OHS Algebra 1 Summer Packet Good Luck to: Date Started: (please print student name here) 8 th Grade Math Teacher s Name: Complete each of the following exercises in this formative assessment. To receive full credit for this assignment, you must show all your work in this packet and complete ALL of the problems in the packet. You may use a calculator to assist you, but this cannot serve as a replacement for showing work. This assignment is due on the first day of school (at the start of your class). This packet consists of Common Core State Standards review material, from previous grades. Reference sheets are included in this packet to help you complete your work. Failure to complete this packet may put you at a disadvantage. For assistance in completing individual problems, you should refer to your notes from previous classes, online resources, or work with your peers and family members. If you find you are having trouble with an item, skip it, and come back to it later, but persevere in trying to solve the problem. There will be time, with your teacher in class, devoted to answering any questions regarding this summer packet. You will be assessed on this material in class, so make sure you understand how to do all of these items in this packet. You will need a TI-84 graphing calculator for Algebra class. If you have any questions regarding this assignment, please contact Mr. Ron Bergin, Mathematics teacher at berginr@oxfordpublicschools.org or Miss Alicia Salvatore, Mathematics teacher at salvatorea@oxfordpublicschools.org.
Algebra 1 Summer Packet 2015-2016 VOCABULARY Quantity: Variable: Coefficient: Algebraic expression: Numerical expression: Part 1: Operations with Rational Numbers: Add, Subtract, Multiply, or Divide. Keep answers in fraction form, when necessary. 1. ( 4)( 2)( 5) 2. 4 7 ( 8 3 ) 3. 7 6 + 3 4 4. 2 5 4 15 5. Simplify the expression for when x = 2 4(x) 1 2 Part 2: Simplifying and Evaluating Expressions Example: Evaluate the expression when k = 5 Ex 1: k 2 (Plug in 5 where you see k) (5) 2 = 25 Now you try, evaluate the following expressions when n = 3 6. 5n 7. 21 n 8. n 11
9. n 7 10. n 4 11. 27n What word do we use to help us remember the order of operations? Put one letter on each line to spell out the word. Think: Please excuse Use the Order of Operations to evaluate the expression. 12. 3 6 4 13. 24 (8 + 4 2 ) 14. 12(6 3.5) 2 1.5 15. 11 + 5 3 2(5) Translate the verbal phrase into an algebraic expression. 16. The sum of a number x and 14 17. The difference of 9 and the square of a number g 18. The product of 5 and h 19. 4 less than the quantity of 6 times a number y 20. The quotient of a number k and 3 21. Six less than the number p 22. Four more than the number c 23. The quotient of 7 and the product 5h 24. Three times the quantity of the sum of 8 and a number m 25. The difference of a number g and -2
26. 6x + 5 This is an example of an expression equation (circle one) 27. y = 2x 7 This is an example of an expression equation (circle one) 28. In words, explain the difference between an equation and an expression. Simplify each expression. Remember to combine like terms. 29. 5x + 4x 30. 2 + 2m m 6 + 3m 31. 4(x + 2) 32. 4x2 2x 33. k 6k 34. 3(d 4) + 1 35. 8w + 5 10w 36. 2p(3p + 1) 37. The cost of a telephone call is 75 cents plus 25 cents times the number of minutes. Write an algebraic expression that models the cost of a telephone call that lasts t minutes. 38. A plumber charges $65 per hour to fix a leak. What is an equation that relates the total cost of a leak repair c to the number of hours h it takes the plumber to fix the leak?
Part 3: Patterns 39. Create the next figure in the pattern. Then, write an algebraic expression that represents the nth figure of the pattern shown. (Hint: Remember that repeated addition can be written as multiplication.) Algebraic expression: 40. Identify the next two terms in the pattern: 6, 10, 14, 18,, 41. Write an algebraic expression based off of the pattern shown in the table. Dorothy gets paid to walk her neighbor s dog. For every week that she walks the dog, she earns $10. 42. Use the formula for the area of a trapezoid A b b, where A is area, b1 and b2 are the length of 2 1 2 h the bases and h is the height, to answer the following question. What is the area of a trapezoidal pool with a height of 15 yd and bases of 14 yd and 26 yd?
43. A pizzeria charges $12 per pizza, plus a $3 delivery fee. Use a table and an equation to describe the relationship between the number of pizzas delivered and the total cost. 44. Extend the table to find the amount of time it would take you to make 11 ski runs. Part 4: Probability and Statistics 45. Write the percent as a decimal and as a fraction 15% 46. Find the mean, median, mode, and range of the following data set: 12, 12, 14, 15, 12, 13, 11, 9, 12 47. What is the probability of rolling an even number on a number cube? Part 5: Linear Relationships Use the Order of Operations backwards. PEMDAS (Add or subtract before you multiply or divide) Ex 1: Solve the equation 4( 3x 2) = 32 12x + 8 = 32 Distributive property 8 8 Subtract 8 from both sides of equation 12x = 24 12 12 Divide both sides by 12 x = 2
Solve the following equations. Round to the nearest tenth when necessary. 48. 4x = 64 49. k 2 12 = 3 50. 3x + 52 = 82 51. x + 9 = 4 52. 32 x = 8 53. 7 + 2x = 4x + 11 54. Label the graph with the following vocabulary terms: a. Origin b. x-axis c. y-axis d. Quadrant I e. Quadrant II f. Quadrant III g. Quadrant IV 55. Plot and label the following points A(0, 4) B( 3, 1) C(5, 2) D(1, 5) on the coordinate plane. Example: The point P( 4, 2) has been plotted for you P
Part 6: Mixed Review Convert each of the following numbers into scientific notation. Two examples are provided. Example #1: Large number (positive exponent) Directions Example #2: Small number (negative exponent) 5,630,000=?.000000427=? 5,630,000. 5,630,000. Locate decimal point. You may need to place decimal point in appropriate location. Move decimal point until there is only one digit to the left of it. Count how many places you needed to move the decimal point..000000427.000000427 5.63 x 10 6 Do not write the zeroes. Express as a power of ten (raised to the number of places you needed to move the decimal point). 4.27 x 10-7 56. Convert each of the following numbers into scientific notation. a. 43,800,000 c..00061 b..000000000259 d. 7,400 57. Convert each of the following numbers into expanded form. a. 3.2 10 5 b. 5.97 10 7
58. Scientists in a lab were counting how many bacteria they found in their cultures. Each recorded their findings in a different fashion. Put the dishes in order from most to least bacteria. Show your work or explain how you arrived at your answer. Bacteria Dish Number of Bacteria A 5.3 x 10 5 B 6,500,000 C 27 x 10 4 D E One-third of Bacteria B Twice Bacteria C 59. Write the following percents as a decimal and as a fraction. a. 25% b. 5% c. 6.5% 60. The chart shows the top five medal-winning countries in gymnastics from the 2008 Beijing Olympics. Complete the chart before answering the questions. Country GOLD SILVER BRONZE TOTAL CHN 2 5 18 USA 2 6 10 RUS 2 0 2 ROM 1 0 2 CAN 0 2 0 b. What percent of the China s medals are gold? c. What percent of the USA s medals were silver? d. What percent of Russia s medals are not bronze?
61. Determine the perimeter of the square if one side is 14 inches. 62. Determine the area of a triangle with base 6 cm and height 9 cm. 63. Convert the following: 360 in = ft 64. Find the unit rate: 180 miles 3 hours 65. Order the numbers in each exercise from least to greatest. 25 33,, 4. 8, 18 4