Honors Algebra 1 ~ Summer Packet

Transcription

1 COURSE: Algebra 1 Honors (8 th Grade) YEAR: PURPOSE: Prepare for successful 8 8h grade year HOW IT WILL BE COUNTED: 3 Homework Grades, Review & Test to Follow Honors Algebra 1 ~ Summer Packet This packet contains Pre-Algebra concepts that were taught in 7 th grade. It is important that you know and understand these concepts, as we will build on them in Algebra 1. You should be able to complete the packet without the use of a calculator. Be sure to show ALL of your work! This packet is due on the first day of school, Tuesday, September 6 th. The packet will count as three homework grades for the first marking period. After briefly reviewing the information in this packet with additional notes and examples, you will be tested on the material. Enjoy your summer and see you in the fall! -Your Future 8 th Grade Math Teachers

2 8 th Grade Honors Algebra 1 Summer Packet Name Variables & Expressions General Questions: Answer each question using complete sentences. 1. What is the difference between an expression and an equation? 2. Can you name three words or expressions that indicate each operation (+, -, x, )? 3. How do you evaluate an expression? 4. What are like terms? 5. How do you combine like terms?

3 Vocabulary, Equations & Expressions 6. Circle the constant and underline the coefficient for each expression below. a. 5x 3 b. 2x + 7 c. 2 4x d. x Create an algebraic expression with a coefficient of 7 and a constant of Create an algebraic expression with a coefficient of -1 and a constant of Which of the following are algebraic expressions? Circle all that apply. 5x 2 8x w x 2w 6 4x 8 = 9 Translating between Words & Expressions Translate the words into an algebraic expression times x 11. The sum of x and The product of 9 and y 13. w less than more than x 15. The difference of 6 and x times the sum of x and The product of 5 and y divided by 3

4 18. The quotient of 300 and the quantity of x times x less than The quotient of 35 and the quantity of x minus The product of 7 and x minus the quantity of 4 less than y 22. The quantity of 9 more than x divided by the quantity of 12 less than y Tables & Expressions Complete the table. 23. n -n n less than n Write an expression for the following situations. 25. Bob weighs 7 more pounds than Jack. Jack weighs x pounds. Bob s weight: 26. Tiffany has 6 dollars less than Jessica. Jessica has x dollars. Tiffany s money: 27. The recipe calls for twice the amount of sugar than flour. There is F amount of flour in the recipe. Amount of sugar: 28. Mark s quiz grade is one more than twice Ted s quiz grade. Ted s quiz grade is x. Mark s quiz grade:

5 29. Laura paid x dollars for her prom dress. Beth paid four dollars less than Laura. Beth s prom gown price: 30. David ran the 5k in x minutes. Harry ran the same race in five minutes less than double David s time. Harry s time: 31. The beans grew K inches. The tomatoes grew 3 inches more than triple the height of the beans. Tomato height: Evaluating Expressions 32. Evaluate the expression for the given value a. (2n + 1) 2 for n = -3 b. 3(x 3) for x = 7 c. 8(x + 5)(x 2) for x = 4 d. -3x 2 for x = 2 e. x 2 for x = 6 f. (-y) 2 for y = 12 g. x + 17 for x = 12 and y = ½ y

6 h. 6x + 8y for x = 9 and y = ¼ i. x - (2x 8) for x = 10 Like Terms 33. Create a like term for the given term. j. 4x k. 13y l. 15x 2 m. 16xy n. x Combining Like Terms 34. Simplify the expression if possible. o. 7x + 8x p. 6x + 8y + 2x q. 15x 2 + 5x 2 r. 5x +2(x + 8) s. -10y + 4y t. 9(x + 5) - 7(x 3) u. 8 + (x 4)2 v. 7y + 8x + 3y + 2x

7 w. x + 2x x. x 2 + 5x 2 y. 2x + 4x + 3(x + x) z. 6y 3y 2(y 1) aa. 9y + 4y 2y + y bb. x + 5x + x (x + y) cc. 8x 3x + 2x (x 2) dd. -9(x 4) (x + 5) ee. (x + 3) + 3(-x 6) ff. 2(x y + z) -4(x y + z) 35. A group of 15 parents buys tickets to a fundraiser show and receives a group discount of $2 off the regular ticket price p. Which expression represents the total cost of the tickets, in dollars? a) 15 p + 2 b) 15 (p - 2) c) p d) p (15-2) 36. A music store sells CDs for $15 and tapes for $3. Which expression could be used to find the dollar total of the sales for an hour if the store sold 8 CDs and 5 tapes? a) (8 + 15) (5 + 3) b) (8 15) + (5 3) c) (8 3) + (5 15) d) d) (15 8) + (5 3)

8 37. There were three times as many adults as students attending a school play. If the attendance was 480, how many adults and how many students attended the play? a) 360 students b) 240 students 120 adults 240 adults c) 120 students d) 160 students 360 adults 320 adults 38. Claire has had her driver s license for three years. Bill has had his license for b fewer years than Claire. Which expression can be used to show the number of years Bill has had his driver s license? a) 3 + b b) b + 3 c) 3 - b d) b < Which situation is best modeled by the expression 25 x? a) George places x more video games on a shelf with 25 games b) Sarah has driven x miles of a 25 mile trip c) Ameilia paid $25 of an x dollar lunch she shared with Ariel d) George has 25 boxes full of x baseball cards each 40. Nine decreased by the quantity eight times a number x. a) 8x - 9 b) 9 8x c) 9x - 8 d) 8 9x 41. Four more than the quotient of 25 and y. a) 25 4 y + b) y c) 22+4 y d) y What is the coefficient of x in the expression 4y x? a) 5 b) 1 c) -1 d) 0

9 Variables & Expressions Short & Extended Constructed Response 43. A rectangle is 6 inches longer than it is wide. Write and simplify an expression for the perimeter of the rectangle in terms of the width w. 44. You and a friend worked in the school store last week. You worked 4 hours less than your friend. Let h be the number of hours your friend worked. Write an expression in simplest form that represents the total number of hours you both worked. 45. A trail mix contains peanuts, raisins, and M&Ms. In the mix, the amount of peanuts is three times the amount of M&Ms; and the amount of raisins is two times the amount of M&Ms. Let m represent the amount of M&Ms. Write and simplify an expression for the total number of pieces of food in the trail mix. 46. Write an expression that has four terms and simplifies to 16x + 5. a) Identify the like terms b) Identify the coefficients c) Identify the constant terms

10 47. A cell phone company is offering 2 different monthly plans. Each plan charges a monthly fee plus an additional cost per minute. Plan A: Plan B: $ 40 fee plus $0.45 per minute $70 fee plus $0.35 per minute a) Write an expression to represent the cost of Plan A b) Write an expression to represent the cost of Plan B c) Which plan would be least expensive for a total of 100 minutes?

11 Solving Linear Equations Answer the following question using complete sentences. 48. What are inverse operations? Name them. Inverse Operations 49. Name the inverse operation needed to solve for the variable. a. x + 9 = 17 b. y 8 = 5 c. m + 5 = 21 w d = e. 9v = -108

12 One Step Equations 50. Solve each equation. Be sure to show all work. a. n + 7 = 20 b. x + 9 = -8 c. a 15 = 27 d. y 21 = -15 e w = 92 f m = 18 m g = h. 30 = 12m i. -5m = 25

13 j. 1 t = 12 6 k. -10c = -80 l. n (-6)= 12 m x = -20 r n. 5 2 = Two Step Equations Solve x 2 = ½ (m 3) = (h + 1) = 30

14 54. -5(x + 4) = = -3y = 14y r 5 = = 16y x + 6 = 6 x = (x 1) + 2(x + 3) = 12

15 Extended Constructed Response Questions 62. The clerk at the bank desk says there is an initial charge of $50.00 to open up a bank account at the Sunny Farms Bank. He then explains that after, every account added on will cost an additional $15.50 each. The Smith Family is thinking of opening an account for the family. a. Write an equation that represents the cost to open accounts for the family members. b. What is the greatest amount of family members that could open a bank account without exceeding a fee of $500? c. How much money would it cost if Mom Smith, Dad Smith, Sister Smith, and Brother Smith want to open an account, and Mom Smith has a special discount coupon of 15% off the final price?

16 63. The Rainbow Phone Service Company has a monthly fee of $100 and an additional charge of $6.00 for every data one goes over a month. The Cellular Phone Service Company has a monthly fee of $80 and an additional charge of $10.00 for every data one goes over. The Gomez family is deciding which of these two phone providers to subscribe to. a. Write an equation that represents the cost of each phone company s monthly fee. Let p = cost. b. For what number of data over will the total monthly fee for both companies be the same? c. The Gomez family s daughter went over 6 data last month. Which phone service will save the Gomez family the more if the daughter repeats this bad habit next month?

17 Geometry and Algebra Connection Find the value of the missing angles in the following triangles x x 65. x (x 30) 66. x 2x (x + 10)

18 Do you know the Pythagorean Theorem? It is used to find the missing side length of any right triangle. a c Formula: a 2 + b 2 = c 2 Leg 2 + Leg 2 = Hypotenuse 2 b Ex. 1: If a = 5m, b = 12m, c =? Ex. 2: If a = 10 cm, c = 15 cm, b =? a 2 + b 2 = c 2 a 2 + b 2 = c = c b 2 = = c 2, so c 2 = b 2 = = c, c = 13 m Subtr.100 from both sides to get b 2 = = 11.2, so b = 11.2 cm Find the missing side length x 8 x Is a triangle with side lengths 18, 25, and 33 a right triangle?