Honors Geometry Summer Work 2015 due date: third day of class estimated time: 10 hours (for planning purposes only; work until you finish) Dear Honors Geometry Students, This assignment is designed for you to review all of your algebra skills and make sure you are well prepared for the start of Honors Geometry in the fall. The assignment is in two parts: written problems in this packet, and problems on ixl.com. See the next page for detailed instructions. We anticipate that the work will take about 10 hours to complete. Both the written work and the online work are due on the third day of class. At that time you will have a short quiz with problems taken directly from both this packet and the ixl sections listed on the next page. A portion of the quiz grade will be based on the completeness of your summer work. We are really looking forward to the upcoming school year and hope you are, too! Please email any of us if you have questions. Barbara.Filler@stewardschool.org Todd.Serr@stewardschool.org Jennifer.Maitland@stewardschool.org Karen.Hudson@stewardschool.org Page 1 of 22
Assessment of Summer Work 1. On the third day of class, you will submit your written work, and your teacher will check your online work. 2. You will have a quiz made up of problems taken directly from the on-line and written work. 3. Your written and online work will be evaluated for completeness; that grade will form part of the quiz grade. On-Line Work 1. Log in to ixl.com with the username and password you were given in your math class. Students new to Steward: your parents will receive an email with your username and password. 2. Work the problems listed below, until you earn a score of at least 60% for each section. If you find that the name of the section does not match the numbers below, go by the section name. 3. If you are having difficulty of any sort with ixl, reach out to a teacher at one of the email addresses above. 1. click this tab 2. find these sections 3. work these problem sets Algebra I Factoring Quadratic equations Radical expressions Rational functions and expressions AA.7 - Factor polynomials BB.5 - Solve an equation using the zero product property EE.1 - Simplify radical expressions EE.2 - Simplify radical expressions by rationalizing the denominator EE.3 - Multiply radical expressions EE.4 - Add and subtract radical expressions GG.3 - Simplify rational expressions GG.4 - Multiply and divide rational expressions Written Work 1. Complete each problem on the following pages. 2. Do the problems on separate paper. Do the problems in order and number them clearly. o Exception: print the graphing problems (pages 8-12, 19) rather than drawing your own graphs. 3. Please show all of your work as was required of you throughout the entire school year. o Remember: no work, no credit. Page 2 of 22
I. Order of Operations For help with these problems, use the following search term on Khan Academy: Order of operations: PEMDAS Simplify each expression using the orders of operations, without a calculator. 1) 6 + 9 3 2) 4 (2 + 3) 2 3) 3(4 + 11) 10 3 3 4) 47 3[ 6 + 8 2] 5) 4 ( x + 2) + 3x 6) 3(2x + 5) (5 3x) 7) 3 2 3 1+ 14 2 6 3 + 6 2 8) 2(x-1) 5(x-3) 9) 2(5 2) 2 + 2(4 2) 2 Evaluate each expression if a = 2, b = 3, c = -2, d = 4, f = -5, without a calculator. 10) cf 11) c d 2 12) ca Page 3 of 22
13) ( b + cd)( ac) 14) ( cf ) ( ab) a 15) dc 2 16) a 2 b 17) 5c + 3bc 18) a b c d Page 4 of 22
II. Order of Operations, continued For help with these problems, use the following search terms on Khan Academy: Exponent properties involving products Exponent properties involving quotients Combining like terms Simplify each of the following. 19) 3x 4 + 7x 8 10x 2 20) 4x + 2(x + 5) 21) 3(x + 5) 4(x 6) 22) 5x 3 + 2x 2-7x x 3 + 5x 2 18 23) (5x 2 + x 4) (9x 2 4x 11) 24) 12x 3 (x 4 5x 2 + 2) 25) (x + 2)(x 2 5x + 1) 26) 5xy 20x + 6y (10xy + 10x) 27) 2x(3x 2 4x + 2) 5x(2x + 3) 28) 5x 2 y 2 + 3xy 3x 2 y 2 + 2x 3 y 2 + 5xy Page 5 of 22
III. Solving Linear Equations For help with these problems, use the following search terms on Khan Academy: Simple equations: examples solving a variety of forms Variables on both sides Solve the following equations and check your solutions. 29) -3x + 4 = 11 30) 1 x- 8 = 3 2 31) 8x 24 = -6 + 18 32) -6 + x 4 = 7x + 2 33) 2 x + 6 = 18 3 34) 6 x 5 = -4x 3 x 35) -5 + 4 b = 7 36) 4.2m +4 = 25 37) 4t + 7 + 6t = -33 38) 6 = -z 4 39) 4m + 2.3 = 9.7 40) 2a + 5 = 9a 16 Page 6 of 22
41) 1 4 2 + y = 3 6 3 42) 6(y 2) = 8 2y 43) n + 3(n 2) 10.4 44) m = 2.7 12 45) -4.7 = 3x + 1.3 46) 3w + 2 w = -4 47) Solve 2x -4 = -7 48) A rental company charges a flat fee of $185 for a moving van, plus an additional $.50 per quarter mile. a) Write a formula to find the cost for each rental. b) Use the formula to find the cost to use the van for a total of 80 mi. 49) Find the dimensions of the rectangle given the area = 164 sq. ft. 3x+5 4 Page 7 of 22
IV. Using Slope and y-intercept to Graph Linear Equations and to Write Equations of Lines For help with these problems, use the following search term on Khan Academy Graph from slope-intercept equation example Sketch each of the lines on the graphs below. 50) y = 2x 51) y = -3x 52) yy = 5 4 xx 53) yy = 4 3 xx Page 8 of 22
54) y = 6 55) x = -4 56) yy = 4 5 xx 6 57) yy = 5 3 xx + 8 Page 9 of 22
58) y = 3x 2 59) y = -4x+6 60) x = 2 61) y = -5 Page 10 of 22
62) 2x + 3y = 12 63) -3x + 27y = 8 Page 11 of 22
64) An airplane is currently at an altitude of 10,000 feet. The pilot begins to descend at a rate of 50 feet per minute. a) Write an equation for the altitude (a) of the airplane as a function of the time (t). b) Find the altitude of the airplane after i. 10 minutes ii. 30 minutes iii. 1 hour c) How long will it take for the airplane to be i. 7000 feet ii. 2000 feet iii. on the ground? d) Create a table showing the altitude in feet for times 0 min, 10 min, 30 min, and 60 min. Graph the altitude of the airplane as a function of the time in minutes that the airplane takes to begin its descent and land on the ground. 65) This summer you and a friend designed a bracelet with the school s logo. In order to massproduce your bracelet, you need to hire a design firm to make a mock-up. One firm you called charges $250 for making the first bracelet and $3 to make each one after that. a) Write an equation to model the cost of making the bracelets. b) How much will it cost to make 75 bracelets? c) How many bracelets can you make for $3000? Page 12 of 22
For the equations in problems 66-71, find the following: a) slope b) y-intercept (let x = 0) c) x-intercept (let y = 0) 66) y = 4x 2 67) 6x 3y = 15 68) y = 2x 5 69) 4x + 3y = 12 70) 3y = 4x 9 71) 5x y = 15 Page 13 of 22
V. Using Slope and y-intercept, continued For help with these problems, use the following search terms on Khan Academy: Slope from two ordered pairs example 1 Finding the slope of a line from its graph Equations of parallel and perpendicular lines Parallel and perpendicular lines intro For each line described in problems 72-74, a) find the slope b) find the y-intercept c) write the equation in slope-intercept (y = mx+b) form. 72) a line that passes through the point (-5,6) with a slope of 4 73) a line that passes through the points (4,1) and (7,-11) 74) a line that is perpendicular to the line 6xx 3yy = 15 and passes through the x-axis at 3 For each line graphed in problems 75-82, a) find the slope b) find the y-intercept c) find the x-intercept d) write the equation in slope-intercept (y = mx+b) form. 75) Page 14 of 22
76) 77) 78) Page 15 of 22
79) 80) 81) Page 16 of 22
82) Page 17 of 22
83) A tanker filled with honey pulls into the factory where it will be bottled for sale.. The tanker is going to offload the honey as shown in the graph below. 120 Volume vs. Time Volume (in 1000's of gallons) 100 80 60 40 20 0 0 2 4 6 8 10 time (in hours) a) How many gallons of honey are in the tanker when it pulls into the factory? b) At what rate, in gallons per hour, is the tanker unloading the honey? c) Write an equation for the amount of honey (l) after h number of hours. d) Find the amount of honey after: i. 15 hours ii. 25 hours e) How long will it take for the tanker to have: i. 60,000 gallons left ii. 25,000 gallons left f) How long will it take for all the honey to be offloaded? Page 18 of 22
VI. Linear Systems For help with these problems, use the following search terms on Khan Academy: Systems of equations word problems example 2 Linear systems word problems with substitution Systems of equations word problems example 4 Solving systems of two linear equations example Solve the following systems by graphing. 84) 85) 86) 87) Page 19 of 22
Solve the following systems using substitution. 88) 89) 90) 91) Solve the following systems using elimination. 92) 93) 94) 95) Page 20 of 22
VII. Properties of Exponents For help with these problems, use the following search terms on Khan Academy: Exponent properties involving products Exponent properties involving quotients Simplify each expression. 4 2 96) 3 3 3 5 2 97) x x x 3 4 98) 2m 4m 3m 99) 5y 6y 100) 101) 102) 8m 3 m 5 3 6xy 6xy 7x 5x x 0 1 5 3 103) ( xy ) 0 104) 9xy 0 7x 4 3 5 105) ( 2m p ) 3 Page 21 of 22
VIII. Quadratics For help with these problems, use the following search term on Khan Academy: FOIL for multiplying binomials Multiply using the FOIL method. 106) (x 2)(x + 6) 107) (3x + 6)(x 1) 108) (x + 9)(2x 7) 109) (5x + 1)( 3x 2) 110) (x 8)(2x + 3) 111) (5n + 6)(5n 3) 112) (7a 6)(8a + 2) 113) (5a 3) 2 Page 22 of 22