Hiram High School. Honors Geometry. Summer Packet

Transcription

1 Hiram High School Honors Geometry Summer Packet (This packet is for students entering Honors Geometry) All of this information will be used at some point in the upcoming year. These topics should have been covered in previous years (not necessarily last year). You are responsible for all of this material and will be tested on it. You are expected to bring this completed packet with you to class on the first day of school. Your work must be done neatly and in order on notebook paper. Be sure to number each problem and show the steps taken to solve each problem. You must put your answers on the provided answer sheets. You should staple your notebook paper to the answer sheets but do not turn in the problem packet. Remember: this is the first grade you will receive for Accelerated Algebra/Geometry. Again, do your work on a separate page, record answers on the answer sheet. Attach all work to the answer sheet but do not turn in the question packet. DO NOT DO WORK ON QUESTION PACKET!! YOU MUST SHOW WORK OR WRITE AN EXPLANATION FOR EVERY PROBLEM!!!! Problems without work or an explanation will receive no credit regardless of answer. Answers not recorded on the answer sheet will not receive credit. If you have questions during the summer, please one of the following teachers. will be checked periodically, and questions will be addressed. Beth Turner Teacher Susie Poe Teacher Tracy Brown Department Chair baturner@paulding.k12.ga.us spoe@paulding.k12.ga.us tbrown@paulding.k12.ga.us Name: Name of Middle School:

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4 Name: Honors Geometry Summer Packet Directions: All work must be shown to receive credit. Do all work on a separate sheet of paper. Work must be neat and readable. If you have questions, try to find the answers using internet resources like Khan Academy. 1. Evaluate the expression when 2. Is the following a function? {(0, 1), (1, 0), (3, 5), (2, 1)} a. yes b. no c. not enough information d. Yes and it is a one to one function. 3. Make an input-output table (t-table) to represent the function. Use 1, 2, 3, 4, and 5 as the domain. 4. The table shows the study times and test scores for a number of students. Draw a scatter plot of the data. Put study time on the horizontal axis and test score on the vertical axis. Study Time (min) Test Score Solve the equations. 5. 3x x + 21 = 2 a. 22 b. 3 c. 22 d x 9 = x + 9 a b c d. 1 8

5 8. Michelle wants to earn $900 selling 22 knit scarves. She wants to sell each scarf for $4 less than her competitor. If x is the price charged by her competitor, which equation models the situation? 9. The perimeter of a rectangular garden is 690 ft. The two long sides of the garden are each 270 ft long. You are asked to find the length of the other sides. Which equation models this situation? 10. The car rental company Jody uses charges $24.95 for a single-day rental, plus $0.45 for each mile in excess of 75 miles. If Jody paid $39.80 for a 1-day rental, how many miles did she drive the rental car that day? 11. Solve the equation. Round the solution to two decimal places. 12. One hiking club charges $20 to become a member and $5 to participate on each hike. Another club charges no membership fee, but charges $7 to participate on each hike. How many hikes must you go on to make the first club more economical? 13. Solve for. 14. The coefficient of friction is a ratio that compares the friction acting on a dragged object to its weight, w. The relationships between the mass m and the acceleration a of an object that is being dragged across a flat surface, such as a table top, by a force F, is given by the equation. What formula can you use to find the coefficient of friction?

6 15. When x pounds of force is applied to one end of a lever that is L feet long, the resulting force y on the other end is determined by the distance between the fulcrum (the lever's pivot) and the end of the lever on which the x pounds of force is exerted. The formula relating the forces is What formula can you use to find the length of the lever? 16. A group is going on a boat tour. The cost, in dollars, of the tour for groups larger than 25 is given by the equation where n is the number of people in the group. If the cost of the tour is $600, how many are in the group? Graph the equation. 17. a. 10 y c. 10 y x x b. y d. y x x 10 10

7 18. Which point, or, is on the graph of? 19. Which point, or, is on the graph of? 20. Sketch the graphs of x = 2 and y = 4. Find the point at which the two graphs intersect. 21. Find the slope of the line that contains and. a. 2 5 b. 5 2 c. 0 d. undefined 22. Which graph below would match the situation described? A car travelling at 23 mi/h accelerates to 45 mi/h in 5 seconds. It maintains that speed for the next 5 seconds, and then slows to a stop during the next 5 seconds. 23. During the first 30 minutes of flight, a jet climbs from ground level to an altitude of about 43,000 ft. What is the jet's rate of change in altitude during this time? Round your answer to the nearest hundred.

8 24. The Abdul family is comparing the costs of two different high-speed Internet services. With plan A, equipment installation is $199, and the monthly fee is $50. With plan B, the installation is $50, with a $90 monthly fee. The cost of plan A is given by f(x) = 50x and the cost of plan B is given by g(x) = 90x + 50, where x is the number of months of service. a. Make two tables that you could use to graph the functions. Let x = 0, 1, 2, 3, 4, 5, and 6. b. Graph both functions. c. The Abduls plan on using the Internet service for one year. Based on cost, which plan would you recommend? Explain. 25. Which picture shows a reflection of the flag? 26. A point P has coordinates (6, 4). What are its new coordinates after point P is reflected over the y-axis? a. (6, 4) b. ( 6, 4) c. (6, 4) d. ( 6, 4) 27. Place a square on a coordinate graph and label each vertex with variables. Prove that the diagonals of a square are congruent and perpendicular to each other. 28. An oceanographic research ship's submersible vehicle is at a depth of 1583 meters when it begins a steady ascent. If it rises at a rate of 68 meters per minute, how many minutes will it take the submersible to reach a depth of 631 meters? 29. Write an equation of the line containing the points and. 30. What is the missing number in the sequence? 1 5, 2, 34 5,, 72 5,...

9 31. Find the equation of the line that passes through point A and is perpendicular to the line shown in the graph below. 10 y A x Which of the following lines is NOT parallel to the line shown in the graph? 10 y x 10

10 33. The weights of ten Holstein calves of different ages are given in the table. Sketch a scatter plot of the data. Then describe any pattern that you see in the scatter plot. Age (months) Weight (pounds) 34. Solve the inequality Find the length of the leg of this right triangle. Give an approximation to 3 decimal places. a c b d A scuba diver has a taut rope connecting the dive boat to an anchor on the ocean floor. The rope is 110 feet long. The water is 55 feet deep. To the nearest tenth of a foot, how far is the anchor from a point directly below the boat? a ft c ft b ft d ft 37. A power pole broke and fell as shown. To the nearest tenth of a meter, what was the original height of the pole?

11 38. Writing: A mistake has been made in the solution. Explain the error and how to correct it. Solve by elimination: 39. a. (5, 1) b. (0, 3 2 ) c. (10, 1 6) d. no solution 40. Which choice best describes the solution(s) of the system of equations? a. many solutions c. (1, 48) is the only solution. b. ( 1, 0) is the only solution. d. no solution Simplify: 41. a. b. c. d. Simplify. Write your answer using exponents. 42.

12 Which of the following is equal to 1 when multiplied by? a. b. c. d. 45. Write an exponential function to model the situation. Tell what each variable represents. A price of $130 increases 5% each year. 46. The coordinates of quadrilateral PQRS are P( 3, 0), Q(0, 4), R(4, 1), and S(1, 3). What best describes the quadrilateral? a. a rectangle b. a square c. a rhombus d. a parallelogram 47. Which statement is false? a. All rhombuses are kites. b. All squares are rhombuses. c. Every kite is a rectangle. d. All squares are quadrilaterals. 48. Which statement is false? a. Every square is a parallelogram. b. Some rhombuses are rectangles. c. Every rhombus is a quadrilateral. d. Every parallelogram is a rhombus. 49. Which statement is false? a. If a quadrilateral is a square, then it is not a kite. b. Some parallelograms are rhombuses. c. All parallelograms are quadrilaterals. d. If a quadrilateral is a rectangle, then it is a kite , 4, 2, 8, Write a rule for the nth term of the arithmetic sequence with and the common difference of. 52. Find the sum of the first 10 terms of the arithmetic series.... a. 350 b. 170 c. 175 d Find the sum of the first 22 terms of the arithmetic sequence, if the first term is 2 and the common difference is 5. a b. 545 c d. 2398

13 54. Find the common difference of the arithmetic sequence. 0, 0.4, 0.8, 1.2,... a. 0.3 b. 0.3 c. 0.4 d Tell whether the sequence is arithmetic. If it is find the common difference. a. b. 56. Identify the sequence as arithmetic, geometric, or neither. 1, 1, 2, 3, 5, 8, 13,... Write a rule for the nth term of the geometric sequence Give the first four terms of the geometric sequence for which and. a. 28, 112, 448, 1792 c. 7, 11, 15, 19 b., 16, 7, 7 d. 7, 28, 112, So far in geography class, a student's quiz scores are 86%, 84%, 76%, and 72%. What score does the student need on the fifth quiz to have a mean quiz score of 81%? All the quizzes have equal weights. a. 82% b. 88% c. 79.5% d. 87% 60. The scores for the 33 participants in a fund-raising golf tournament are represented in the graph below. In which interval is the median score found? a b c d

14 61. The graph below shows the heights and shoe sizes of the members of the Grant High School varsity basketball team. The heights shown in the graph are rounded to the nearest half inch. Approximate the mean height, in inches, of the basketball team members. Round to the to the nearest inch. 62. The pulse rates of students before physical education class are recorded in the table. What is the mode for the pulse rates? Use the diagram below for questions Name 2 parallel planes. 64. Name a pair of parallel lines. 65. Name a pair of perpendicular lines. 66. Name a pair of skew lines.

15 Use the diagram below for questions List all pairs of angles that fit the description. 67. Corresponding angles 68. Alternate Exterior angles 69. Alternate Interior angles 70. Same Side Interior angles Find the values of x and y using angle pair relationships. Assume lines that appear parallel are parallel. 71. x = y = 72. x = y =