Attached is a packet containing items necessary for you to have mastered to do well in Algebra I. Practicing math skills is especially important over the long summer break, so this summer assignment is meant to be completed over the entire summer, not all at once. Aim to spend around 30-40 minutes each week completing these problems. The entire assignment should take around 3-4 hours at most. This packet must be completed by the second day of school. The packet will be graded for correctness and completion and assigned a minor assessment grade. Your teacher will review the packet and all the concepts and may follow up with an additional assessment. If they choose to test you on this material, they will let you know during your first class period. No late submissions of the summer assignment will be accepted, so please be prepared to hand it in on time. Enjoy your summer. PS: A good website to check out if you need some help would be www.purplemath.com or www.math.com
1. Factors: Write the pairs of factors for each of the following numbers: Example: a) 48 b) 72 Give the factor pairs of 12: 1 12 2 6 3 4 2. Find the Greatest Common Factor (GCF) of each of the following pairs of numbers: a) 12 and 20 b) 54 and 81 3. Write the prime factorization of 360 in exponential form. 4. Name the following as a fraction in simplest form: a) 45% b).125 c).66 5. Computations with Whole Numbers and Decimals a) Subtract 12.67 from 32.01 b) Find the quotient of 2.61 and 0.9 c) What does 0.642 x 100 = d) What is the product of 5.2 and 7.3?
6. Decimal Comparisons: Fill in the blank with the symbol that makes the statement true <, >, or =. a) 0.36 0.63 b) 13.100 13.1 c) 6.25 6.20 d) 0.02 0.002 7. Convert the following to a decimal: a) 7 = b) 5.6% = 8 8. Percentages a. What is 85% of 800? b) 44 is what percent of 132? c) 90 is 75% of what? D) What is 5% of 40? 9. A city youth program has a total yearly budget of $220,000. Of the total budget, 17% is spent on administrative costs, 25% is spent on supplies, and 30% is spent on art programs. The rest of the budget is spent on sports programs. How much is spent on sports programs? 10. Connie got 18 out of 30 questions correct on her test. What is this as a percent?
11. Sally purchased a sweater on sale for 30% off. If the original price is $45.00, then how much did she save with the sale? 12. Kyle spent $75 of his $325 paycheck. What percent did he spend? Ratios and Proportions 13. If the ratio of oil to vinegar in the salad dressing is 2 to 3, which of these should be used? a) 4 parts oil, 8 parts vinegar b) 1 part oil, 2 parts vinegar c) 10 parts oil, 30 parts vinegar d) 9 parts oil, 13.5 parts vinegar 14. Paul worked 15 hours and earned $127.50. At this rate, how long would it take for Paul to earn $ 170? 15. Find the rate a car travels if it goes105 miles in 2 hours and 30 minutes. (d = r t) PROBABILITY AND STATISTICS For questions 16-18, use the table below. Tickets Seat Location Price Main floor, center $125 Main floor, side/back $75 Mezzanine $65 Balcony $50 16. What was the mean price per ticket if a person bought 1 ticket of each price? What is the median ticket price?
17. If John has $120 and he needs to buy 2 tickets, in which seats could he sit? a. Main floor, center b. Main floor, side/back c. Mezzanine d. Balcony 18. How many different lunches can be made with a choice of hot dog, salad, or chili; soda, milk, or lemonade; and crackers, bread, or a roll? 19. A spinner has the numbers 1 8 on it. What is the chance of the spinner landing on an even number? 20. Sam has eight quarters, five dimes, and three nickels in his pocket. If one coin is selected at random, what is the probability that it will not be a quarter?
Scientific Notation 21. Write the following in Scientific Notation: a) 15,109,000,000 b) 0.0000025 22. Write the following in standard form: a) 1.579 x 10 4 b) 4.5 x 10-5 23. Fraction (Express answers as fractions only. DO NOT use a calculator.) Show all work. a) 2 1 b) 3 2 5 5 4 3 c) 5 4 d) 2 5 8 10 9 3
Pre-Algebra Concepts 24. Complete the T Chart below. You must know these squares and cubes. n n 2 n 3 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
25. Order of Operations: a) 4 16 + 8 0 5 b) 24 8 5 6 c) 8(3 + 4) 2 8 (5 3) d) 27 3 4 2 Insert parentheses to make the statement true: e) 8 + 12 4 5 = 1 f) 3 4 + 2 8 = 10 Choose a matching term from the word bank for # 26 32: 26. A number that replaces the variable in an equation to make the equation true. 27. The point where the x-axis and the y-axis intersect on a grid. 28. A sentence that uses mathematical symbols instead of words. A. Absolute values B. Integers C. Coordinates D. Origin E. Variable F. Solution G. Linear equation H. Terms I. Expression 29. The distance of a number from zero on the number line 30. The variable and the numbers in a mathematical expression. 31. A letter used to represent a number in a mathematical expression. 32. Positive numbers (1,2,3 ), negative numbers (-1, -2, -3, ), and zero.
33. Write the absolute value: a) 7 b) 34 34. Write the integers in order from least to greatest: 7, -9, 8, 0, 9, -3 35. Perform the indicated operations without using a calculator: a) -43 + -17 = b) (-3)(-2)(-5) = c) 20 (-18) = d) (-40) (-8) = e) (-1) 9 = f) 29 100 = 36. Combining Like Terms a) 15 n + 2n 8n b) 9x+ 6 5x c) -4(2x +7y) d) 3(y + 6) 37. Solve One Step Equations a) z 7 = -3 b) p + -7 = 9 d) 17 x 3 38. Evaluate the following expressions for each given value of x: x = 4 and x = -3 a) 2x b) x 2 c) x + 6 d) 5x 3
Algebraic Representation Translate each of the following into symbols. Let x = the number. Three more than five times a number. Twice a number decreased by seven. Twelve less than eight times a number. Twenty decreased by four times a number. Fifty increased by three times a number. The product of three and a number. The sum of triple a number and seventeen. The difference of fifty and ten times a number. The quotient of fifteen and twice a number. Eight less than the product of five times a number. 5x 2 x + 1 3x + 1 x 4 9/x