Name: 8 th grade Teacher: Algebra 2 Honors Summer Packet Wethersfield High School Home of the EAGLES Welcome to Wethersfield High School! Your Algebra 2 teacher for next year is either Mrs. Belanger (Shouldice) or Mr. Weber. We are very excited to meet you and share our love for mathematics. In order for us to assess your skills and to better understand what you may need some extra help with; we have developed this summer math packet. This packet contains topics that you are expected to have mastered prior to entering Algebra 2 Honors. We want you to use this assignment to practice these skills. You are encouraged to watch videos to review concepts since we will not be reviewing this material in class. If you need some assistance in solving these problems, Khan Academy www.khanacademy.com, is an excellent resource for reviewing these topics. Additionally, you can search Google for videos and extra practice problems. This assignment should be completed independently. Please show all of your work. If you need more space, please attach your scrap paper, so we can see how you solved the problems and correct mistakes if necessary. This packet is due the first day of class. You will be assessed on your knowledge and understanding of these foundational Algebra skills during the second and third weeks of school. If you have any questions, please contact Mrs. Belanger (Shouldice) at sshouldice@wethersfield.me or leave a voicemail message at 860-571-8200, extension 1775. Happy Summer! We are looking forward to meeting you in the fall! We strongly recommended having a graphing calculator. The recommended calculator is the TI 84 Plus CE.
Part 1: Order of Operations Complete the following questions without a calculator. 1) Graph the numbers on a number line. Then write the numbers in increasing order. 0, 2, 2, π, 6, 6 5 Evaluate the expression. 2) 3 6 2 12 3) 1 + 2(7 10) 2 4) 6(3) 2 5) 6 2 6) ( 6) 2 7) ( 5) 3 8) (4 + 3)( 1 + 5) 2 9) ( 8 + 6) (3 1) 2 Evaluate the expression for the given values of the variables. 10) 3ab 2 + 5a 2 b 1, when a = 2 and b = 2 11) 7x + 3y 3 when x = 6 and y = 2 12) (m+n) 2 3 when m = 1 m+n and n = 3 2 2 13) 4 ( a b ) + 3a 2b when a = 4 and b = 1 2 Simplify the expression. 14) 7y 2x + 5x 3y + 2x 15) 4(3 x) + 5(x 6) 16) 6x 2 3x + 5x 2 + 2x 17) 2(x 2 + x) 5(x 2 4x) 18) (3x + 2) 2 4
Translate the equation from words into symbols. 19) The sum of a number x and 8 is less than 12. 20) The product of 15 and a number y is equal to 8. 21) Five less than a number x equals 15. 22) The difference of 12 and a number x is greater than 3. Part 2: Solving Linear Equations Solve the equation. Check your solution. 23) 4(3 x) + 6 = 2(x 3) 24) 3(1 x) 3 + x = 8 25) 3x + 2 = 3(5 + x) 26) 1 5 (5 x 10) = 4(x + 3) 27) 2 (3x + 6 ) = 1 (5x 1) 28) 5x + 2 = 2(2x + 1) + x 2 3 5 5 Solve (rewrite) the equation for y. 29) 5x y = 10 30) x + 4y = 8 31) 2x = 3y + 9 Answer the following application problems. 32) Jade is charged $35 for her cell phone plan plus $0.75 per text. If her total bill for the month of September was $308, how many texts did she send? 33) The ratio of students to faculty members in a certain high school is 23:5. If there are 80 faculty members, how many students are there? 34) At Fitness Fun you pay $150 for the membership plus $5 per visit. At Lazy Fitness you pays $270 for the membership and $2 per visit. In how many visits will it take for the cost of the two health clubs to be the same?
Part 3: Solving Linear Inequalities Solve the inequality. Graph your solution, if possible. 35) 4 2x > x + 1 36) 5x 7 7x 6 37) 5 1 2 x 1 8 38) 2x + 7 < 2(x 3) 39) 5 4 1 6 x 3 2 40) 5(4 x) 4x + 20 x 41) 1 2x < 3 or 3 x > 5 42) 4 < 3(x + 2) 1 2 Part 4: Graphing Linear Functions Find the slope of the line passing through the given points. 43) (6, 3), ( 4, 1) 44) ( 5, 3), ( 7, 6) 45) ( 1, 6), ( 1, 7) 46) ( 1, 1 3 ), (3, 2 3 ) 47) ( 3 5, 3), ( 6 5, 0) Find the x and y-intercepts for the given linear function. 48) 3x + 4y = 12 49) 2x y + 8 = 0 50) 2y 3x = 5
Graph the following. Identify the x- and y-intercepts. 51) y = 3x + 5 52) y = 3 53) y = 1 2 x 7 54) x = 4 55) 2x + 5y = 10 56) y < 2 3 x + 2 57) 4x 3y > 12 Part 5: Writing Equations of Linear Functions Write an equation of the line using the given information. 58) m = 3 2, b = 12 59) m = 4, passing through ( 3, 12)
Write an equation of the line passing through the given points. 60) ( 5, 3), (2, 2) 61) (3, 8), ( 1, 8) Part 6: Systems of Equations and Inequalities Solve the system using either substitution or elimination. x = 2y + 11 62) { 7x 2y = 13 63) { x 3y = 8 2x + 3y = 7 64) { x 3y = 18 x + 3y = 12 65) { 2x + 3y = 12 3x 4y = 1 You are expected to be able to do all of the problems from sections 1-6. Sections 7 and 8 you did in Algebra 1, but we will be reviewing in class. We would like to see what you remember.
You may need to look up the properties of exponents, since Part 7: Properties of Exponents these are easy to confuse. Simplify the expression completely. (One expression and no negative exponents) 66) 9 6 (9 2 ) 4 67) ( 2 3y 68) 6 x 3)6 y 2 69) (xy) 4 xy 1 70) 10x 3 y 5 2x 4 y 2 71) y 10 20x 14 2x 3 xy 6 y 3 Part 8: Factoring Polynomials Factor the expression completely. 72) 4x 3 + 24x 2 36x 73) x 2 + 6x 27 74) x 2 14x 72 75) 2x 2 + 7x + 3 76) 3x 2 + 32x 11 77) 5x 2 + 5x 10 78) x 2 + 4x + 4 79) x 2 + 2x 1 80) 4x 6 30x 5 + 36x 4 81) 6x 3 16x 2 + 21x 56 82) 28x 3 + 16x 2 21x 12 83) 4x 2 81 84) 18x 2 2