New Students Entering Geometry - DeBakey High School

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DeBakey High School For Health ProfessionsMathematics DepartmentSummer review assignment for rising freshmen who will take GeometryParents: Please read this page, discuss the instructions with your child, before handing it off toyour child. This is an assignment for rising freshmen who will be taking Geometry in their first year atDeBakey. These problems cover most of the concepts taught in Algebra 1 in which students are expected to knowwell. It is very important for the student to master those skills because they will be applied throughout theGeometry course, as well as all four years of high school.'H%DNH\¶V PDWK FXUULFXOXP LV ULJRURXV EHFDXVH DOO Rgraduate with a DeBakey Health Science Diploma. Your child must begin the first year already proficientlytrained in middle school math. Please do not rely on the math class grades that your child received in middleschool to determine how ready he or she is for this high school, as grades may be inflated. This assignmentpacket will actually give you a better idea of his/her readiness as he/she work through it. Students will be given aquiz during the first or second week of the school year. This review quiz will be based on the concepts coveredin this packet. Students will have the opportunity to ask questions before they are given the quiz.3DUHQWV DUH UHTXHVWHG WR VHH WKDW WKLV DVVLJQPHQW Lfirst semester depends on the correct completion of this packet and on understanding of the concepts covered.IMPORTANT: Absolutely NO CALCULATOR or electronic device is to be used on the ENTIRE packet. Ifyour child feels he or she cannot do this packet without one, it indicates that he or she will have to work on thosefundamental skills during summer vacation. Your child should show organized work with detailed steps; ifnecessary, additional worksheets can be attached. Again, this is to demonstrate readiness for this school. We donot allow the use of a calculator in-class when students are asked to do these types of problems. Please planaccordingly in the summer. Answer key will be available on http://debakeyhigh.weebly.com/ orhttp://www.houstonisd.org/Page/114414 after May 31, 2017. If you realize later that you need another packet ora different packet, you can just download a copy from this link.Part 1:Solve each equation (no calculator)1.3x 12 243.8r 5 3r45.3 x 510122.3x 444.62w6. 0 24x2 x12

7. 6 x9.11.2128. x 7 x 22163x 2 6 x 2 4 5 x 7 x 2 110 2a210. xPart 2: Simplifying and Evaluating Expressions1f a, b ab 2 a 3ac2for a 10 , b 6 , c 41. Evaluate:3.Simplify: 5 x y 7 x y 2 x y5.Simplify:7.Simplify: 10 6 2 2 3 39.Simplify: 3 x 5 y4 5x 222x 24 4 6n 623202434 4 y 3 3x3 6 y 2(no calculator)f a, y, z 2.5x3 x 2 y xzfor x 4 , y 8 , z 32.Evaluate:4.Simplify:6.Simplify: 8 3 3 27 8.Simplify:10. Simplify: 5 y 6 23002 2 3 3 5 2 4 3 2 3 2x 3 y 3

Part 3: Exponents and Radicals (no calculator)Simplify the following radical expressions, no decimal answers allowed.1.502.4 323.6 724.2 28 635.6 8 986.2 10 3 66 48 2 278.7.10.9.Part 4: Working with Like and Unlike Terms (no calculator)Combine any like terms to simplify each of the following expressions.1.2.3. x5. 8x2 3x 3 x 2 x 1 3 1 20 x3 2 x2 x 5 4. 14 12x 10x 5 6.6 x 22 x 3 36 x 2 x3

7. 4x2 15x 16 2 x 20 8. 7x3 2 x2 13x 4 x3 10 Part 5: Solving or Factoring (no calculator)Factor each expression or equation, if possible. Solve for x if you are working with an equation.Solve for x, find the roots, find the solution, find zeros, and find x intercept mean the same.1.Factor 4 x 20 x3.Solve x x 6 03225. Solve x 2 x 1 0Factor 3 x 19 xy 20 y2Solve x 10 x 214.Solve x 49 0226. Solve 2 x 5 x 327.2.228.Factor 25 x 16 y22

9.Factor 10 x 17 xy 3 y210. Solve 4 x 10 x 24 x223(careful there are 3 answers here!)Part 6: Pythagorean Theorem (no calculator, as radical simplification is a vital skill)Use the Pythagorean Theorem to find n. Express n as a radical in simplest form. Show your work.1.2.3.nn2 75984.5.4 146.n25n2 26n877.8.2 14nn594

Part 7: Word Problems (no calculator is allowed as your child need to be proficient in multiplyingdecimal numbers)1. A book costs 7.95 with a sales tax rate of 8%. What is thetotal cost of the book?2. A car rental agency charges a fee of 35 per day plus .20for each mile driven. How much will it cost to rent the car for6 days and drive 800 miles?3. A chef cooks 1 ½ potatoes for each serving of mashedpotatoes. How many servings can he make from 18 potatoes?4. Suppose you are selling stuffed animals for 6 each to raisemoney for your club. You sold six more rabbits than monkeys.If you sold 120 worth of stuffed animals, how many of eachtype did you sell?5. Suppose a video store charges non-member 4 to rent avideo. A membership costs 21 and then videos cost only 2.50 to rent. How many videos would you need to rent inorder to justify a membership?6. Suppose you decide to make and sell silk flowerarrangements. You spend 220.00 on materials. You sell eachflower arrangement for 10.50 each. How much profit wouldyou make if you sold 23 silk flower arrangements?

7. The new parking lot has spaces for 450 cars. The ratio ofspaces for full sized cars to compact cars is 11 to 4. How manyspaces are for full-sized cars? How many spaces are forcompact cars?8. You are designing a cylindrical storage container forcompost. You want it to hold 110 ft3 and be 8 ft high. Use9. A ladder is 25 ft long. The ladder needs to reach to awindow that is 24 ft above the ground. How far away from thebuilding should the bottom of the ladder be placed?10. There is a large building on fire. Fire trucks from twodifferent stations respond to the fire. One station is 1 mile eastand 2 miles north of the fire. The other station is 2 miles westand 1 mile south of the fire. How far apart are the two firestations?the formula V r h to find the radius of the storagecontainer.2Part 8: Graphing (absolutely no calculator is allowed here)Graph each of the following equations or inequalities.1. x y 63.x 52.y 34. 2 x 6 3 y

5.1y x 336.1x y 827.3y x48.3 y 12Part 9: Systems of Equations (no calculator)Find the solution to each system of equations using either substitution or elimination.1.x y 12x y 22.3x 2 y 7 x 3y 84.x y 7x y 9M 10, 2 and W 10, 5 3.x 3y 16x y 6

5.y 2x3x y 56.x 4y 3x 57.3y 2 x2x 7 3 y8.2 x 3 y 13x 5 y 22.2x yx y 3Find the solution to each system by graphing (no calculator)1.y 2x 1 4 x y 7Part 10: Working with Formulas (Distance, Midpoint, Slope) (no calculator)Find the distance between each of the following pairs of points. Put all answers in reduced radical form.d ( x2 x1 )2 ( y2 y1 )21.B 3, 8 and C 9, 2 2.X 5,3 and Z 4,1

3.M 8, 4 and N 2, 28 4.Find the coordinates of the midpoint between each pair of points.5.A 5, 4 and B 3, 2 E 4, 4 and F 0, 4 x x y y M 1 2 , 1 2 2 26.C 3,3 and D 2, 1 M M T 3, 4 and R 5, 7 7.S 1,0 and V 5, 5 M M Find the slope of the line between each pair of points.8.A 2,8 and B 10, 8 m y2 y1x2 x19.T 0, 8 and R 10, 8 m m 10.B 8,1 and R 2,5 11.M 10, 2 and W 10, 5 m m

Free Response Question:A tank is filled with water up to a height of 10 meters. The tap at the top is opened and water is filled in the tank at the rate of3 meters per minute for 1/2 hour. Then the tap at the top is closed. After 5 minutes the tap at the bottom of the tank isopened and water is drained out at the rate of 5 meters per minute till the tank is completely empty.A) Model the above events in terms of a graph of the level (height) of water in the tank vs. time. Does this graph representcase of Direct Variation?B) What is the slope of the graph when water is being filled in and when it is being drained out of the tank?C)What is the significance of positive and negative slope in this situation?D)Write equations indicating the relation between level (height) of water in the tank and time when:a)Water is being filled in the tank from time 0 minutes to 30 minutes.b) The top tap is closed and the bottom tap is opened from time 30 minutes to 35 minutes.c)10 mWater is being drained out of the tank from the time 35 minutes until the tank is empty.

Factor each expression or equation, if possible. Solve for x if you are working with an equation. Solve for x, find the roots, find the solution, find zeros, and find x intercept mean the same. 1. Factor 4 20xx32 2. Solve xx2 1 3. Solve xx2 60 4. Solve x2 49 0 5. Solve xx2 2 1 0 6. Solve 2 5 3xx2 7. Factor 0y22 8. Factor 25 16xy22

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