GEOMETRY HONORS SUMMER REVIEW - Morton High

GEOMETRY HONORS SUMMER REVIEWWelcome to Honors Geometry at Morton High School!Dear Parents and Students,Mathematics is a discipline that constantly builds on previous knowledge. Students enteringHonors Geometry are expected to recall and apply the material that they learned in Algebra Ifrom day one. We begin the year with brand new Geometry content and do not reteachconcepts or begin with a “review chapter.” When you return to school in the fall, there will bea test over major Algebra 1 concepts on the second full day of class to help determine yourplacement and readiness for Honors Geometry. Your performance on this test will be asignificant factor in determining if you maintain your placement in honors. To help youprepare for this test and for Honors Geometry in general, the high school mathematicsdepartment has compiled a list of problems that represent some of the most frequently usedAlgebra I concepts. Students are expected to complete the entire packet over the summer andto begin the semester ready to ask questions about problems they did not understand. Werecommend doing 1/3 of the problems from each section/topic each month. This will help keepthe material fresh and identify areas that need improvement.Class time will be provided on Thursday, August 16th for questions, as the Geometry HonorsPrerequisite Content Test is scheduled for Friday, August 17th. Teachers will help clarifydirections when necessary, but will not answer questions such as “Am I doing this right?” or“Can you give me a hint?” The purpose of this test is to determine what you know, not whatwe know. Honors mathematics classes at Morton High School do not permit extra time onquizzes or tests, and this test is no exception. Students who are thoroughly prepared shouldhave no problem completing the test within 45 minutes.If you should happen to lose this packet, you can find it posted on the Morton High Schoolwebsite at http://mhs.morton709.org/my-class/mathYou will find a listing of all of our classes. Please select Geometry Honors Summer Review.If you have any questions, contact Mrs. Durand at rosie.durand@mcusd709.org.Have a wonderful summer!The Mathematics DepartmentMorton High SchoolNote: For those students who will be purchasing a graphing calculator:Please read the attached letter regarding graphing calculator requirements for MHSmathematics courses. You may send your student to school with the calculator’s packagingintact to for the math teacher to verify the correct calculator was purchased. CAS versions ofthe TI-Nspire are NOT allowed for students enrolled in Geometry.1

GEOMETRY HONORS SUMMER REVIEWFOR STUDENTS NEEDING TO PURCHASE A CALCULATOR:MORTON HIGH SCHOOL Required Calculator: TI-Nspire CXAt Morton High School, all students use graphing calculators extensively in their math classes,whether they are in Algebra I through AP Calculus. This requirement has existed for a couple ofyears now; students are making great strides in mathematical understanding and performance aswe continue to implement the use of the TI-Nspire CX. It is of critical importance that studentsobtain a calculator from the approved list because MHS math teachers have demonstrationsoftware for these specific devices, and it reduces the amount of class time spent on teachingstudents how to use the calculator.In past years, Texas Instruments has offered schools a special opportunity to collect proof ofpurchase cards from students to be used towards a free TI-Nspire Navigator system or other TINspire products. This system would allow us to wirelessly network graphing calculators to theteacher’s computer, giving us the ability to let students demonstrate what they are doing to theclass, receive document files from their teacher on their Nspire, and even use their calculator as away to answer questions the teacher has posed to the class.If you will be purchasing a new TI-Nspire CX (the latest version of the Nspire, which has a colorscreen) between now and the start of the 2018-19 school year, would you please return the entire“compare models” card that comes with the calculator to your child’s math teacher? It will helpus to obtain the Navigator system at no cost to the district. There is a picture of this card includedon the next page. You must return the entire card, not just the “TI Points.” Do NOT purchase acalculator with CAS as part of its name.If your child will be using a hand me down TI-Nspire from an older sibling, such as thegreyscale model, we will no longer be able to install the latest operating system nor will we beable to use this calculator with the Navigator system. It does, however, have most all of thefunctionality of the CX and can still be used with much success.DO NOT PURCHASE THE TI-NSPIRE CAS OR TI-NSPIRE CX-CAS. Although the CAS isallowed on the SAT, these calculators are not allowed on the ACT and thus not allowed forstudents enrolled in MHS courses other than AP Calculus.Thanks for helping us make sure your child receives the best possible math education with thelatest tools available.If the purchase of a graphing calculator will place an undue financial burden on your family,please contact your counselor or your math teacher.Be sure to save the entire card with the TI Technology points and turn it in to any math teacher! Withenough collected, the department will be able to earn software for use with your students!2

GEOMETRY HONORS SUMMER REVIEW3

GEOMETRY HONORS SUMMER REVIEWI. ORDER OF OPERATIONSExample: Simplify22 3 4 7 4 3 4 7 5 22 3 6 5 4 3 6 4 12 75 12 6 1 1 1 Simplify.1. 23 32 2. 2 3 4 2 7 3. 5( 1) 6( 2) 4. ( 2)(3) ( 1)(7) ( 2) 5. 3 22 16 32 6. 6 (3 4) 2 7. 6 3 (4 2) 8. 32 8 2 72 35 9. 4(23 ) 6 10. (8 2) 2 11. (4 6) 212. 4 62 13. 32 ( 4) 2 14. 32 ( 4) 2 4 3215. 2 8 272 82 1316. 3 2 2 3 2317.18.19.20.2(8 3) 4(7 2) 5(6 1) 3(8 6)32 2 4 44 9 3 6 1 8 42 3 5 4 2 32 92 3 4 5 6 20 5 8 II. FACTORING POLYNOMIALSExamples: Factor Completely.a. 4 x 3 12 x 2 8 x 4 x( x 2 3x 2)b. 5 x 3 - 3x 2 20 x -12 x 2 (5 x - 3) 4(5 x - 3) (5 x - 3)( x 2 4)c. x 2 2 x 35 ( x 7)( x 5)d. 3x 2 5 x 2 (3 x 1)( x 2)e. x 2 18 x 81 ( x 9) 2f. 4 x 2 25 y 2 (2 x 5 y )(2 x 5 y )Factor Completely.1. x 2 6x 16 2. 4 y 2 7 y 2 3. 5a3 25a2 15a 4. 9 x2 16 5. x2 64 6. a2 12a 27 7. 6x2 12x 6 8. x3 2x2 5x 10 9. x3 2x2 5x 10 10. x2 10x 21 11. 6 y 2 54 21. y 2 10 y 25 12. 4 y 2 17 y 15 22. 3a2 12a 3 23. x4 81 24. 9 y 2 12 y 4 13. 6x2 7 x 2 14. 5x2 5 15. y 5 3 y 3 4 y 2 12 16.17.18.19.20.x2 7 x 18 x2 8x 16 a2 9a 14 49 x2 1 8x4 4x3 12x2 25.26.27.28.29.30.a2 11a 30 8t 2 2t 3 75x2 30x 3 3t 2 8t 3 x2 3x 8x 24 y 2 22 y 121 4

GEOMETRY HONORS SUMMER REVIEWIII. RADICALSExamples:Simplify 48Simplify 18 32 7548 16 3 16 3 4 318 32 75 9 2 16 3 2 4 2 5 32 25 3 5 3 7 253Simplify5 353 5333 151or1533Simplify.1.2.3.4.5.6.7.49 3115.2116.5417.2249. 5 1810. 4 94278.7232982002011.32 4212.52 12213.14.148618.6319. 4 3 7 320. 7 2 3 6 3 212 2722. 72 75 4821.IV. SLOPE AND EQUATIONS OF LINESExamples:a) Find a slope-intercept equation for the line with slope 2 that contains (0,5)y mx bThe slope-intercept equationSubstitute 2 for m and 5 for by 2x 5b) Find an equation of a line that contains the points (5, -2) and (-2, 1)1 ( 2)33m First find the slope. 2 5 77y 3x b731 ( 2) b761 b71 b731y x 77Use the slope-intercept form and substitute for m.Use the point (-2, 1)* and substitute for x and y.*(We could have just as easily used (5, -2))Substitute for b.5

GEOMETRY HONORS SUMMER REVIEWFind an equation of the line containing the given point and having the given slope.1. (4, 3), m 15. (6, 2), m 32. ( 5, 6), m 26. (5, 2), m 23. ( 7, 2), m 37. (7, 0), m 34. (3, 5), m 28. (0, 9), m 29. (5, 1), m 1510. ( 3, 2), m 14Find an equation of the line that contains the given pair of points.11. 1,5 and (4, 2)14. (0,3) and ( 2,6)18. (3, 4) and ( 3, 4)12. ( 4, 2) and (1, 3)15. ( 8,3) and ( 4,1)19. ( 7, 4) and ( 4,7)13. ( 5, 3) and (1, 1)16. (6, 2) and ( 3,0)20. (9, 5) and (7,7)17. (1,3) and (4,6)V. SYSTEMS OF EQUATIONSExamples:a) Solve using the substitution method:5x 2 y 4y 5 xSubstitute 5 x for y.5x 2 y 45 x 2(5 x) 4Then substitute 2 for x and solve for y.5x 10 2x 47 x 14y 5 2y 5 xy 3The solution is (2,3)x 2b) Solve using the elimination method.2x 7 y 1 x 2 y 2Multiply the second equationby 2 and then add.2x 7 y 1 2 x 4 y 4Then substitute 1 for y and solve for x2x 7 y 12 x 7(1) 12x 7 12 x 8x 4The solution is ( 4,1)3y 3y 1Solve.1.4x 3y 1x 1 y2.2x y 6 x y 13.6x y 34 x 2 y 24.2x 3 y 7x 1 4 y6

GEOMETRY HONORS SUMMER REVIEW5.2x 3 y 6x 3 y 159.6.7x 5y 4y 3x 410.7.2 y 5 x 1x 2y 56x 5 y 34 x 3 y 2111.4x 3 y 18.3x 5 y 13x y 43x 4 y 10 3x y 27x 8y 113.9 y 2 x 7x 3y 514.3x 5 y 84 x 7 y 1215.5 x 2 y 123x 4 y 2x 4y 716.3x 7 y 67x 2 y 212.x 2 y 1417.5x 8 y 25 x 4 y 718.8x 6 y 013x 9y 421x y 183419.13x y 668VI. QUADRATIC EQUATIONSExamples: Solve for xx 2 10 x 16x 2 10 x 16 0( x 8)( x 2) 0x 8 0 or x 2 0x 8 or x 2Solve for x1. x2 5x 6 02. x2 4x 12 03. x2 8x 15 04. x2 18 3x 05. x2 36 9xx2 5x 0x( x 5) 0x 0 or x 5 0x 0 or x 56. x2 5x 36 07. x2 4x 08. x2 10x9. x2 2x 11x10. 5x x2 3x11. 3x2 5x 7 x2 8x 2812. 12x2 15 11x13. 8x2 7 x 9 2x2 6x 7VII. QUADRATIC FORMULAExample: Solve 3x2 5x 1 0 using the Quadratic Formula3x2 5x 1 0a 3x b 5Quadratic Formulac 1x b b 2 4ac2a ( 5) ( 5) 2 4(3)(1)2(3)5 25 12 5 13 66Solve.1. x2 3x 42. y 2 6 y 83. x2 10x 257

GEOMETRY HONORS SUMMER REVIEW4. 2 y 2 7 y 15 010. y 2 7 y 1 05. x2 36 06. y 2 49 011.12.13.14.15.7. x2 3x 3 08. x2 5x 7 09. y 2 8 y 11 016. 6x2 6x 817. 4 y 2 6 y 1 0x2 6 x 8 4x2 3x 1 64 x2 7 x 2 05x2 3x 1 02x 2 3x 318. 2 y 2 5 y 319. 8x2 20020. 9x2 144ANSWER KEYI. Order of Operations1. 12. 53. 174. 35. 1326. 3II. Factoring Polynomials1. ( x 8)( x 2)2. (4 y 1)( y 2)3. 5a (a 2 5a 3)4. (3x 4)(3x 4)5. ( x 8)( x 8)6. (a 9)(a 3)7. 6( x 1)213. 414. 16 515.661416. 97. 78. 79. 3810. 3611. 412. 3211. 6(y 3)(y – 3)12. (4 y 3)( y 5)13. (2 x 1)(3x 2)14. 5( x 1)( x 1)15. ( y 3)( y 4)2316. ( x 9)( x 2)17. ( x 4) 28. ( x 2 5)( x 2)18. (a 7)(a 2)9. ( x 5)( x 2)10. (x – 7)(x – 3)20. 4 x 2 (2 x 2 x 3)2III. Radicals1. 22. 3 33. 6 219. (7 x 1)(7 x 1)10. 1311. 512. 13141918. -4719.820. 1617. 21. ( y 5) 222. 3( a 2 4a 1)23. ( x 2 9)( x 3)( x 3)24. (3 y 2) 225. (a 5)(a 6)26. (4t 3)(2t 1)27. 3(5 x 1) 228. (3t 1)(t 3)29. ( x 8)( x 3)30. ( y 11) 216.5517. 2 218. 2 35. 7 22 313.36. 10 214. 7 3215.220. 8 2 7 37. 2 54. 4 28. 2 619. 11 321. 5 322. 6 2 39. 15 28

GEOMETRY HONORS SUMMER REVIEWIV. Slope and Equations of Lines1. y x 12. y 2 x 43. y 3x 234. y 2x 115. y 3x 166. y 2x 127. y – 3x 218. y 2x 919. y x 25V. Systems of Equations1. ( 2,3)6. (2, 2)15x 4411. y x 612. y x 216. y 10. y 22x 9317. y x 2418. y x319. y x 1120. y 6x 491413. y x 33314. y x 32115. y x 1212. (2, 6)2. (5, 4)7. ( 1, 3)13. (8,1)3. 1,3 8. (4, 5)14. ( 4, 4)4. 5, 1 9. (3,3)15. (2,1)5. ( 3, 4)10. (6, 2)16. ( 5,3) 11 5 17. , 3 6 1 1 18. , 4 3 19. 18, 24 11. ( 1, 1)VI. Quadratic Equations1. 6, 1 7. 0, 4 2. 2, 6 8. 0,10 3. 5,3 9. 0,13 4. 6, 3 10. 0,8 5. 12, 3 7 11. 5, 2 6. 9, 4 VII. Quadratic Formula1. 1, 4 2. 2, 4 3. 5 3 4. ,5 2 5. 6,6 6. 7,7 3 21 7. 2 5 53 8. 2 9. 4 5 7 53 10. 2 11. 3 5 3 29 12. 2 5 3 12. , 3 4 1 13. , 2 6 7 17 13. 8 3 29 14. 10 3 33 15. 4 3 57 16. 6 3 134 3 18. 1, 2 19. 5,5 17.20. 4, 4 9

Honors Geometry are expected to recall and apply the material that they learned in Algebra I from day one. We begin the year with brand new Geometry content and do not reteach concepts or begin with a “review chapter.” When you return to school in the fall, there will be a test over major Algebra 1 concepts on the second full day of class .