Mathematics 1 Final Review

Transcription

1 Mathematics 1 Final Review 1. Graph y x 2. You have $47 to spend at the music store. Each cassette tape costs $5 and each CD costs $10. Write and graph a linear inequality that represents this situation. Let x represent the number of tapes and y the number of CDs. 3. Your club is baking vanilla and chocolate cakes for a bake sale. They need at most 25 cakes. You cannot have more than 10 chocolate cakes. Write a system of inequalities to model this system. 4. A rental car agency charges a flat fee of $32.00 plus $3.00 per day to rent a certain car. Another agency charges a fee of $30.50 plus $3.25 per day to rent the same car. Brian has c dollars to spend on a rental car. Write a system of inequalities to represent the cost c for renting a car at each agency for d days 5. Which is a solution to the inequality a) (3, 0) b) (0, 3) c) (-3, 0) d) (0, -3) 6. Which is a solution to the inequality? a) (3, 0) b) (0, 3) c) (-3, 0) d) (0, -3)

2 7. Graph 8. Graph y y x x 9. 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. The system of linear inequalities represent the situation. He has no more than y dollars to spend. What does the solution (5, 60) represent? 10. When graphing a linear inequality, how do you know if the line should be dashed or solid? Use the following data for # , 10, 16, 22, 23, 24, 27, Make a dot plot. 12. Make a box-and-whisker plot. 13. Make a stem-and-leaf plot. 14. Describe the data distribution? 15. What is the mean? 16. What is the standard deviation? What does it tell you about the data? 17. What does the median? 18. What is the interquartile range? 19. What are the upper and lower fences? 20. What percentage of information can be found between Q1 and Q3?

3 21. Use the histogram to answer the following questions. a) How many days had a temperature lower than 84 degrees? b) How many days were surveyed? c) How many days had a temperature between 86 and 88 degrees? 22. What type of information should be displayed on a two-way frequency table? 23. The manager of a small restaurant wants to offer soup and sandwich combination meals for lunch specials. To decide what to include in each special, she records the types of soup and sandwiches customers order for several days. The table shows the results. What was the most popular soup and sandwich combo? 24. Brian surveyed his class about their favorite type of movie. The results are in the table. Which gender and genre have the majority of the vote?

4 25. Trisha decides to survey her family to help her decide where she should have her graduation party. She organizes the data in the table below. a) Which location was the overall favorite? b) What was the adults least favorite location? 26. A television station collects data about which topics are most popular on its website from visitors in different regions of the city. The graph represents the data. Write true or false next to each statement. a) The most popular topic for all areas is traffic. b) The least popular topic for all areas is news. c) People in the northeast of the city are most interested in sports. e) People in the southwest of the city are most interested in weather. 27. Sam surveyed his class about their favorite color. The overall favorite color of the class will be used for the color of the class t-shirt. The results are shown below. a) Which color is the boys favorite? b) Which color will be used for the class t-shirt? g) How many more people blue over green?

5 28. Find the distance between points P(8, 2) and Q(3, 8) to the nearest tenth. 29. What is the definition of a segment bisector? 30. Sam bisects PMR. She labels a point on the bisector N. The measure of PMR is 136Find the measures of PMN and NMR. Hint: Draw a sketch that shows the given information. 31. Tell whether the lines for each pair of equations are parallel, perpendicular, or neither. Explain your reasoning. a) y = 1 6 x + 8 b) y = 1 2x 11 2x + 12y = 11 16x 8y = Label each figure created by the following constructions 33. An initial population of 895 quail increases at an annual rate of 7%. Write a function to model the quail population. 34. Solve 35. In January, you start saving money. You have the following amount of money saved. $45 in January $90 in February $135 in March $180 in April Write an equation for this situation. 36. What is? 37. What is?

6 ( 38. In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by ASA? a. c. b. d. 39. What else must you know to prove the triangles congruent by the AAS Theorem? 40. What else must you know to prove the triangles congruent by SAS? A B ( D C 41. Are and are congruent? State the congruence theorem and the congruent statements. 7 7

7 42. a. Graph the quadrilateral WXYZ with vertices W(3, 5), X(1, 3), Y( 1, 5), and Z(1, 7). b. Rotate the figure 90 counterclockwise around the origin and graph the rotation. y x 43. Write a rule to describe the transformation that is a reflection in the x-axis. 44. The vertices of a triangle are P( 3, 8), Q( 6, 4), and R(1, 1). Name the vertices of the image reflected in the x- axis. 45. Write a rule to describe the transformation that is a reflection in the y-axis. 46. The vertices of a triangle are P( 2, 4), Q(2, 5), and R( 1, 8). Name the vertices of the image reflected in the y- axis. 47. Which congruence statement is true about the below figures? a) b) c) d)

8 48. The vertices of a triangle are A( 0.5, 2), B(1, 2), and C( 2, 2). What are the coordinates of each vertex if the triangle is translated 2 units right and 3 units down? 49. What are the coordinates of each vertex if the figure is rotated clockwise about the origin? 10 y 5 C x A B Find the area and perimeter of each figure. a) Rectangle DEFG b) Triangle DEF

9 c) Parallelogram WXYZ d) Figure EFGH e) Trapezoid BEST f) Composite Figure 51. If a figure is translated, does the perimeter change? Does the area change? 52. Kendra owns a restaurant. She charges $1.50 for 2 eggs and one piece of toast, and $.90 for one egg and one piece of toast. Let x represent the number of eggs and y the number of pieces of toast. a) Write and solve a system of equations to determine how much she charges for each egg and each piece of toast. b) How much would it cost for a breakfast of 3 eggs and 2 pieces of toast. 53. An ice skating arena charges an admission fee for each child plus a rental fee for each pair of ice skates. John paid the admission fees for his six nephews and rented five pairs of ice skates. He was charged $ Juanita paid the admission fees for her seven grandchildren and rented five pairs of ice skates. She was charged $ What is the admission fee? What is the rental fee for a pair of skates?

10 54. Square TUVW on the coordinate plane has points T(0, 0), U(5, 5), and W(-5, 5). What are the coordinates of point V? 55. Triangle MNP is an isosceles triangle. Which could be the location of point P? 56. Circle K is reflected over the x-axis. What is the diameter of circle? 57. Quadrilateral DEFT has vertices D, E, F, and T. What is the best name for quadrilateral DEFT? 58. Circle T has its center at and passes through the point. What is the radius of circle T? 59. Triangle BAT has points B, A, and T Which of the following best describes triangle BAT?

11 60. Rob wants to place point X on the coordinate plane so that quadrilateral UVWX is a trapezoid. He draws a horizontal line through point U. Which could be the coordinates of point X? 61. Classify the triangle by sides and angles. 62. What is this figure called? Why?

12 63. Circle P intersects the y-axis at point W intersects the y-axis?. What are the coordinates of the other point where circle P 64. Consider the following statements. What is a valid conclusion? Statement: If Jenna does not have any homework this weekend, she is going to Dsineyland with her friends. Statement: Jenna is not going to go Disneyland with her friends. a. Jenna is going to Disneyland with her friends. b. Jenna has homework this weekend. c. Jenna is not going to do her homework this weekend. d. Jenna does not have homework this weekend. 65. What is the converse of the conditional statement If a quadrilateral has four congruent sides, then it is a rhombus? 66. Give an example of the Associative Property of Addition. Jairo, Tan, and Elizabeth went out for dinner. Each person ordered a different entree: baked chicken, Greek salad, or a hamburger. After dinner, each person ordered a different dessert. The person who ordered the hamburger ordered ice cream. Jairo ordered chocolate cake, while another person ordered apple pie. Neither Jairo nor Elizabeth ordered baked chicken. Elizabeth did not order the Greek salad, but she did order ice cream. 67. Which person ordered the Greek salad? a. Jairo b. Tan c. Elizabeth d. There is not enough information to answer the question. 68. What property is illustrated by the following statement?