# Name: Honors Geometry Summer Assignment 2016

## Comments

## Transcription

Name: Honors Geometry Summer Assignment 2016

Name:_________________________________ Honors Geometry Summer Assignment 2016 Find the volume of the solid. Round to the nearest tenth if necessary. ____ 4. 6 in. Multiple Choice ____ 1. Write using an exponent. a. b. c. d. 4 in. Use a net to find the surface area of the figure. 2 in. Drawing not to scale ____ 2. a. 24 in.3 10 m b. 96 in.3 c. 48 in.3 d. 16 in.3 ____ 5. A large aquarium is 8 m by 6 m by 5 m. What is the difference in the volume of the aquarium if its dimensions are doubled? a. 240 m3 b. 1680 m3 c. 360 m3 d. 480 m3 ____ 6. Marcus has 68 feet of fencing. He wants to build a rectangular pen with the largest possible area. What should the dimensions of the rectangle be? a. 19 ft by 21 ft c. 17 ft by 17 ft b. 21 ft by 13 ft d. 19 ft by 15 ft ____ 7. There are 60 pages in your journal. If you number all of the pages, starting with 1, how many digits will you have to write? a. 62 b. 120 c. 111 d. 60 8 m 14 m drawing not to scale a. 332 m2 b. 504 m2 c. 440 m2 d. 664 m2 not drawn to scale Find the missing length(s) of the triangle. Round to the nearest tenth. Find the area of the figure. ____ ____ 8. 13 in. 3. 45° 7 in. 11 in. 13 in. h 45° 9 in. Drawing not to scale Drawing not to scale a. 31.5 in.2 b. 173.3 in.2 c. 27 in.2 d. 63 in.2 a. h = 6.5 in. b. h = 22.5 in. c. h = 26.0 in. d. h = 18.4 in. Solve the equation. ____ ____ 13. A 16-oz bottle of water costs $1.44. What is the cost per ounce? a. $0.09/oz b. $0.18/oz c. $0.90/oz d. $1.78/oz ____ 14. A car is driving at a speed of 60 mi/h. What is the speed of the car in feet per minute? 9. a. –31 b. 85 2 5 c. –50 d. –35 a. 5,280 ft/min b. 3,600 ft/min c. 316,800 ft/min d. 2,580 ft/min ____ 10. a. –8 b. 2 c. –10 d. –4 ____ ____ 11. Which properties of equality justify steps c and f? ____ 15. The length of a rectangle is 5 centimeters less than twice its width. The perimeter of the rectangle is 26 cm. What are the dimensions of the rectangle? a. length = 5 cm; width c. length = 6 cm; width = 5 cm = 7 cm b. length = 7 cm; width d. length = 4 cm; width = 6 cm = 9 cm 16. Peter is reading a 193-page book. He has read three pages more than one fourth of the number of pages he hasn’t yet read. a. How many pages has he not yet read? b. Estimate how many days it will take Peter to finish the book if he reads about 8 pages per day. a. Subtraction Property of Equality; Multiplication Property of Equality b. Addition Property of Equality; Division Property of a. 144; about 18 days b. 147; about 18 days c. 152; about 19 days d. 141; about 18 days Equality c. Addition Property of Equality; Subtraction Property of Equality d. Multiplication Property of Equality; Division ____ Property of Equality ____ 12. The perimeter of the rectangle is 24 cm. Find the ____ value of x. 3 cm 17. Evaluate a. –11 b. 1 18. Evaluate a. –9 b. –4 c. –6 c. –8 for x = 3. d. 11 for x = –3. d. 4 Use inductive reasoning to describe the pattern. Then find the next two numbers in the pattern. 3x cm ____ a. 3 b. 12 c. 8 3 d. 18 19. –9, –4, 1, 6, . . . a. add 5 to the previous term; 11, 16 b. multiply the previous term by 5; 30, 150 c. subtract 5 from the previous term; 1, –4 d. multiply the previous term by 5; 11, 150 ____ 20. –5, –10, –20, –40, . . . a. multiply the previous term by 2; –80, –160 ____ b. add –5 to the previous term; –35, –30 c. subtract 5 from the previous term; –80, –160 d. multiply the previous term by –2; 80, –160 State whether the slope is 0 or undefined. 24. y 5 4 3 2 Find the slope of the line. 1 –5 –4 –3 –2 y ____ 21. –1 –1 1 2 3 4 x 5 –2 5 –3 4 –4 –5 3 2 1 –5 –4 –3 –2 –1 –1 1 2 3 4 5 x ____ –2 a. undefined 25. b. 0 y 5 –3 4 –4 3 –5 a. 1 4 b. 1 4 2 c. 4 1 d. 4 –5 –4 –3 –2 –1 –1 1 2 3 4 5 x –2 –3 Find the slope of the line that passes through the pair of points. ____ 22. (1, 7), (10, 1) a. 3 b. 2 2 3 c. 3 2 d. 2 3 –4 –5 a. 0 b. undefined Write an equation of a line with the given slope and y-intercept. ____ ____ 23. A student finds the slope of the line between (14, 1) and (18, 17). She writes . What ____ mistake did she make? a. She should have added the values, not subtracted them. b. She used y-values where she should have used x-values. c. She mixed up the x- and y-values. d. She did not keep the order of the points the ____ same in numerator and the denominator. 26. m = 1, b = 4 a. y = 4x + 1 b. y = x – 4 1 3 27. m= ,b= 4 4 a. 3 y = 4x – 4 b. 1 3 y= x– 4 4 c. y = –1x + 4 d. y = x + 4 c. 3 1 y= x+ 4 4 d. 1 3 y= x+ 4 4 Find the x- and y-intercept of the line. 28. (Short Answer) 2x + 3y = –18 29. (Short Answer) A line passes through (1, –5) and (–3, 7). a. Write an equation for the line in pointslope form. ____ Are the graphs of the lines in the pair parallel? Explain. 33. a. b. b. Rewrite the equation in slope-intercept form. c. d. y = 5x + 6 –18x + 3y = –54 No, since the slopes are different. Yes, since the slopes are the same and the yintercepts are different. No, since the y-intercepts are different. Yes, since the slope are the same and the yintercepts are the same. Tell whether the lines for each pair of equations are parallel, perpendicular, or neither. ____ 30. 7x – 4y = 4 x – 4y = 3 Simplify the radical expression. a. perpendicular 1 ____ 31. y = x – 11 2 16x – 8y = –8 b. parallel c. neither ____ 34. a. 12 b. 12 2 c. 6 d. Simplify the expression. ____ 35. a. a. neither b. perpendicular c. parallel ____ ____ 32. Find a solution to the following system of equations. b. c. d. 36. Find the GCF of the terms of the polynomial. 8x6 + 32x3 a. x3 a. (–8, –15) b. (–2, –15) c. (0, 1) b. 8x3 c. 8x3 d. 8x6 d. (2, 5) y Short Answer 6 37. The vertices of a triangle are A(–0.5, 2), B(1, –2), and C(–2, –2). Graph the triangle and its image after a translation of 1 units right, 1 units up. 4 2 38. Graph the point M(2, 3) and its image after a reflection over y = 4. y 2 –2 2 –2 –4 –2 2 –2 –6 4 –4 –4 –4 6 –6 –6 4 6 x 4 6 x 41. Justify each step. Write a reason why you get from one step to the next one. 39. Graph the point R(–4, –5). Then rotate it 180° degrees counterclockwise about the origin and graph the new point. y 6 4 2 –6 –4 –2 2 4 6 x –2 4 42. –4 writes the odd equation: The42. sumAofclass 3 consecutive integers is 87. Find n + n + 1 + n + 2 = 87 the three integers. to solve the following problem. –6 The sum of 3 consecutive odd integers is 87. Find the three integers. 40. The vertices of a triangle are E(1, 0), F(5, –1), and G(4, –4). Graph the triangle and its image after a rotation of 90° about the origin. y 43. L(4, –2), M(3, –5), N(0, –3); Reflect over the line What y =error 1 did they make? 8 6 y Name the property that the statement(s) illustrates. 6 4 4 43. If –b = 14, then 14 = –b. 2 –6 –4 –2 Name the property that 2 the statement(s) illustrates. 2 –2 –4 –6 4 6 x –8 44. 45. –6 –4 If –2 2 and–2 –4 –6 –8 4 then d = 4. 6 8 x 44. The sum of four consecutive odd integers is . Write an equation to model this situation, and find the values of the four integers. y = 2x – 3 y = –x + 3 47. y 5 4 3 2 1 –5 –4 –3 –2 Graph each system. Tell whether the system has no solution, one solution, or infinitely many solutions. –1 –1 1 2 3 4 x 5 –2 –3 –4 y = 5x – 4 y = 5x – 5 45. –5 y 5 Are the graphs of the lines in the pair parallel? Explain. 4 3 1 x+8 6 –2x + 12y = –11 2 48. y = 1 –5 –4 –3 –2 –1 –1 1 2 3 4 5 x –2 –3 49. Solve the following system of equations by graphing. –4x + 3y = –12 –2x + 3y = –18 –4 –5 46. y=x+4 y–4=x y 5 y 4 5 3 4 2 3 1 2 1 –5 –4 –3 –2 –1 –1 –2 –3 –4 –5 –6 1 2 3 4 5 x –5 –4 –3 –2 –1 –1 –2 –3 –4 –5 1 2 3 4 5 6 x 57. Niki has 8 coins worth $1.40. Some of the coins are nickels and some are quarters. a. Let q = the number of quarters and n = the number of nickels. Write an equation relating the number of quarters and nickels to the total number of coins. Graph the function. 50. y 5 4 3 2 1 –5 –4 –3 –2 –1 –1 1 2 3 4 5 b. Write an equation relating the value of the quarters and the value of the nickels to the total value of the coins. c. How many of each coin does Niki have? x –2 –3 –4 –5 Factor the expression. 51. 6x2 + 5x + 1 52. 12d2 + 4d – 1 53. d2 + 10d + 9 54. w2 + 18w + 77 58. The standard method for solving an equation like is to use the Subtraction Property of Equality and then the Division Property of Equality. It is possible to solve the equation using the properties in the reverse order. Explain why the standard method is better. Simplify the product using FOIL. 55. (3x – 7)(3x – 5) 56. Ronald is setting up an aquarium in his new office. At one pet store, fish cost $2 each and an aquarium cost $40. At another pet store, fish cost $3 each and an aquarium cost $36. Write and solve a system of equations to represent the cost of x fish and an aquarium at each store. Solve this the system. What does this solution represent? If Ronald wants 5 fish, from which pet store should he buy his aquarium? Explain. 59. Explain the error in the student’s work. 60. Without solving, what method would you choose to solve the system: graphing, substitution, or elimination? Explain your reasoning.