Summer Packet Geometry PAP IMPORTANT INSTRUCTIONS FOR STUDENTS!!! We understand that students come to Geometry with different strengths and needs. For this reason, students have options for completing the packet and getting assistance! Students should try to answer all the questions if possible; you must show all work. Students must answer a minimum of 70% of the questions to receive full credit. So, if you really can t answer certain questions, students may write the word pass on up to 0% of the questions without penalty. (The purpose of this option is to allow students to show what they know on certain concepts while informing the teacher of concepts that may need to be reviewed with students after school starts). Khan Academy video tutorials may be very helpful to you. HISD has aligned Khan Academy with Algebra I, are available by clicking this link: http://www.houstonisd.org/cms/lib/tx01001591/centricity/domain/8050/khan_acad_video_algmt_algpdf Need face-to-face help with packet? Come to WHS on August 9 th between 9-1pm! WHS Geometry teacher(s) will be on hand to give you assistance! There will be a test over this material on or before September 6, 0 Finally, honor and integrity is at the heart of a Westside Wolf! Smart wolves never cheat. You are only hurting yourself by attempting to copy someone else s work. This packet is to help you be ready for Geometry and help your teachers know what you can do. All eisting and new students who are enrolled at WHS on or before August 17 th, must submit their summer packet to their math teacher no later than Friday, August 0, 0 Students who enrolled at Westside High School on or after August 19 th, must submit their summer packet within two weeks of their enrollment date at Westside. Now! Get Ready, Get Set, and Do Your Best!
A. Find the slope of the line containing each pair of points. 5,0 and 6,8., and 6,., and 9, 7 B. Find the slope of each line.. y 7 5. 6. y 15 7. y 7 C. Find the equation of the line with the given slope through the given point. Write the answer in slope-intercept form. 8. m ;, 9. m ;,7 10. m ;, 1 D. Find the equation of the line containing the following points. Write answer in standard form. 1,6 and,1,5 and 5,, and, 6 E. Write the equation of the line in standard form. The line with -intercept and y-intercept of 5. 15. The line containing 0, and,0. F. Write the equation of the line in point-slope form. 16. The line containing, and 5,. 17. The horizontal line passing through,5. G. Write the equation of the line in slope-intercept form. 18. The line containing,1 and,8. 19. The line containing, and 6,9. 0. The line with slope 5 and containing 1,7.
Graph the following equations. Graph three points and label the line with its equation. y 1. y 5. y 5 y. 1 y 5. y y 8. y 6. 6y 1 K. Simplify each epression using appropriate Order of Operations.. 15 5. 10 6 1 5 6. 7 5 5. 1 0 17 6 6. 7 0 5
L. Solve for the variable in each problem. 1 1 5 5. 6 0 1 7. r r 5 8 16 1 1. 1 c c c 5. 8y 17 y 8 6. 1 5 1 M. Solve each system of linear equations. y y 7. ba b a 8. r s 0 r s 15. y 0 7y 17 N. Multiply the following binomials.. 6. 6 5 1 O. Factor each of the following polynomials. 8 15. a 1a 8.. 81 P. Solve each quadratic equation using the square root property. 11. 0. 5 0 Q. Solve each quadratic equation using factoring. 7 0. p 16p 8 0. 7 6 0
. m m 1 5. t 9t 1 6. 1 10 R. Use Pythagorean Theorem to find the missing side of the right triangles. If c is the measure of the hypotenuse of a right triangle, find each missing measure. Round to the nearest hundredth if necessary. It is better if you can leave as a simplified radical like in Section S. (Simplified radicals will be the type of answers used in Geometry) a 5, b 1, c?. a 6, b, c?. a 5, b 8, c?. a?, b 10, c 11 S. Simplify the following radicals (you answer will not be a decimal) 18.. 7. 5. 0 6. 5 7. 8 8. 75 T Simplify each problem using eponent rules 6 5 =. c c c =. 5 6 7 =. a 5a = 5. y y = 6. cd c cd 7. 5a = 8. 6 = = U Solve each equation. c 1) 6 ) 15 ) 7 1 ) 5) 1 5 6) 5t t 16 7) 7 h 11 8) 10t 8 5 9) 1 y 1 y
1 A. Slope formula m Eamples for Summer Packet Westside High School y y 5 8 E: 1, and,5 m 1 1 B. Slope intercept formula: y 1 Eample: y 1 y y m b slope y-intercept Slope is y-intercept is 0, Special Cases: Horizontal lines are Vertical line y a number slope is 0 a number slope is No slope C. Point slope formula: y y1 m ( 1 ) Use point slope when you have a point and slope and y of slope of want an equation of a line in slope intercept. Solve ordered ordered pair pair the equation for y once the point and slope are plugged in. Eample: y ( ) ( 6) plug in ordered pair and slope y Distribute y Solve for y, now equation is in slope intercept form D. Use eamples from A to find slope. Take slope and one of the points and plug into point slope, and use eample from C. Once equation is in slope intercept, get and y on one side and multiply by common denominator of and y, so that there is not any fractions. Eample: (, ) and (6, 0) 0 m 6 y ( ) ( ) y y y y y 1 E. Use information from A,B,C,D to figure out E. F. Use information from A,B,C,D to figure out F. G. Use information from A,B,C,D to figure out G.
H. Graph from point slope, y y m ( ) 1 1 y of slope of ordered ordered pair pair y ( 1) ( 1, ) m Equation Pull out point and slope from equation. Plot point Use slope to plot other points Draw line Slope is rise up or down up and 1right run right or left 1 I. Graphing from slope intercept, y m b slope y-intercept 1 y Equation 1 m (0,) Pull out slope and y-intercept Graph y-intercept Use slope to graph other points J. Graphing from standard form, A By C Take equation solve for slope intercept form, then use the steps from I. K. PEMDAS = Parentheses, Eponents, Multiplication/Division, Add/Subtract from left to right L. The five steps to solving an equation are: Get rid of parentheses Simplify the left side and the right side of the equation as much as possible, i.e. combine any and all like terms Get the variable term on just one side Get the variable term by itself Solve for the variable. Remember, you always use the opposite operation to get rid of something. When problems have fractions try clearing the fractions by multiplying by the least common denominator and the problem will be easier to solve.
M. Solving a system of equations by elimination multiplyby y 5 1 9y 75 multiplyby 8y 10 1 y 0 y 115 y 5 This is so that the part of the equation will cancel (5) 5 15 5 0 10 Plug y into one of the equations and solve for the other variable. (10,5) Write answer as an ordered pair N. Multiplying binomials 5 6 10 1 0 6 0 First Outer Inner last combine like terms terms terms terms terms 9 1 1 16 9 16 O. Factoring Eamples: First Outer Inner last combine like terms terms terms terms terms 1) a b a ba b EX: a 16 a a ; 5a 6 5a 6 5a 6 6 ) a ab b a b k 10k 5 k 5 k 5 k 5 k & 5 are perfect squares & 10 1 5 EX: ) a ab b a b EX: 1 9 & 9are perfect squares & 1 ) a b c EX: 6 8 since 6 a b c 8 15 5 since 5 8 a b c a 1a 5 a 15a a b c y y 1 y y since 1 P. Square root method and 8 and 5 15 since 15 1 and 15 5 and 1 5 75 0 Problem 5 75 Get numbers on one side of equation 5 5 15 Divide by 5 15 Square root both sides
6 1 Problem 6 1 square root both sides 6 1 square root of 6 6 6 6 subtract 6 from each side 1 6 answer Q. Solve using factoring a 1a 5 a 15 a First factor the problem a 15 0 and a 0 Make each factor equal to zero and solve for "" 15 15 a 15 a Answer R. Pythagorean Theorem A B C, A and B are the legs and C is the hypotenuse (longest side). a, b 6, c? a, b?, c 1 a b c Pythagorean Theorem a b c 6 c 9 6 c 5 c Plug in values square numbers combine numbers 5 c square root both sides b 1 Plug in values 16 b 1 square numbers 6.71 c answer b 10.95 answer b b Pythagorean Theorem 10 Get all numbers on one side 10 square root both sides S. E: Write in simplest form 8 = = = perfect square T. Eamples: 5 5 7 c c c c 6 6 9 Eamples: 8 7 Eamples: 5 Eamples: 8 u u u u u u u u 15 1 1 1 1 16 1 1 1 6k 6k 6k 6k 6 6 6 k 16k a a a a 5 15 6 U. See Section L