HONORS GEOMETRY SUMMER REVIEW PACKET (01) The problems in this packet are designed to help you review topics from previous mathematics courses that are important to your success in Honors Geometry. Please do each problem and show the work needed to arrive at your answer. Answers are provided on the final two pages of the packet. Bring the packet with you to your Honors Geometry class on the first day of school. Additional copies of this summer packet can be printed from the Phoenix Union High School District website (in pdf) at: http://www.phoenixunion.org/mathsummerpacket All work should be completed and ready to turn in on the first day of school. This packet will count as part of your first quarter Geometry or Honors Geometry grade. Enjoy your summer. We are looking forward to seeing you in the fall.
GEOMETRY H Summer Packet SHOW ALL WORK. Identify final answers clearly. NAME Class period PART 1: Linear Equations and Inequalities 1 10: Solve the equation 1. ( x 5) 14 6. x1 4x 5 15. 4.x 6.4 40 7. 8 x 10. x x 4 7 8. y y 4. 5 1 x 9. x x x 15 180 5. x 18 1 x 10. 104 60 x Page 1
11 1: Solve the inequalities 11. 8( x ) 96 15 16: Plot and label the points. Draw the line that passes between them. Calculate the slope using the slope formula. The slope of the line between A( x1, y 1) and y y1 B( x, y ) is: m x x 1 1. x 15. A( 0,) and B(6,1) 8 6 4 1. 10x -10-5 5 10 - -4-6 -8 PART : Graphing Linear Equations 14. Sketch a line with the appropriate slope. 16. A(, ) and B( 1, 6) ; draw AB. C( 4, ) D( 5, 4) ; draw CD Calculate the slopes and explain if the lines are parallel or not. 8 6 4 Positive Negative -10-5 5 10 - -4-6 -8 Zero Undefined Page
17 19: Rewrite each equation in slopeintercept form, y = mx + b. Identify the slope, m, and the y-intercept, b. Then graph. 19. x6y 1 17. xy 6 18. 4xy 8 0. Graph both equations. Identify the point of intersection 4x y 14 4x y 9 Page
1 : Find the x and y intercepts of the equation. Plot the intercepts and graph the line. Remember: to find the x intercept, let y = 0 to find the y intercept, let x = 0 1. 6xy 1 9: Write the equation of the line in slopeintercept form using the given information Follow these steps: 1: identify the slope (if necessary- use the slope formula) : identify the y intercept (if necessary- substitute the slope and the coordinates of one of the points into y = mx + b. solve for b) : use the results of the first two steps to write the equation. slope = ; y intercept is (0, 5) 4 4. slope = -; passes through (4, ). 5x10 y 50 5. slope = ; passes through (, 5) 6. passes through (, ) and (5, 9) Page 4
7. passes through ( 5, ) and (7, 9) PART : Linear Systems 0 5: Solve each system of equations using the method of your choice (substitution or combination) 0. x y 1 x y 8. Write the equation of the line in the graph 1. x y 5 x 14 9. Sketch the line that passes through the two points. Write the equation of the line.. 4 x y 1 y x 4 Page 5
. 4 x y 4 6xy 8 PART 4: Quadratic Equations, Polynomials, and Radicals 6 9: Simplify the expressions by using the distributive property 6. x 11 7. x 4 4. 1 5 x y 5x y 1 8. 5xx 4y 9 9. x x x 7 5. xy6 6x9y9 40 41: Solve the equation by taking the square root of both sides (there are two solutions!) 40. x 50 41. 5 b 1 Page 6
4 45: Solve by factoring Example: x 5x 6 original equation x 5x 6 0 put in standard form x x 0 factor x 0 or x 0 zero product property x or x two solutions 46-47: Solve by using the quadratic formula: x b b 4ac a (Use a calculator to estimate answers to the nearest hundredth) 46. x x1 0 4. x 6x8 0 4. x 5x 6 x x 44. x 7x8 10 47. 5x x 0 45. x 4x 0 Page 7
48 51: Simplify the radical expression (Do not estimate with a calculator) Example: 4 4 6 6 48. PART 5: Geometry and Applications 54. Given triangle ABC: ma 65, m B n mc 4n. Find the measure of, each angle. (Remember, the sum of the three angles of a triangle equals 180 ) Equation: + + = 49. 75 50. 4 51. 5 6 ma 65 mb mc 55. The length of line segment AC is 4 units. Segment AB is x and segment BC is. What is the length of segment AB? What is the value of x? 4 units 5 5: Simplify by rationalizing the denominator Example: 15 15 5 15 5 5 5 5 5 5 A x units B units C 5. 15 56 59: Sketch the given figure and label its dimensions. Find the area and perimeter. 56. A rectangle with length.6 cm and width 4. cm 5. 40 Page 8
57. A square with a side length of 9 mm. 6. Find the area of the rectangle 58. Find the circumference and area of a circle with a radius of 4 in. (use.14 for pi and round answers to the nearest tenth of a unit) 59. Find the area of a triangle with base length of 10 cm and a height of 8 cm. 6. Answer in complete sentences where appropriate. Show all your work to receive full credit. Square Deal Pizza offers square pizza that is 15 inches long on each side. A cheese pizza costs $9.00. Roundoff Pizza offers circular pizza that is 16 inches in diameter. A cheese pizza at Roundoff costs $8.75. Which restaurant s pizza is bigger? Justify your answer using words, symbols, or both. Which restaurant s pizza is a better buy? Justify your answer using words, symbols, or both. 60 61: Use the Pythagorean theorem ( c a b ) to find the missing side length in the triangle. 60. ft 5 ft b 61. 8 in c 15 in Page 9
HONORS GEOMETRY SUMMER PACKET ANSWERS 18. 1. 1. 8. 1 4. 4 5. 1 6. 7. 1 8. 4 9. 10. 76 11. x 15 1. x 5 1. x 14. 19. 0. (, 1) Positive Negative 1. (, 0) and (0, 4). (, 0) and (0, 5). y x 5 4 4. y x 9 15. 1 Zero Undefined 16.. Yes they are parallel; both lines have 17. the same slope 5. y x 7 6. y x 1 7. 1 11 y x 8. y x 9. y x Page 10
0. (7, 5) 1. (7, 9). (1, ). (, ) 4. 1, 5. No solution (parallel lines) 59. A=40 cm 60. b=4 ft 61. c = 17 in 6. A=6 units 6. The Square Deal pizza is bigger and the better buy 6. 7. 8. x x 11 9x 4x 16 10 0 45 x xy x 9. 40. 5 41. 1 x 6x 1x 4., 4 4., 1 44. 1, 45. x = 1 46. 0.8,.6 47. 0.46, 0.86 48. 4 49. 10 50. 48 51. 45 5. 5 5. 0 54. ma 65, mb, mc 9 55. AB=1, x=7 56. P=15.6 cm A = 15.1cm 57. P=6m A = 81mm 58. C 5.1 in A 50. in Page 11