DeBakey High School For Health Professions Mathematics Department

Transcription

1 DeBakey High School For Health Professios Mathematics Departmet Summer review assigmet for sophomores who will be doublig up Algebra ad Geometry 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 ad Geometry i their secod year at DeBakey. These problems cover most of the cocepts taught i Algebra 1 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 Algebra 1. 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 prepare for the upcomig year whe your child will be takig two cocurret math classes! We do ot allow much use of a calculator i the first semester of algebra. Idepedece from its use ca oly be accomplished through practice. 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 : Simplifyig ad Evaluatig Expressios (o calculator) f a, b ab a ac for a 10, b 6, c 4 1. Evaluate: 1 f a, y, z.5x x y xz. Evaluate: for x 4, y 8, z. Simplify: x y 7x y x y 4. Simplify: 5y 6 5. Simplify: 5x 4y x 6y 6. Simplify: Simplify: Simplify: 5 4 x 5y 9. Simplify: 10. Simplify: x y Part : Expoets ad Radicals (o calculator) Simplify the followig radical expressios, o decimal aswers allowed

3 Part 4: Simplify the expressios (o calculator) x 9 7x x x 18. xx 4 9x x x x 4 x a x

4 Part 5: Solvig or Factorig (o calculator) Factor each expressio or equatio, if possible. Solve for x if you are workig with a equatio. Solve for x, fid the roots, fid the solutio, fid zeros, ad fid x itercept mea the same. 1. Factor 4x 0x. Solve x 10x 1. Solve x x Solve x Solve x x Solve x 5x 7. Factor x 19xy 0y 8. Factor 5x 16y 9. Factor 10x 17xy y 10. Solve 4x 10x 4x (careful there are aswers here!)

5 Part 6: Pythagorea Theorem (o calculator, as radical simplificatio is a vital skill) Use the Pythagorea Theorem to fid. Express as a radical i simplest form. Show your work Part 7: Word Problems (o calculator is allowed as your child eed to be proficiet i multiplyig decimal umbers) 1. A book costs $7.95 with a sales tax rate of 8%. What is the total cost of the book?. 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? 4. 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? 5. 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? 6. 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. 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? 8. You are desigig a cylidrical storage cotaier for compost. You wat it to hold 110 ft ad be 8 ft high. Use the formula V= rh to fid the radius of the storage cotaier. 9. A ladder is 5 ft log. The ladder eeds to reach to a widow that is 4 ft above the groud. How far away from the buildig should the bottom of the ladder be placed? 10. There is a large buildig o fire. Fire trucks from two differet statios respod to the fire. Oe statio is 1 mile east ad miles orth of the fire. The other statio is miles west ad 1 mile south of the fire. How far apart are the two fire statios?

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

8 Part 9: 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. 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 10: Fid the solutio to each system by graphig (o calculator) 1. y x1 4x y 7. x y x y

9 Part 11: Workig with Formulas (Distace, Midpoit, Slope) (o calculator) Fid the distace betwee each of the followig pairs of poits. Put all aswers i reduced radical form. d ( x x ) ( y y ) B, 8 ad C 9,. X 5, ad Z 4,1. M 8,4 ad N,8 4. E 4, 4 ad F 0, 4 Fid the coordiates of the midpoit betwee each pair of poits. M x x, y y A5,4 ad B, 6. C, ad D, 1 T, 4 ad R5, 7 M = 7. S 1,0 ad V 5, 5 M = M = M = Fid the slope of the lie betwee each pair of poits. 8. A,8 ad B10, 8 y y m x x T 0, 8 ad R10, B8,1 ad R,5 m = 11. M 10, ad W 10, 5 m = m = m =

10 Part 1: 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 1: 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

11 9. 4x x x 6 Part 14: 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 15: Graph each equatio. (o calculator) y 48. y x 4

12 49. 1x 0 50 x5y 15 Part 16: 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 17: Pythagorea Theorem: (o calculator) Use the Pythagorea Theorem to fid. Express as a radical i simplest form. Show your work

13 Part 18: 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?

14 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 19: 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

15 Part 0: Simplifyig ad Evaluatig Expressios of expoets ad radicals (o calculator) Simplify the followig radical expressios, o decimal aswers allowed Simplify: Simplify: 5 4