Honors Geometry Summer Packet NHHS and VHS

Transcription

1 NAME_ STUDENT ID # Honors Geometry Summer Packet NHHS and VHS This summer packet is for all students enrolled in Honors Geometry for the upcoming school year. The entire packet will be due and collected on the FIRST DAY of the school year and will count as part of your first quarter grade. The TEST on the material in this packet will be during the second week of school. The objectives in this packet are Algebra I objectives, and all of the objectives are NON CALCULATOR objectives. The score on this test is a strong indicator of success in the class. Be sure to master the objectives before the test. Follow all the directions, work neatly, and show all work to get the best possible grade on the packet. The summer assignment grade is based on completion of the packet and ability to follow these directions. Complete the packet in PENCIL. Either circle your final answers or write the final answer on the blank if one is provided. FOLLOW the directions in the packet and on this cover sheet, and complete all the eercises, neatly SHOWING ALL of your work in the packet. DO ALL WORK WITHOUT A CALCULATOR. Rework any incorrect problems until you able to reach the correct answer. Answers are provided at the back of the packet, so you may check your work as you go. However, NO CREDIT will be given if work is not shown for EACH problem. If you have forgotten how to do any of the problems in the packet, use the internet, Khan Academy etc. to google and review the objectives. PLEASE NOTE: The decision to take an Honors class is a serious one. The work in this class will require the following: o Eemplary work habits. o Eemplary time management skills. o A genuine desire to learn. o Personal responsibility for attendance and work requirements. o Independent review and study habits. o Self discipline and determination to succeed. For the upcoming school year, we highly recommend that you purchase a TI-8+ or TI-84+ calculator prior to the start of the school year. They are required for the PARCC eam, and for future High School math classes. Also, be reminded that after the first two weeks of school, the option to Drop Honors Geometry will not be opened again until the end of the first quarter.

2 I. SLOPE AND GRAPHING 1. Find the slope of the line through. Find the slope of the line with -intercept,1 5, 7 7,5 the points ( ) and ( ) 4 which goes through the point ( ). Graph each line and label it as (a) and (b). Label two points on each line with their coordinates. a. slope =, y-intercept = -4 b. slope =, y-intercept = 6 4. a. Find the slope of the line with y-intercept of 6, which passes through the point (, 4 ). b. Write the equation of the line in part a. in slope-intercept form c. Write the equation of the line in part a. in standard form

3 5. Find the slope and y-intercept of each of the following lines. Write slope as m = and y-intercept as a coordinate pair. 1 a. y = + 7 b. y = 8 4 c. 6 y = 1 d. = 9 e. y = 7 4 slope y-int 6 &7. Graph the equations from #5: a,b c,d,e II. SOLVING LINEAR EQUATIONS Solve for the variable. Be sure to show all work and give the EXACT answer. (Do not write any answers as decimals) = = 10. ( ) = = = = ( )

4 = ( ) = 41 ( ) ( ) ( ) 8 5= = ( 8) + 7 = 5( + ) ( ) 7 1+ = III. SYSTEMS OF LINEAR EQUATIONS y = 5 0. Solve the system of equations by graphing accurately. State the final answer. y = 5

5 1. Solve the following systems of linear equations algebraically (i.e. by substitution or addition) a. y = 4 + 4y = b. 5+ y = y = 19 c. 6+ y = 1 + y = 4 d. y = y = 9 e. y = y = 15 f. 8y = 7 5 = 6y + IV. BASIC GEOMETRY. A triangle has angle measures of 75, and. Set up an equation and solve for.

6 . The measures of the three angles of a 4. The two acute angles of a right triangle are 9, 9, and. Find triangle are 14 and What the measure of each angle. Is the measure of each angle? V. QUADRATICS/RADICALS You should be able to simplify radicals (no decimals) and give EXACT value solutions to quadratic equations. 5. Simplify the following. Give EXACT values (no decimals) a. 5 b. 50 c. 48 d. e Solve. Find all real solutions. Give EXACT answers. (Eact means to use radical or fraction form, if necessary.) a. 18 = 0 b. + 5= 0 c. = 8 d. + 10= 7 e = 0 f = g = 0 h =

7 7. Simplify the following. Write in standard form, where applicable (i.e., order of descending eponents). a. ( p+ 5)( p ) b. ( + )( 4 1) c. ( m + ) d. ( y)( y) + + e. ( )( 5) + + f. ( a+ b+ c)( a+ b c) g. ( ) + 4

8 ANSWERS TO SUMMER PACKET QUESTIONS. (Remember, you will get ZERO credit if your work is not shown throughout the packet.) = 7 5. A No Solution B = 0 C = D. 1 a. 18. All Real Numbers E. 8 b. yy = = 4 6. A. = ± c. + yy = {(, 1)} B. = 0, 5 C. = 0, ± 5. a. mm = 1 5, (0, 7) 1. A., 7 D. = 5 ± 4 4 b. m=-, (0, 4) E. No Solution c. m=, (0, -4) B. {(1, )} F. = 1, 1 5 d. undefined, none C. All points on + y = -4 G. = 5, 8 e. m= 0, (0, -7) D. No Solution H. =, 5 E. 7, 8 7. A. pp + pp F. 9, 1 9 B = 7 C. mm + 4mm = 7. 8, 4, 5 D yy 9. = , 61 E = 5 F. aa + bb cc + 5aaaa + bbbb + aaaa 11. = 11 G = = 18 7