Algebra 1 2nd Semester Exam Review 2015

Transcription

1 Algebra 1 2nd Semester Exam Review Sketch the line given by. Label the x- and y-intercepts. 2. Find the slope of the line through the points (4, 7) and ( 6, 2). 3. Writing: Explain the difference between positive slope and negative slope. Include sketches of lines showing each type of slope. 4. Find the slope of the line that contains ( 5, 8) and ( 5, 5). 5. Rewrite the equation in slope-intercept form. 6. Find the slope and y-intercept of the line with the equation. 7. Write the equation in slope-intercept form. 8. Write the equation in slope-intercept form, and sketch the line. 9. Determine if the line is parallel to the line. 10. What is the value of the function when? 11. A sunflower in Julia Rosario's garden was 12 centimeters tall when it was first planted. Since then, it has grown approximately 0.6 centimeters per day. Write an equation expressing the sunflower's height, H, in terms of the number of days, d, since it was planted. 12. Write an equation of the line shown.

2 13. Write an equation of a line with slope 2 passing through the point (3, 2). 14. Write the equation in slope-intercept form of the line that passes through the points (7, 1) and (2, 9). 15. A grocer knows that if he sells his canned hams for $6 each, he can sell 550 per month, and if he sells the same hams for $9, he will sell 400 per month. Assuming the relationship between price and sales is linear, write an equation you could use to predict sales for other prices. 16. Write the equation of the horizontal line passing through the point (4, 7). 17. Write an equation of the line with undefined slope that passes through the point (2, 4). 18. Write an equation of the line that passes through ( 10, 6) and is parallel to the line Solve. Graph your solution x 10 4 a. 7 3 b. or c. d. or 20. Solve each inequality. 21.

3 22. Solve 23. Graph the solution of. 24. Solve. Graph your solution. 25. is equivalent to which of the following? A. B. or Graph. 26.

4 Sketch a graph of the inequality 29. Your goal is to make at least $500 selling jewelry at a crafts fair. You plan to sell earrings for $5 a pair and necklaces for $10 each. a. Let x be the number of pairs of earrings you sell and y be the number of necklaces you sell. Write and graph an inequality to describe your goal in terms of x and y. b. Give two possible combinations of numbers of earrings and necklaces that you can sell in order to exceed your goal of making $ The Stevens family is going to the county fair. They have two ticket options as shown in the chart below. A. Write an equation that shows the cost per person for each option. B. Use graphing to solve the system of equations. C. Find the number of rides for which the total cost is the same with both ticket options.

5 31. Reggie receives three points for each correct answer on a test and loses one point for each incorrect answer. a. Write an equation showing that Reggie received 60 points. b. Write an equation showing that Reggie answered all 40 questions on the test. c. Solve the system of equations you wrote for parts a and b by graphing. 32. Solve by substitution: a. no solution b. (5, 1) c. d. 33. A rental car agency charges $15 per day plus 11 cents per mile to rent a certain car. Another agency charges $18 per day plus 8 cents per mile to rent the same car. How many miles will have to be driven for the cost of a car from the first agency to equal the cost of a car from the second agency? Express the problems as a system of linear equations and solve using the method of your choice. 34. The length of a rectangle is 8 cm more than four times the width. If the perimeter of the rectangle is 46 cm, what are the dimensions? a. width = 3 cm, length = 20 cm b. width = 3 cm, length = 40 cm c. width = 6 cm, length = 32 cm d. width = 6 cm, length = 40 cm 35. The Golden Age Club is trying to book a location for their annual retirement dinner. The Blue Room restaurant quoted a price of $380 for the room and $20 per person for the dinner while the Wagon Wheel restaurant quoted a price of $30 per person. a. Write an equation that models each booking. b. How many people would have to attend so that the Blue Room is the better choice? so that the Wagon Wheel is the better choice? Solve by elimination: 36. a. (4, 2) b. c. (12, 2) d. no solution 37. Solve the system.

6 38. Solve the linear system: 39. Find two numbers whose sum is 33 and whose difference Solve the linear system by any method. 41. Marc sold 461 tickets for the school play. Student tickets cost $3 and adult tickets cost $4. Marc's sales totaled $1624. How many adult tickets and how many student tickets did Marc sell? a. 220 adult, 241 student c. 236 adult, 225 student b. 225 adult, 236 student d. 241 adult, 220 student 42. Find the solution of the system, if it exists. 43. Express each equation in slope-intercept form. Then determine, without solving the system, whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. 44. Does the system of equations have no solution, one solution, or many solutions? Explain how you can tell without graphing the system. 45. Graph the system of linear inequalities. 46. Simplify. Leave your answer in exponential form. a. b. c. d. 47. Simplify:

7 Simplify: Simplify the product: 50. Simplify 51. Which is equivalent to? a. b. c. d. Simplify the expression Rewrite using only positive exponents: 54. Which expression is equivalent to? a. b. c. d. 55. Write your answer on a separate piece of paper. Does the expression simplify to a negative number, a positive number, or 0? Explain how this can be determined without actually calculating the value of the expression. 56. Rewrite 50,800,000 in scientific notation. 57. Rewrite in scientific notation.

8 58. Rewrite in standard form. 59. Evaluate. Write the result in standard form. 60. Write the polynomial so that the exponents decrease from left to right. 61. Classify the expression by the number of terms and state its degree. a. trinomial, 2 c. monomial, 7 b. binomial, 1 d. binomial, Which expression is a polynomial? 63. Find the sum. Simplify the expression. 64. Find the difference. 65.

9 66. Melissa found the sum of and to be. a. Is her answer correct? If not, what is the correct answer? b. What error does it appear that Melissa made in adding the polynomials? 67. Find the product Write a variable expression for the area of the rectangle. 71. A rectangular garden, with length four times its width, is to be expanded so that both sides are increased by 3 yards. Let x represent the original width of the garden. Which expression models the area of the expanded garden? Find the product. 74.

10 75. Solve the equation 76. Solve the equation 77. The area of a rectangle is 24 square centimeters and its side lengths are x centimeters and centimeters. a. Find the side lengths of the rectangle. Justify your answer. b. Find the perimeter of the rectangle. 78. A rectangle with an area of 24 square units has length and width. Find the value of x. Factor the trinomial Factor the polynomial completely. 84. Simplify:

11 Simplify: a. b. c. d a. b. c. d. 92. Find the product. Simplify the expression Solve: 96. a. 33 c. no real number solutions b. 33, -39 d a. 9 b. no solution c. 9, 8 d. 8

12 Solve Jill and Eileen decided to take a shortcut through the woods to go to their friend's house. When they went home they decided to take the long way around the woods to avoid getting blackberry vine scratches. If the length of the shortcut is equal to the square root of the sum of the squares of the other two sides, what total distance did they walk?