MHCA Math Summer Packet 2015

Transcription

1 MHCA Math Summer Packet 2015 Directions: For students entering Geometry Honors You are to complete all the problems assigned in this packet by Friday, September 4 th. If you don t turn in your summer packet when it is due, you will be required to work on your summer packet in the library during your Club period time, every day until your summer packet is complete. You will also lose 10 points from your overall summer packet grade. The summer packet will count as your 1 st Marking Period Project. Failure to complete this on time or to take it seriously will drastically reduce your 1 st Marking Period Grade. Students in Honors class who don t turn in their packet on time WILL NOT be recommended for Honors the following year. You may use as much scrap paper as you want for this packet, but you will ONLY turn in the 7 answer sheet pages for a grade. Any answers not written on the answer sheet will be assumed to have not been answered and you will lose the point for that problem. When you get your graded answer sheet back you can look back at your work to see where you made the mistake. If you can t find it, you are encouraged to see your teacher before school, during club or after school for help. All the material in this packet is what you learned in your math class this past year; so none of it should be new. You will be expected to know all the material in this packet for your Geometry Honors class this year. Your teacher WILL NOT reteach the material found in this packet; they will only review it with you at appropriate points in the class. If you do encounter questions where you are not sure how to solve, you may use the links to my YouTube videos for the Algebra 1 and Geometry classes. You should also watch videos from Khan Academy if you can t find your topic in the Algebra 1 and Geometry videos or if you need more supplemental videos. If you have any questions regarding the completion of the MHCA Math Summer Packet please contact me at fmcmahon@maryhelp.org. Have a great summer and we look forward to seeing you at the start of the school year! Fred McMahon Mathematics Department Chair

2 Answer Sheet Use Graph 52. Use Graph 53. Use Graph 54. Use Graph 55. Use Graph 56. Use Graph 57. Use Graph 58. Use Graph 59. Use Graph 60. Use Graph

3 #51 #52 #53 #54

4 #55 #56 #57 #58 #59 #60

5 #77 #78 #79 #80 #81 #82

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9 Solve each equation for x. Round to the nearest thousandths place if necessary. 1) 2x + 9 = 17 6) 6x x 3 = 180 2) 5x + 4 = 16 7) 9x x = 7x 16 3) 7x + 3 = 5x ) 2 x + 5 = ) 4x + 7 = 2x 19 5) 5x x 12 = 90 9) 4 7 x 1 = 3 5 x ) 3(2x + 4) 5 = 2x + 13 Solve the following absolute value equations. Round to the nearest thousandths place if necessary. 11) 2x + 5 = 13 13) 4x 7 = 14 15) 5x + 9 = 23 12) 3x 6 = 18 14) 2x 1 = 11 Solve the following proportional equations. Round to the nearest thousandths place if necessary. 16) 2 5 = 16 x 18) 5 4 = 15 2x 4 20) 2 3 = 4x 2 6x+3 17) 4 9 = x 36 19) 11 = 4x Solve each system of equations for x and y 21) y = 2x 5 3x + y = 0 22) y = 4x + 2 5x 2y = 30 23) x = 3y + 4 3x + 6y = 6 24) x = 2y + 9 5x 6y = 13 25) 3x + 5y = 2 6x + 5y = 16

10 26) 4x + 9y = 22 4x 3y = 10 27) 2x 7y = 16 5x + 7y = 40 28) 8x + 5y = 41 8x + 2y = 26 29) 3x + 5y = 23 2x 4y = 14 30) 6x + 8y = 12 5x 3y = 21 Solve the following exponential equations. Round to the nearest thousandths place if necessary. 31) 2 x+3 = 32 32) 4 2x 7 = 64 33) 5 3x+8 = ) 9 x 1 = 27 Solve the following Growth/Decay problems 35) Katie s dogs are plotting the overthrow of the United States government. Her dogs currently have 70 dogs involved in their hostile takeover. Katie s dog are able recruit at a rate of 11% per week. How many dogs will be in the revolution after 12 weeks? If they need 20,000 for a successful takeover, will they have enough after 1 year? 36) Miley Cyrus is suffering from the deadly Twerking Virus. There are currently 275,000 virus cells in her body when doctors start to treat her. If doctors can remove the virus cells at a rate of 9% per minute, how many will there be left after 20 minutes? If they need to bring the number of virus cells to fewer than 1,000 after 1 hour to save her, can they do it? Solve the following square root equations. Round to the nearest thousandths place if necessary. 37) 2 7x = 7 39) 3 5x = 9 38) 3x = 1 40) x + 3 = x 3 Solve each quadratic equation by factoring 41) x 2 5x 36 = 0 44) x x 24 = 0 42) x x + 56 = 0 45) x 2 12x + 36 = 0 43) x 2 16x + 63 = 0 46) x 2 4x 32 = 0

11 47) 2x 2 9x 35 = 0 48) 3x x + 16 = 0 Solve each quadratic equation by using the quadratic formula. Round to the nearest thousandths place if necessary. 49) 2x 2 7x 15 = 0 50) 5x 2 + 9x + 8 = 0 Graph the following linear functions in slope-intercept form 51) y = 2x ) y = 4 3 x ) y = 3 5 x ) y = 3x 1 54) y = 2 7 x 3 Graph the following linear functions in standard form 56) 6x 4y = 24 58) 3x + 4y = 12 60) 9x 6y = 18 57) 8x + 5y = 40 59) 5x 4y = 20 Use the given information to write the equation of the line (b is the y-intercept and m is the slope) 61) m = 2, b = 1 66) m = 3 ; (0, 6) 4 62) m = 0, b = 2 67) m = 5 ; (9, 1) 3 63) m = 6 7, b = 8 68) (8, 1), (5, 7) 64) m = 1; ( 4, 3) 69) ( 6, 3), (0, 6) 65) m = 5; (2, 6) 70) (4, 2), (4, 8)

12 Solve the following linear inequalities. Round to the nearest thousandths place if necessary. 71) 6x + 4 > 16 73) 5x + 9 < 7 72) 2x ) 8x 3 25 Solve the following compound inequalities 75) 7 < 5x ) 9 2x + 5 < 19 Graph the following linear inequalities 77) y < 3x ) 6x + 4y 24 78) y 2 3 x 1 80) 5x + 8y > 40 Graph the following quadratic functions in standard form 81) f(x) = x 2 + 2x ) f(x) = 2x 2 + 4x 3 82) f(x) = x 2 4x ) f(x) = 3x 2 6x + 2 Graph the following quadratic functions in vertex form 85) f(x) = (x 1) ) f(x) = (x + 3) ) f(x) = (x + 2) 2 1 Graph the following absolute value functions 88) f(x) = x ) f(x) = x ) f(x) = x + 1 5

13 Graph the following Exponential Functions 91) f(x) = 3 x 93) f(x) = 2 4 x 5 92) f(x) = 2 x 1 94) f(x) = 3 2 x + 3 Graph the following Square Root Functions 95) f(x) = x 5 97) f(x) = x ) f(x) = x ) f(x) = 2 x Graph the following Piecewise Functions 2x + 5, if x < 1 99) f(x) = { 3x 2, if x 1 } 2 x 4, if x 3 100) f(x) = { 3 2x + 4, if x > 3 }