Math 7 Mid-Winter Recess

Transcription

1 MOUNT VERNON CITY SCHOOL DISTRICT Children of Promise Math 7 Mid-Winter Recess Student Name: School Name: Teacher: Score:

2 Module 1: Ratios and Proportional Relationships 1. It is a Saturday morning and Jeremy has discovered he has a leak coming from the water heater in his attic. Since plumbers charge extra to come out on weekends, Jeremy is planning to use buckets to catch the dripping water. He places a bucket under the drip and steps outside to walk the dog. In half an hour the bucket is 1/5 of the way full. a. What is the rate at which the water is leaking? b. Write an equation that represents the relationship between the number of buckets filled, y, in x hours. c. What is the longest that Jeremy can be away from the house before the bucket will overflow? 2

3 2. Farmers often plant crops in circular areas because one of the most efficient watering systems for crops provides water in a circular area. Passengers in airplanes often notice the distinct circular patterns as they fly over land used for farming. A photographer takes an aerial photo of a field on which a circular crop area has been planted. He prints the photo out and notes that 2 centimeters of length in the photo corresponds to 100 meters in actual length. a. What is the scale factor of the photo? b. If the dimensions of the entire photo are 25 cm by 20 cm, what are the actual dimensions of the rectangular land area in meters captured by the photo? c. If the area of the circular area on the photo is 64π cm 2, what is the actual area of the circular crop area in square meters? 3

4 3. A store is having a sale to celebrate President s Day. Every item in the store is advertised as one fifth off the original price. If an item is marked with a sale price of $140, what was its original price? Show your work. 4. Over the break, your uncle and aunt ask you to help them cement the foundation of their newly purchased land and give you a top-view blueprint of the area and proposed layout. A small legend on the corner states that 4 inches of the length corresponds to an actual length of 52 feet. a. What is the scale factor? b. If the dimensions of the foundation on the blueprint are 11 inches by 13 inches, what are the actual dimensions in feet? 4

5 c. You re asked to go buy bags of dry cement and know that one bag covers 350 square feet. How many bags do you need to buy to finish this project? d. After the first 15 minutes of laying down the cement, you had used 1/5 of the bag. What is the rate you are laying cement in bags per hour? What is the unit rate? e. Write an equation that represents the relationship between the number of bags used, y, in x hours. 5

6 f. Your uncle is able to work faster than you. He uses 3 bags for every 2 bags you use. Is the relationship proportional? Explain your reasoning using a graph on a coordinate plane. g. What does (0, 0) represent in terms of the situation being described by the graph created in part (f)? h. Using a graph, show how many bags you would have used if your uncle used 18 bags. 6

7 Module 2: Rational Numbers 1. The water level in Ricky Lake changes at an average of 7 inch every 3 years. 16 a. Based on the rate above, how much will the water level change after one year? Show your calculations and model your answer on the vertical number line, using 0 as the original water level Original Water Level (in inches) 0.2 b. How much would the water level change over a 7-year period? c. When written in decimal form, is your answer to part (b) a repeating decimal or a terminating decimal? Justify your answer using long division. 7

8 2. Kay s mother taught her how to make handmade ornaments to sell at a craft fair. Kay rented a table at the fair for $30 and set up her work station. Each ornament that she makes costs approximately $2.50 for materials. She sells each ornament for $6.00. a. If x represents the quantity of ornaments sold at the craft fair, which of the following expressions would represent Kay s profit? (Circle all choices that apply.) A x 2.50x B. 6x x C. 6x 30 D. 4.50x 30 E. 3.50x 30 b. Kay does not want to lose money on her business. Her mother told her she needs to sell enough ornaments to at least cover her expenses (costs for materials and table rental). Kay figures that if she sells 8 ornaments, she covers her expenses and does not lose any money. Do you agree? Explain and show work to support your answer. c. Kay feels that if she earns a profit of $40.00 at this craft fair, her business will be successful enough to attend other craft fairs. How many ornaments does she have to sell to earn a $40.00 profit? Write and solve an equation; then explain how the steps and operations used in your algebraic solution compare to an arithmetic solution. 8

9 3. Travis received a letter from his bank saying that his checking account balance fell below zero. His account transaction log is shown below. CHECK DESCRIPTION OF DATE NO. TRANSACTION PAYMENT DEPOSIT BALANCE /17 Beginning Balance $ /18 CBC Audio (Headphones) $ $ Line /22 NY Sport (Basketball Shoes) $ $ Line 2 Debit 10/25 Gary s Country Market $ /25 Iggy s Skate Shop (Skateboard) $ $ Line 3 $8.00 Line 4 Cash Deposit (Birthday 10/25 $ Money) $28.00 Line 5 Debit 10/30 McDonuts $ $22.05 Line 6 a. On which line did Travis make a mathematical error? Explain Travis mistake. b. The bank charged Travis a $20 fee because his balance dropped below $0. He knows that he currently has an outstanding charge for $7.85 that he has not recorded yet. How much money will Travis have to deposit into his account so that the outstanding charge does not create another bank fee? Explain. 9

10 4. The length of a rectangular envelope is 2 1 times its width. A plastic band surrounds the front 2 and back of the envelope to secure it as shown in the picture. The plastic band is 39 3 inches 8 long. Find the length and width of the envelope. J. Smith 999 Main Ave. Jamesville, NY Plastic Band ACME PRODUCTS 1225 Industrial Ave. Collinsville, NY

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12 5. Juan and Mary are playing the integer card game. The cards in their hands are shown below: Juan s Hand 3, 4, 9, 12 Mary s Hand 2, 3, 1, a. What are the scores in each of their hands? Juan s score: Mary s score: b. Lydia says that if Juan and Mary both take away their 3s, Juan s score will be higher than Mary s. Marcus argues and says that Juan and Mary s scores will be equal. Are either of them right? Explain. c. Juan picks up another set of cards that is exactly like each card in his hand. Which of the following would make Mary s score equal to Juan s? Place a check mark by all that apply. Double every card in her hand Take away her 3 and 1 Pick up a 4 Pick up a 7 and 3 Take away her 2 and d 2 Pick up one of each of Juan s cards Explain why your selections will make Juan and Mary s scores equal. 12

13 Module 3: Expressions and Equations 1. Gloria says the two expressions 1 (12x + 24) 9x and 6(x + 1) are equivalent. Is she 4 correct? Explain how you know. 2. A grocery store has advertised a sale on ice cream. Each carton of any flavor of ice cream costs $3.79. a. If Millie buys a combination of strawberry ice cream and chocolate ice cream cartons, write an algebraic expression that represents the total cost of buying the ice cream. b. Write an equivalent expression for your answer in part (a). c. Explain how the expressions are equivalent. 13

14 3. A new park was designed to contain two circular gardens. Garden A has a diameter of 50 m, and the garden B has a diameter of 70 m. a. If the Gardner wants to outline the gardens in edging, how many meters will be needed to outline the smaller garden? (Write in terms of π.) b. How much more fencing will be needed for the larger garden than the smaller one? (Write in terms of π.) c. The Gardner wishes to put down weed block fabric on the two gardens before the plants are planted in the ground. How much fabric will be needed to cover the area of both gardens? (Write in terms of π.) 14

15 4. A play court on the school playground is shaped like a square joined by a semi-circle. The perimeter around the entire play court is ft., and 62.8 ft. of the total perimeter comes from the semi-circle. a. What is the radius of the semi-circle? b. The school wants to cover the play court with sports court flooring. Using 3.14 for π, how many square feet of flooring does the school need to purchase to cover the play court? 15

16 5. Marcus drew two adjacent angles. a. If ABC has a measure one-third of CBD, then what is the degree measurement of CBD? b. If CBD = 9(8x + 11) degrees, then what is the value of x? 6. The dimensions of an above-ground, rectangular pool are 25 feet long, 18 feet wide and 6 feet deep. a. How much water is needed to fill the pool? 16

17 b. If there are 7.48 gallons in 1 cubic foot, how many gallons are needed to fill the pool? c. Assume there was a hole in the pool, and 3366 gallons of water leaked from the pool. How many feet did the water level drop? d. After the leak was repaired, it was necessary to resurface (lay a thin layer of concrete to protect) the sides of the pool. Calculate the area to be covered to complete the job. 17

18 7. Gary is learning about mosaics in Art class. His teacher passes out small square tiles and encourages the students to cut up the tiles in various angles. Gary s first cut tile looks like this: 3m (m 10) a. Write an equation relating TIL with LIE. b. Solve for m. c. What is the measure of TIL? d. What is the measure of LIE? 18