DeBakey High School For Health Professions Mathematics Department. Summer review assignment for rising sophomores who will take Algebra 2

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1 DeBakey High School For Health Professios Mathematics Departmet Summer review assigmet for risig sophomores who will take Algebra Parets: Please read this page, discuss the istructios with your child, before hadig it off to your child. This is a assigmet for risig sophomores who will be takig Algebra i their secod year at DeBakey. These problems cover most of the cocepts taught i Algebra 1 ad Geometry i which studets are expected to kow well. It is very importat for the studet to master those skills because they will be applied throughout the sophomore year, as well as all four years of high school. DeBakey s math curriculum is rigorous because all of our studets must take AP Calculus AB i order to graduate with a DeBakey Health Sciece Diploma. Your child must begi the secod year with all cocepts mastered ad retaied from Geometry. This assigmet packet will give you a good idea of his/her readiess as he/she work through it. Studets will be give a quiz durig the first or secod week of the school year. This review quiz will be based o the cocepts covered i this packet. Studets will have the opportuity to ask questios before they are give the quiz. Parets are requested to see that this assigmet is completed properly ad seriously. Your child s success i the fall semester depeds o the correct completio of this packet ad o uderstadig of the cocepts covered. IMPORTANT: Absolutely NO CALCULATOR or electroic device is to be used o the ENTIRE packet. If your child feels he or she caot do this packet without oe, it idicates that he or she will have to work o those fudametal skills durig summer vacatio. Your child should show orgaized work with detailed steps; if ecessary, additioal worksheets ca be attached. Agai, this is to determie readiess for the upcomig year. We do ot allow much use of a calculator i the first semester of algebra. Please pla accordigly i the summer. Aswer key will be available o or after May 1, 017. If you realize later that you eed aother packet or a differet packet, you ca dowload a copy from this lik. Part 1: Solve. (o calculator) 1. 6x1 5x 0. x x x x 4. x 1 x x x 7 7. x x 8. x x

2 Part : Solve each system. (o calculator) 9 5x4y x y x y 4 x6y yx5 y x 1. x y 1 4xy 6 1. x y 1 y x x y 4 x y 9 Part : Simplify the expressios (o calculator) x 9 7x x x 18. xx 4 9x x x x 4 x a x

3 Part 4: Multiply ad simplify. (o calculator). x1 x = 4. x5x 5. x5x 5 = 6. x 1x = 7. x x 4y5x 4y 9. x x x 0. x Part 5: Factor completely. (o calculator) 1. x 15 x=. 5x 15x 4. x 5x 4.. 9x 5 5. x 5x 6 6. x 8x 4 7. x 4x x

4 9. 4x x x 6 Part 6: LINEAR EQUATIONS (o calculator) 41. Fid the x itercept, y itercept, ad the slope of the lie yx 4. Fid the x itercept, y itercept, ad the slope of the lie x y 4.Fid the slope ad y itercept of the lie x Fid the x itercept, y itercept, ad the slope of the lie y4x 1 45.Write equatio of a lie parallel to the lie yx 1, ad passig through (0,-1) 46. Write equatio of a lie perpedicular to the lie yx 1, ad passig through (0,-1) Part 7: Graph each equatio. (o calculator) y 48. y x 4

5 49. 1x 0 50 x5y 15 Part 8: Draw the lie passig through the poit whose coordiates are give ad havig the slope that is give P(, 1); m 5. P(,5); m 1 Part 9: Pythagorea Theorem: (o calculator) Use the Pythagorea Theorem to fid. Express as a radical i simplest form. Show your work

6 Part 10: Word Problems (o calculators!) 60 A book costs $19.95 with a sales tax rate of 8%. What is the total cost of the book? 61. A car retal agecy charges a fee of $5 per day plus $.0 for each mile drive. How much will it cost to ret the car for 6 days ad drive 800 miles? 6. A chef cooks 1 ½ potatoes for each servig of mashed potatoes. How may servigs ca he make from 18 potatoes? 6. Suppose you are sellig stuffed aimals for $6 each to raise moey for your club. You sold six more rabbits tha mokeys. If you sold $10 worth of stuffed aimals, how may of each type did you sell? 64. Suppose a video store charges o-member $4 to ret a video. A membership costs $1 ad the videos cost oly $.50 to ret. How may videos would you eed to ret i order to justify a membership? 65. Suppose you decide to make ad sell silk flower arragemets. You sped $0.00 o materials. You sell each flower arragemet for $10.50 each. How much profit would you make if you sold silk flower arragemets?

7 66. The ew parkig lot has spaces for 450 cars. The ratio of spaces for full sized cars to compact cars is 11 to 4. How may spaces are for full-sized cars? How may spaces are for compact cars? 67. You are desigig a cylidrical storage cotaier for compost. You wat it to hold 55 ft ad be 8 ft high. Use the formula V= rh to fid the radius of the storage cotaier. Part 11: Free respose type questio: A tak is filled with water up to a height of 10 meters. The tap at the top is opeed ad water is filled i the tak at the rate of meters/mi. for 1/ hour. The the tap at the top is closed. After 5 miutes the tap at the bottom of the tak is opeed ad water is draied out at the rate of 5 meters/mi. till the tak is completely empty. A) Model the above evets i terms of a graph of the level (height) of water i the tak vs. time. Does this graph represet a case of Direct Variatio? B) What is the slope of the graph whe water is beig filled i ad whe it is beig draied out of the tak? C) What is the sigificace of positive ad egative slope i this situatio? D) Write equatios idicatig the relatio betwee level (height) of water i the tak ad time whe: a) Water is beig filled i the tak. b) The top tap is closed ad the bottom tap is opeed. c) Water is beig draied out of the tak till it is empty. 10 m

8 Part 1: Simplifyig ad Evaluatig Expressios of expoets ad radicals (o calculator) Simplify the followig radical expressios, o decimal aswers allowed Simplify: Simplify: 5 4 Part 1: Systems of Equatios (o calculator) Fid the solutio to each system of equatios usig either substitutio or elimiatio. 1. x y 1 x y. xy 7 x y 8

9 . xy1 6x y6 4. x y 7 x y 9 5. y x x y 5 6. x 4 y x5 7. y x x7 y 8. x y 1 x 5y Part 14: Graphig (absolutely o calculator is allowed here) Graph each of the followig equatios or iequalities. 1. x y 6. y x 4. x6 y. 5

10 5. 1 y x x y 7. y x y