Mathematics Department Summer Course Work. Geometry Honors

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1 Bergenfield High School Bergenfield, New Jersey Mathematics Department Summer Course Work in preparation for Geometry Honors Completion of this summer work is required on the first day of the school year. Student Name:

2 Bergenfield Public Schools Mathematics Department 80 South Prospect Avenue Bergenfield, New Jersey (01) June 018 Dear Parents and Guardians: Attached are the summer curriculum review materials for Geometry Honors. This booklet was prepared by the Bergenfield High School Math department and contains topics that reflect content learned in prerequisite courses. These materials must be completed and brought to class on the first day of school in September. Your child is required to complete this booklet over the summer. A test based on the material in the packet will be given to your child during the second week of school. It will count as the first test of the year and the grade will be determined as follows: Completion of the packet on time will count 0% of the grade Performance on the test will count 80% of the grade. Students will not be permitted to use calculators on this exam, therefore this packet should be completed without the use of a calculator. Thank you for your cooperation. Sincerely, Jim Fasano Carmen Archetto Principal Director of Mathematics K - 1

3 Bergenfield High School Mathematics Department Summer Course Work Geometry Honors TABLE OF CONTENTS 1. Solving Equation. Solving Inequalities 3. Word Problems 4. Proportions 5. Grids 6. Graphing All pages MUST show the work in order for the work to be accepted. If more paper is needed, the work may go on the back of each page or neatly on a separate page. This booklet must be kept neat and in order and is to remain in your notebook as a reference guide. Completion of this booklet is required by the first day of the school year. 3

4 Equations # 1-10 Solve each of the following equations. Show all work. 1) 4x x 11 6) x 6 18 ) 6x 14 x 10 7) x ) (w 5) (3w 7) 18 8) x 4) x x 30 x ) x 9 5 5) (3x 15) (x 5) 90 10) a

5 Inequalities # Solve each of the following inequalities. Show all work. 11) 6x 4x 6 1) x x 3 3x 13) 5( x 3) x 6 Word Problems 14) If x 1, which of the following expressions has the greatest value? a) x b) 1 c) x x d) 1 x e) x 3 15) If the perimeter of the triangle shown to the right is 30, find the length of each side. x 3 x 4x 1 16) The ratio of girls to boys in a certain geometry class is 1 to. If there are 16 boys in this class, how many girls are in this class? 5

6 17) The championship game will be held next Saturday and they expect 100 fans to attend. If the ratio of adult fans to children is 73:7, how many children will be attending the game? 18) Two angles add up to 90. If their measures are in a ratio of :7, find the smaller angle. Proportions: For # 19, solve each of the following proportions. Show all work. 19) x ) 8 x 1 1 1) x 1 x 1 10 ) x 9 4 x 6

7 Coordinate Graphing 3) On a piece of graph paper, start at the origin. Move 3 units to the left and then 5 units down. What point is this? 4) On the grid to the right, plot the following points. A( 1, 4) B( 5,1) C ( 1, 1) Now connect these three points to form ABC. On the same axes, plot these points: D(5,1) E(1, 4) F (1,1) Connect them to form DEF. What do you notice about ABC and DEF? 5) Graph y x 5 6) Find the slope and y-intercept of y 3x. 7) Find the slope and y-intercept of 6x 3 y 9. 7

8 Graphing 8) Which of the following could be the graph of y x 1? a) b) c) d) 9) Sketch a line that has a slope of 0. 30) Write an equation of a line whose slope is 4 and contains the point ( 1, ). 31) Write an equation of a line that contains the points (1, 6) and ( 3, 10). For questions 3-34 Without graphing, identify each of the following pairs of lines as either parallel, perpendicular, or neither. 3) 33) y 3x 6 y 3x 1 y 4x 4 y 4x 3 34) 6x 3 y 1 x 4 y 8 8

9 35) Using the following definitions, find 9 x x x 36) As a decimal rounded to the tenths place, 30 =. 37) 83 is between what two integers? and 38) Simplify 48. Leave your answer in radical form. 39) If b 10 and h 5, find A using this formula: A 1 bh. 40) If r 8, find A using this formula: A r. 41) If a 6 and P 8, find b using this formula: P a b. 4) Find x. x 1 (70 30). 43) Find x. x 1 (100 40). 44) Find x ( x 60). 45) Find x (00 x). 9

10 46) Using the map shown to the right, how many different routes can John take to travel from Albany to Brownsville? He may not visit any city more than once and he must stay on the roads shown on this map. a) 1 b) 9 c) 6 d) 4 Sinclair Albany Oakwood Brownsville 47) Which of the following equations describes the relationship shown in this table? a) y 4 3x b) y 3x c) y x 3 d) y x 1 x y ) How many of the following figures can be folded to create a cube? a) 1 b) c) 3 d) 4 49) The large block shown to the right is made up of 64 unit cubes. Suppose that the outside of the large block is painted red. How many of the 64 unit cubes will have paint on only 1 side? 10

11 50) Which of the following represents the perimeter of the rectangle shown to the right? I. x y x y II. x y III. xy IV. 4xy x y a) I only b) III only c) I and II only d) II and IV only 51) Solve the following equation: x 5x 1 5) Solve the following system of equations. Use any method you choose. 3x 17 y 4x y 4 53) Use the distance formula d ( x x 1) ( y y 1 ) to find the distance between A and B if A( 3, 4) and B( 1, 5). 54) Simplify the following. Leave answers in simplified radical form. a) 50 b) 40 c) 7 11

12 55) Simplify the following. Be sure to rationalize the denominator (if necessary). Leave answers in simplified radical form. a) 50 b) 0 4 c) ) Perform the indicated operation. Simplify all answers (to simplified radical form). a) 5 15 b) 6 3 c) 7 3 d) 7 9 1

Algebra II Honors Summer Packet Summer 2017

Algebra II Honors Summer Packet Summer 2017 Name: The following packet contains content that you should have learned in previous Mathematics courses. You will be expected to demonstrate proficiency with