SUMMER MATH PACKET 2016 FOR RISING EIGHTH GRADERS WHO WERE IN PRE-ALGEBRA

Transcription

1 SUMMER MATH PACKET 2016 FOR RISING EIGHTH GRADERS WHO WERE IN PRE-ALGEBRA 1

2 DIRECTIONS FOR COMPLETING THE PACKET The following page contains the list of help topics available on the Glencoe website. Each topic includes a brief explanation and review of problems like those you will see in your packet. If you are having trouble with a specific topic or question, you may use this site as a resource. This work should be attempted without the use of a calculator. However, some sections will require the use of a calculator. These sections will be noted. If the section is not noted for use of a calculator, you must show all work. Solve part I in June, part II in July, part III in August. The idea of the review is to do little work (each of these 3 packets should take about 3 4 hours of work), but spread in time so it refreshes your memory every now and then and keeps alive the knowledge you acquired during the year. Of course, you can do everything in August, but by then your memory will be stale beyond the rejuvenating power of this packet. Or you can do it all now, but by late August, when classes begin, you will have trouble to retrieve this knowledge from the dungeons of your memory. If you want to invest your time poorly, go ahead. If a problem or group thereof is still driving you crazy, you will find help at rvilarrubi@barrie.org. USE IT! Be explicit about what you did, what you got, and/or what you find puzzling. A couple of sentences. You may include a scan in your . Help may delay a day or two. Turn in the packet with your solutions the first day of classes. It will be a conversation piece the first week of class. Enjoy your vacation! 2

3 MATH REVIEW TOPICS AVAILABLE ONLINE Number Sense Adding and Subtracting Whole Numbers Comparing and Ordering Whole Numbers Divisibility Patterns Estimating with Whole Numbers Estimation Strategies Greatest Common Factor Least Common Multiple Multiplying and Dividing Whole Numbers Place Value and Whole Numbers Powers of 10 Prime Factorization Decimals Adding and Subtracting Decimals Comparing and Ordering Decimals Dividing Decimals Estimating Products Multiplying Decimals Place Value and Decimals Rounding Decimals Fractions Estimating Products and Quotients of Fractions and Mixed Numbers Estimating Sums and Differences of Fractions and Mixed Numbers Expressing Fractions as Decimals and Percents Mixed Numbers and Improper Fractions Operations with Fractions: Adding and Subtracting Operations with Fractions: Multiplying and Dividing Simplifying Fractions The Percent Proportion Integers Comparing and Ordering Real Numbers Operations with Integers Problem-Solving Guess and Check Make a Table or List Solve a Simpler Problem Work Backward Measurement Converting Measurements w/ Customary System Converting Measurements w/ Metric System Units of Time Statistics and Graphs Box and Whisker Plots Making Bar and Line Graphs Making Circle Graphs Mean, Median and Mode Stem and Leaf Plots Algebraic Concepts Evaluating Algebraic Expressions Factoring to Solve Graphing Ordered Pairs Graphing Using Intercepts and Slope Multiplying Polynomials Solving Eqns. w/ the Variable on Both Sides Solving Inequalities Solving Multi-Step Equations Solving One-Step Equations Solving Systems of Linear Equations Square Roots and Simplifying Radicals Geometry Area and Circumference of Circles Congruent and Similar Figures Identifying 3-Dimensional Figures Identifying 2-Dimensional Figures Measuring and Drawing Angles Perimeter and Area of Squares and Rectangles Pythagorean Theorem Volume 3

4 JUNE Lesson 1: Operations with Fractions: Adding, Subtracting, Multiplying and Dividing (NO CALCULATORS) Find each sum or difference Simplify Find each sum or difference. Write in simplest form Find each product

5 Name the reciprocal of each number Find each quotient Lesson 2: Operations with Rational Numbers (NO CALCULATORS) ( 23) (15) 16. ( )( 2 ) (-64) ( 8) 18. (32.25) ( 2.5) 5

6 19. Hannah is making pillows. The pattern states that she needs yards of fabric for each pillow. If she has yards of fabric, how many pillows can she make? 20. The price of a computer dropped $34.95 each month for 7 months. If the starting price was $1,450, what was the price after 7 months? Lesson 3: The Percent Proportion (CALCULATORS PERMITTED) Express each percent as a reduced fraction % % Use the percent proportion to find each number is what percent of 125? % of what number is 80? 6

7 25. Find 12% of Maddie usually makes 85% of her shots in basketball. If she shoots 20 shots, how many will she likely make? 27. A glucose solution is prepared by dissolving 6 millimeters of glucose in 120 milliliters of solution. What is the percent glucose in the solution? 28. The U.S. Food and Drug Administration requires food manufacturers to label their products with a nutritional label. The sample label shown at the right shows a portion of the information from a package of macaroni and cheese. For a healthy diet, the National Research Council recommends that no more than 30% of total Calories come from fat. What percent of the Calories in a serving of this macaroni and cheese come from fat? 7

8 JULY Lesson 4: Expressing Fractions as Decimals and Percents. (NO CALCULATORS) Write each fraction as a decimal Write each decimal as a fraction Write each decimal as a percent Write each percent as a decimal % % Write each fraction as a percent. Round to the nearest tenth of a percent if necessary Write each percent as a fraction % % 8

9 Lesson 5: Mean, Median and Mode (CALCULATORS PERMITTED) 41. Bill s scores on his first four science tests are 86, 90, 84, and 91. What is Bill s average test score based on these scores? 42. Sue s average for 9 games of bowling is 108. What is the lowest score she can receive for the tenth game to have an average of 110? 43. The ratings for the top television programs during one week are shown in the table at the right. Find the mean, median, and mode of the ratings. Round to the nearest hundredth. (There are no questions #44-53! Go take a break in the sunshine in place of those missing problems.) Lesson 6: Order of Operations / Evaluating expressions (CALCULATORS PERMITTED) Evaluate each expression

10 [5(7 + 6)] (5 + (30 6) ) [(8 + 5)(6 2) ] (4 17 2) [(24 2) 3] Evaluate each expression if a = 2, b = 5, x = 4 and n = a + b 63. (2x) 2 + an 5b 64. a(6 3n) 65. [a + 8(b 2)]

11 AUGUST Lesson 7: Simplifying and Solving Algebraic Expressions (CALCULATORS PERMITTED) 66. 5(-3a) 6a (2m 3n) x 15y (-x) + 13x Solve each equation. Then check your work m = x = f ( ) = p = 35 11

12 w p = = x + 5 = t 9 = m 3 = 9 1.2a 79. 5r + 4r = x + 1 = 3x (y - 5) = 18 2y 12

13 Lesson 8: Plotting Points on the Coordinate Plane (CALCULATORS PERMITTED) Plot the following points on the coordinate plane to the right. 82. (2,3) 83. (-4,1) 84. (5,-2) 85. (0, 7) 86. (-4,0) Write the ordered pair for point E and point K. 87. E = (, ) 88. K = (, ) Fill in the following table of values for each linear equation below. Then graph the points on the coordinate plane. 89. y = 2x - 1 x y 13

14 90. y = 3 x x y Lesson 10: Mixed Problem Solving As you ascend in the Earth s atmosphere, the temperature drops about 3.6 degrees every 1,000 feet in altitude. 91. If you ascend 10,000 feet, what is the change in temperature? 92. If the temperature drops from 70 degrees Fahrenheit at sea level to -38 degrees Fahrenheit, what is the altitude you have reached? In the 2000 Olympic games, the winning time for the men s 400-meter run was approximately 44 seconds. The winning time for the men s 400-meter freestyle meter swimming event was about 3 minutes 41 seconds. Round your answer to the nearest meter in questions 93 and What was the speed in meters per second for the 400-meter run? 94. What was the speed in meters per second for the 400-meter freestlye? 14

15 95. How do the speeds of the two events compare? The Congo River in Africa is 2900 miles long. That is 310 miles longer than the Niger River, which is also in Africa. 96. Write an equation you could use to find the length of the Niger River. 97. What is the length of the Niger River? 98. Four teachers went to a baseball game. A vendor selling bags of popcorn came by. Dulaney bought half of the bags of popcorn plus one. DL bought half of the remaining bags of popcorn plus one. Dan bought half of the remaining bags of popcorn plus one. Riki bought half of the remaining bags of popcorn plus one, leaving the vendor with no bags of popcorn. If Riki bought 2 bags of popcorn, how many bags did each of the four teachers buy? Mike is registering for a ski trip in British Columbia, Canada. The cost of the camp is $1,254, but the Canadian government imposes a general sales tax of 7%. 99. What is the total cost of the camp including tax? 100. As a US Citizen, Mike can apply for a refund of one-half of the tax. What is the amount of the refund he can receive? 15