What students need to know for PRE-ALGEBRA 2014-2015 Students expecting to take Pre-Algebra should demonstrate the ability to: General: o Keep an organized notebook o Be a good note taker o Complete homework every night o Be active learners Ask questions and participate in class Seek help outside of class if needed o Work with others o Work with and without a calculator Specific math skills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eview Problems: *NOTE: Show all of your work. Your teacher may give a quiz on this material at the beginning of the year. Don t forget to use the reference sheet on page 2. You should Google the topic if you are unsure how to complete the examples. Khanacademy.org has some good instructional videos.
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
Name: Date: 1. Anthony wants to plant a garden where the length to width ratio is 5 : 2. If he already has a plot that is 12 feet long by 8 feet wide, how much must he add to the length to get the desired ratio? 8ft 12 ft 2. The ratio of boys to girls in a graduating class is 4 to 5. How many boys and girls are there if the class has 360 students? 3. A motor cyclist is competing in a 240 mile race. Create a table showing what his average speed must be if he wants to finish the race in 10 hours, 12 hours, 15 hours, 16 hours, or 20 hours. 4. Mrs. Sedberry is making a fun math activity for her students. The table shows how many pieces of yarn she needs for several students. Number of Number of Students Pieces of Yarn 6 36 8 48 9 54 12 72 According to the pattern in the table, how many pieces of yarn does Mrs. Sedberry need for 1 student? page 1
5. Each grid below represents the number 1. Shade the grids to show these fractions: 70% 3 4 0.65 6. A jet airplane travels at an average of 1,200 miles per hour. About how many miles does it travel in one minute? In one second? 7. An online service provider charges $0.025 per minute for online access. If you used 324 minutes last month, what will your bill be? 8. Manhattan High School is collecting soup and sandwiches for the homeless. Four classes brought in the following amounts. Soup Sandwich Mrs. Smith 12 18 Mr. Frank 15 10 Mr. Lee 6 9 Miss Jones 12 15 Which two classes brought in the same ratio of cans of soup to sandwiches? 9. The perimeter of an equilateral triangle is 19 1 2 feet. What is the length of one of the sides of the triangle? 10. A family is saving for a down payment on a car. If the family needs $1,800 and can save $225 per month, how long must they save? 11. 625.25 25 page 2
12. Study the following sets of numbers: Set I: 2, 6, 8, 10 Set II: 10, 15, 20, 25 Set III: 7, 14, 21, 35 Explain the relationship between the numbers in each set. Support your explanation by showing your work. 13. Explain why 3 belongs to the set of integers and rational numbers. 14. Look at the number line. 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 Which of these is not a correct statement about the numbers that are marked on the number line? A. 4 > 6 B. 6 is less than 4 C. 6 is greater than 4 D. 6 < 4 15. If (x, y) is in Quadrant III, then what are the signs of x and y? 16. Label the number line below so that 0 is between points B and C. Then describe the value of the points that are graphed on the number line. A B C D 17. Which of the following statements is true? A. 2 1 2 > 2 3 4 B. 3 1 2 < 3 1 8 C. 1 3 4 > 1 7 8 D. 5 3 8 < 5 3 4 page 3
18. The lowest daily temperatures in Stockholm, Sweden during the last week of December are listed in the chart: Monday Tuesday Wednesday Thursday Friday Saturday Sunday 5 F 7 F 0 F 2 F 4 F 6 F 9 F Which two days recorded the highest temperatures? 19. Simplify: 2 3 20. What is the length, in units, of a line segment with the endpoints of (2, 5) and (2, 10)? 21. A car stopped at the entrance to a highway. From there, the car increased its speed as it entered the highway. If this information were graphed on a coordinate plane, in which quadrant would the information be found? Explain your answer. 22. If a black circle represents the number positive one and a white circle represents the number negative one, which diagram represents the number 2? A. B. C. D. 23. Lake Middle School is playing Ocean Middle School in football. Lake Middle School gained six yards on their first play and eight yards on their second play. Lake Middle School then lost nine yards on their next play. What was the total yards gained or lost? Solve the problem in at least two ways. Explain each strategy. 24. 9 2 7 = page 4
25. Complete the chart. Fraction Decimal Percent 2 5 0.25 1.5 30% 26. Using the digits 1, 2, 3, and 4, and the order of operations, write expressions that equal the numbers from 1 to 10. You must use each digit only once per expression. Example: 1 = 2 1 (4 3) 27. Imagine that on one day you had a penny. The next day, it doubled to 2 pennies. Then, the next day, the two pennies doubled to four pennies, and continued doubling each day for 30 days. How much money would you have at the end of the month? Explain your reasoning. 28. Evaluate the expression: 4 2 + (2 0 5 0 ) 5 2 4 0 3 5 29. Write an algebraic expression for five more than twice a number. 30. Part 1 A triangle has sides of length 2x, 3x and 4x. Find the perimeter of the triangle if x = 20 cm. Describe how you found your answer. Part 2 What happens to the perimeter if 1 cm is added to the length of each side? Predict what will happen to the perimeter if 2 cm are added to each side? If 3 cm are added? Describe the conclusions you can make. 31. Evaluate n 2 2n, for n = 5 page 5
32. Insert one pair of parentheses, ( ), in order to make each statement true. a) 7 8 2 2=21 b) 3 2+3 4 = 60 33. Simplify 2z + 4(5 z). 34. Express 2x 3 + x 4 as a fraction in simplest form. 35. Look at the following. 3b 3m 3 m 3 Which are like terms? A. 3b and m 3 B. 3b and 3 C. 3m and m 3 D. 3 and 3m 36. Look at the table. f? 6 24 7 28 3 12 2 8 Which expression should go at the top of the second column? A. (f + 3) 2 B. f + 6 C. (f + 2) 3 D. f 4 page 6
37. a) Complete the pattern. Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 b) Label and record your steps and total number of squares on the chart. c) Explain how you completed the pattern and state at least one rule. 38. From last night to this morning the temperature rose 12 F. The temperature this morning was 63 F. Let l equal the temperature last night. Write and solve an equation for the temperature last night. 39. Carpet costs $8.50 per square foot. Mr. Cabral wants to carpet a hallway that requires 12 square feet. He paid $102 for the carpet. Work out the problem to see if he paid the correct amount. Did he pay the correct amount? YES NO Circle the operation you used to solve the problem: addition subtraction multiplication division Could you solve the problem using a di erent operation? Explain or show your answer. 40. 27 = n 12 41. On the number line, graph the inequality x 4. 5 4 3 2 1 0 1 2 3 4 5 page 7
42. A math class would like to make a graph representing the relationship between time of year and rainfall. Which of the two variables would be placed on the x-axis, time of year or rainfall? Support your answer with an explanation. 43. Simplify. 9y (5y 9) 44. Given: x + A = x x A = A What is the value of A? Is there any other mathematical property where the value of A would be the same as in the above problem? 45. This year, the cost of an amusement park pass is twenty percent more than last year. This year s cost is described by an expression where p is last year s cost. p +0.20p Which of these expressions is another way to describe this year s cost? A. 1.20p B. p + 20 C. 1 + 20p D. 0.80p 46. Find the area of the figure and explain the process that you used. page 8
47. A rectangle has an area of 36 square units. The length of the rectangle is 9 units. On the coordinate graph, draw a rectangle that has an area of 36 square units and a length of 9 units. 48. An elevator is 5.5 ft long, 4.5 ft wide, and 7.2 ft high. How many cubic feet of air are there per person if the maximum elevator capacity is 12 people? 49. The edge of a cube measures 2.1 m. Find the volume. page 9
50. On the grid shown, plot the following quadrilateral: C( 5, 5), and Coordinate D(7, 5). Coordinate A( 3, 5), Coordinate B( 5, 5), Coordinate a) What is the shape of the quadrilateral? b) What property is used to identify this quadrilateral? c) What is the area of the quadrilateral? 51. If you stack three cubes one on top of the other, what is the surface area of the tower of cubes? Assume each cube has 3 inch sides. 52. Rhonda drew a larger model of Figure A as shown below in Figure B. Which of the following best describes the length of side L in Figure B? A. 480 cm B. 80 cm C. 62 cm D. 75 cm page 10
53. How could you show more studying improves grades? 54. The following data are test scores for a class of 20 students: 77, 54, 71, 81, 54, 87, 73, 67, 65, 73, 90, 56, 75, 83, 66, 73, 63, 62, 55, 81 a) Complete the table. Interval 91 100 81 90 71 80 61 70 51 60 Number (frequency) b) In which interval does the mode lie? c) In which interval does the median lie? 55. The mean, median, and mode of three numbers is 84. One of the numbers is 82. a) The mean of the numbers is 84. Find two other numbers. Explain your reasoning. b) The median of the three numbers is 84. Find two other numbers. Explain your reasoning. c) The mode of the three numbers is 84. Find two other numbers. Explain your reasoning. 56. Consider the following table showing grades 10, 11, and 12 as well as the number of people receiving various letter grades: A B C + C C D/E Gr. 10 19 41 58 48 37 Gr. 11 28 35 43 21 27 Gr. 12 32 47 69 38 17 a) To the nearest 10, how many grade 11 marks are shown? b) To the nearest 100, how many grade 10 marks are shown? c) How many people got a mark of B? d) If there are a total of 227 grade 12 students, then how many got marks of D and E? e) How many more people got a C+ than an A? page 11
57. The math scores of seven students in your study group are: 22, 24, 25, 26, 25, 34, 35 Which measure of central tendency will you use to give an overall idea about the performance of your group? A. Median: 25 B. Mean: 27 C. Mode: 25 D. Range: 13 58. Annette has earned the following scores on her tests: 83, 86, 92, 86 and 96. a) Find the mean, median and mode of her scores. b) Which measure (mean, median, mode) is best for calculating her final grade? Why? c) If Annette takes another test, and 100 is the top score, what is the highest possible average she could receive on all six tests? d) What score on a sixth test would Annette have to receive if she wants an overall average of at leat 90%? 59. A company has 6 employees earning less than $25,000 per year and one employee earning $150,000 per year. A local newspaper reporter, who is doing a story on income disparity, interviews the owner of the company. a) To reveal as little disparity as possible, what measure of central tendency (mean, median or mode) should the owner use to describe employees earnings? b) What measure of central tendency should employees use to decribe their earnings, to make the disparity most obvious? c) If the newspaper reporter includes only one measure of central tendency in his story, which measure would provide the most revealing information about the employees earnings? 60. A jar contains four di erent colors of marbles. One half are red, 1 4 are white, 1 6 are yellow, and the rest are green. If there are 96 marbles in the jar, how many are yellow? page 12