral surface area of the shed so he will know how much paint to buy. The shed is in the shape of a rectangular prism with the dimensions shown below. Including the doors, what is the lateral surface area of the storage shed in square feet? 64. Quadrilateral PRST is rotated 90 degrees clockwise with the origin as the center of rotation to create a new figure. Write a rule to describe the transformation. 9 ft 16 ft 65. A figure is graphed on a coordinate grid as shown below. The figure is transformed according to the rule (x, y) (x + 3, y + 7) to create a new quadrilateral. Which statement is true? 63. Which measurements could not represent the side lengths of a right triangle? (Choose all that apply.) A 6 cm, 8 cm, 10 cm B 4 cm, 3 cm, 15 cm C 5 cm, 3 cm, 4 cm D 12 cm, 13 cm, 5 cm E 10 cm, 24 cm, 26 cm F 4 cm, 6 cm, 10 cm G 12 cm, 35 cm, 37 cm A The side lengths of the new polygon are twice the corresponding side lengths of the original polygon. B The angle measures of the new polygon are equal to the corresponding angle measures of the original polygon. C The side lengths of the new polygon are 9 units longer than the corresponding side lengths of the original polygon. D The angle measures of the new polygon are greater than the corresponding angle measures of the original polygon.

12 66. Which scatterplot suggests a linear relationship between x and y? 69. Milo is taking out a loan in the amount of $12,500. Her choices for the loan are a 3-year loan at 7% simple interest and a 4-year loan at 5.5% simple interest. What is the difference in the amount of interest Milo would have to pay for each of these two loans? 67. Mrs. Williams made a scatterplot to show the relationship between the number of absences a student in her class has and the student s final exam score. Based on this scatterplot, approximately what score should a student with 3 absences expect to receive on the final exam? 70. Jeremy will deposit $4,320 in an account that earns 4% simple interest every year. Eric will deposit $4,200 in an account that earns 5% interest compounded annually. The deposits will be made on the same day, and no additional money will be deposited or withdrawn from the accounts. Which account will have more at the end of 3 years and by how much? 71. The table shows the scores that seven different students made on their math test. What is the mean absolute deviation for this set of data? 68. Tuition for one year at a state university is about $11,500. Mason would like to attend this university and will save money each month for the next 4 years. His parents will give him $3,200 for his first year of tuition. Determine the minimum amount of money Mason must save to have enough money to pay for his first year of tuition. Person Test Score Student 1 68 Student 2 77 Student 3 94 Student 4 83 Student 5 71 Student Student 7 54