SUMMER MATH PACKET. ENTERING Geometry

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1 SUMMER MATH PACKET ENTERING Geometry Complete all of the following problems using the space provided. Enclosed is a copy of a Mathematics Reference Sheet to assist you if you need to find a formula. Also attached is a scoring rubric to help you determine your grade. This packet is due on the first full day of school and will be worth one test grades.

2 Manville High School Mathematics Department Summer Math Packet Name Score Summer Math Packet Grade Entering (circle one) The following questions are Extended-Constructed Response (ECR) Questions. Remember to: Read the question carefully and thing about the answer Answer all the parts of the question Show all of your work and/or explain your answer The rubric below should be used as a guide to provide the criteria for evaluating and scoring your responses. Scoring Rubric for Mathematics ECRs 3 Point Response The response shows complete understanding of the problem s essential mathematical concepts. The student executes procedures completely and gives relevant responses to all parts of the task. The response contains few minor errors, if any. The response contains a clear, effective explanation detailing how the problem was solved so that the reader does not need to infer how and why decisions were made. 2 Point Response The response shows nearly complete understanding of the problem s essential mathematical concepts. The student executes nearly all procedures and gives relevant responses to most parts of the task. The response may have minor errors. The explanation detailing how the problem was solved may not be clear, causing the reader to make some inferences. 1 Point Response The response shows limited understanding of the problem s essential mathematical concepts. The response and procedures may be incomplete and/or may contain major errors. An incomplete explanation of how the problem was solved may contribute to questions as to how and why decisions were made. 0 Point Response The response shows insufficient understanding of the problem s essential mathematical concepts. The procedures, if any, contain major errors. There may be no explanation of the solution or the reader may not be able to understand the explanation. The reader may not be able to understand how and why decisions were made.

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4 1. The lengths of two sides of a triangle are 5 and 12. The lengths of all three sides are integers. What is the shortest length the third side could be? What is the longest length the third side could be? If these two sides are the legs of a right triangle, what is the length of the third side?

5 2. A line is given by the equation y = 5x + 6. To the nearest tenth, what is the distance between the point where x = 0 and the point where x = 2? To the nearest tenth, what is the distance between the point where y = -6 and the point where y = 31? To the nearest tenth, what is the distance between the point where y = -6 and the point where x = 2?

6 3. A rectangular prism has a length that is twice the width and a height that is twice the length. What is the volume of the prism if the length is 8? What is the volume of the prism if the length is 10? What is the surface area of the prism if the length is 10?

7 4. The figure below is an isosceles trapezoid Q R S T What is the measure of angle Q if angle R measures 110? What is the measure of angle T if angle R measures 110? What is the measure of angle S if angle R measures 120?

8 5. The flag pole in front of the school is 27 feet high and its shadow is 18 feet long. The shadow of the apple tree next to the flag pole is 4 feet long. Explain how you can find the height of the tree without measuring it. Find and label the height of the tree.

9 6. Kosta planted a garden in his backyard that was 64 feet long and 16 feet wide. 64 feet 16 feet What is the perimeter of the garden that Kosta built? What is the area of the garden that Kosta built? Suppose Kosta wanted to alter the shape of his garden from a rectangle to a square, but wanted to keep the same area. What would the perimeter of the square garden be?

10 7. The triangle has vertices at (3, 4), (7, 4) and (5, 8). What will the vertices be if the figure is reflected across the y-axis? What will the vertices be if the figure is reflected across the x-axis? What will the vertices be if the figure is reflected across the y-axis and then the x-axis?

11 8. Dan wants to put a garden and a shed in his yard. His yard measures 50 feet by 60 feet. The shed is 5 feet by 5 feet. He wants the garden to be 10 feet by 15 feet. Using the scale of 1 inch = 10 feet, draw a possible arrangement. Local ordinances require the garden and the shed be at least 5 feet from the edge of the yard and each other.

12 9. Tom is building a storage box for his garden supplies. He drew this plan. 3 ft 5 ft 2 ft He decided to double one of the measurements. Which one should he double to get the largest volume? What would the new volume be? How much more volume would he get?

13 10. Patty works for a company that builds goldfish ponds for a local university. She has to plaster the interior sides of the pond, which is the shaped like a rectangular prism with the dimensions shown below. 4 feet 30 feet 20 feet What is the volume, in cubic feet, of the goldfish pond? What is the total surface area of the interior sides and bottom of the pond? If the company charges $1.50 per square foot to plaster the pond, what will it cost to plaster the four interior sides and the bottom?

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