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Name ___________________________ Date _________________ Period 1 3 4 5 6 7 Semester 1 Exam Study Guide The date and time for my math exam is ______________. 1. What is the solution to the inequality 10x – 7 > 3x + 28? 2. Brianna had 5 rolls of dimes and 3 extra dimes. She used the equation to find n, the number of dimes she had altogether. Rewrite this equation so she can use it to find d, the number of dimes in each roll. 3. What is the solution to the equation 4x – 7 – 9x = 13 + 5x? 4. Gale wants to buy some new clothes, but she cannot afford more than $95 before the sales tax is added. The blouses she wants are priced $16 each and the pants she wants are priced $23 each. Write and solve an inequality to be used to determine b, the number of blouses, and p, the number of pants Gale can afford. After solving, draw a graph to represent the solution. 5. Use the expression to answer the questions: i. ii. iii. iv. 5x2 – 4x + 3 Name the term(s) of this expression. Name the coefficient(s) of this expression. Name the constant(s) of this expression. True or False: 2 is the exponent of the term 5x. 6. The Cross Country Team is sponsoring a bake sale. If their goal is to raise at least $700, how many cakes must they sell at $4.00 each in order to meet that goal? i. Write an inequality that represents this situation. ii. How many cakes must they sell in order to meet their goal? iii. Draw the graph of the solution to this inequality. 7. Julia bought a pair of shoes with a price of $150 from the catalog with 7% sales tax and a $10 shipping fee. Calculate: i. The amount she paid for sales tax ii. The total amount, including the sales tax and the shipping fee, that Julia paid for the shoes was $180. What was the shipping fee, in dollars? Name ___________________________ Date _________________ Period 1 3 4 5 6 7 8. Which number completes the following table? How did you determine your answer? Input (x) 3 6 Output (y) 9 36 9 12 144 9. Raul is buying video games and he wants to spend $200 or less on his purchase. The type of games he likes best, racing games, cost $52 each. Write an inequality that shows how many racing games he can purchase. 10. What is the solution to the equation 3x + 5(4x – 6) – 8 = 3x – 14? Graph the linear equation: 11. 12. List the coordinates of each point: a) ______ g) ______ b) ______ h) ______ c) ______ i) ______ d) ______ j) ______ e) ______ k) ______ f) ______ l) ______ Name ___________________________ Date _________________ Period 1 3 4 5 6 7 Set up proportions to solve #12-15. 13. Convert 175 miles to feet. ____________________ 14. Convert 80 feet to inches. ____________________ 15. Convert 350 seconds to minutes. ____________________ 16. Convert 30 minutes to seconds. ____________________ 17. Convert 108 inches to yards. ______________________ Write the correct algebraic expression for each phrase. 18. 11 divided by x ____________________ 19. triple a quantity decreased by 9 ____________________ 20. ten less a number ____________________ 21. twelve less than a number ____________________ 22. seven times the sum of a number and three ____________________ 23. 5 times a quantity dived by 10 ____________________ 24. What is the solution to the equation 25 = 2x – 7? Write an equation for each of the quantities being compared. Remember: is/was means equal. 25. The length of a rectangle is 20 inches more than double the width. Variable for length _____ Variable for width _____ 26. The value of the exports of Canada is triple the value of the exports of Mexico. Variable for Canada _____ Variable for Mexico_____ 27. The cost of Hannah’s biology book was $15 more than the cost of her history book. The cost of her English book was $5 less than the cost of her history book. (write 2 equations) Variable for biology book_____ Variable for history book____ Variable for English book_____ 28. What is the solution to the equation 4x = 1 ? 64 Name ___________________________ Date _________________ Period 1 3 4 5 6 7 Write the domain and range of the graph below using brackets and inequality notation. 29. Domain __________________ 30. Range____________________ 31. Domain__________________ 32. Range__________________ 33. 3x – 2 = 27 34. 108x - 5 = 1,000 Solve for the bolded letter. 35. w = x + ym 36. p = m- n 37. e = fg 38. y = mx+b 39. Luc received $50 from his grandparents for his birthday. He makes $75 each week as a cashier at the supermarket. Since his birthday, he has saved more than enough money to buy a game system that costs $450. How many weeks ago was Luc’s birthday? 40. After purchasing the game system, will Luc have any money left over? How do you know? 41. The starting balance of Adam’s saving account is $575. Each month (m), Adam deposits $60. Use function notation to write an equation to represent this situation. Name ___________________________ Date _________________ Period 1 3 4 5 6 7 42. What is the form of a linear equation? 43. What does m represent in y=mx+b? 44. What does b represent in y=mx+b? 45. Which 2 variables don’t change in a linear equation? 46. In the equation y = 2x – 9, what is the m? 47. In y = 2x – 9, what is the b? 48. In the equation y = -4x +3, what is the m? 49. In the equation y = -4x +3, what is the b? 50. How do you graph a linear equation? 51. Explain how you would graph the equation y = -3x + 6. 52. How do you find slope on a graph? 53. How do you find the y-intercept on a graph? 54. How do you find slope in a table? 55. How do you find they-intercept in a table? 56. How do you find slope in an equation? 57. How do you find y-intercept in an equation? Find the m and the b for each table shown below. x y x y x y x y 0 2 0 -1 0 -3 5 0 1 1 4 0 2 -3 5 1 2 0 -4 -2 4 -3 5 2 Match graphs below to59. onemof=the 58. m =the ___ b = ____ ___equations b = ____in the box. 60. m = ___ b = ____ 61. m = ___ b = ____ equation: __________ equation: __________ equation: __________ equation: __________ Name ___________________________ Date _________________ Period 1 3 4 5 6 7 Match each graph to one of the equations in the box. 62. ________ 65. ________ (a) y = (g) x= 5 1 x–1 4 (b) y = x - 2 (h) y = -x + 2 63. ____________ 64. _________ 66. __________ (c) y = 67. _________ 3 x – 4 (d) y = 3 4 (i) y = 4x - 1 (e) x = 3 (j) y = x + 1 (k) y = 4 x– 4 3 (f) y = 5 (l) y = x - 1 Match each table to one of the equations in the box. x 5 5 y -1 0 68. ________ x 0 4 y 3 3 69. ____________ x 0 2 y 2 0 70. _________