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BRUNSWICK HIGH SCHOOL SUMMER MATH PROGRAM **Small Group Math Classes** Brunswick High School has reinstated a summer math curriculum for students Math 9, Math 10, Math 11/12 for the 2014-2015 school year. Goal The goal of the summer math program is to help students retain the concepts they learned, which are either lost or reduced over the summer months. Math skills require use in order to be mastered and retained. The topics that were included are chosen because they contain the skills necessary and important to the curriculum. With this in mind, it is our goal that students participating in this program will maintain critical math concepts over the summer months. Instructions The review assignments will be due by the first day of school for a homework grade. Students will be given an opportunity to score their work and ask questions. Assessments will be used to allow students to demonstrate their knowledge of the material they worked on over the summer months. The assessments will be taken for a grade in the first quarter in the form of a single test. Resources Students are allowed to form study groups and receive assistance from peers and parents, but it is understood that each student should do his or her own work and is responsible for understanding the topics on his or her own. Digital resources are also allowed as there are many online math tutorials that are available. Each section has a website that you can go to for additional help. Other websites you may find useful include: • purplemath.com • khanacademy.org Summer Review For Students Entering Math 9 Review of Number Sense Name: Part I: Patterns & Graphing Find the next three terms in each sequence. 1. 18, 32, 46, 60, 74, … 2. 100, 94, 88, 82, 76, … 3. 14, 21, 28, 35, 42, … 4. 1, 2.5, 4, 5.5, 7, … 5. 1, 4, 9, 16, 25, … 6. 2, 5, 10, 17, 26, … Graph each point and label it with the appropriate letter. On the line next to the point write the quadrant or axis where the point lies. (I, II, III, IV, x-axis, y-axis) 7. A (3, -3) _____________ 8. B (0, -1) ______________ 9. C (-2, -4) ____________ 10. D (4, 0) _____________ 11. E (-1, 6) _____________ Determine the quadrant and coordinates for points A, B, C, D. 12. A ___________________ 8 13. B ___________________ 6 4 14. C ___________________ 15. D ___________________ 2 -­‐8 -­‐6 -­‐4 -­‐2 -­‐2 -­‐4 -­‐6 -­‐8 2 4 6 8 Make an x-y chart for each equation, using 1, 2, and 3as the values for x. Then draw a graph by plotting your points to determine if the equation represents a linear pattern. 16. y = 2x - 4 X Y 17. y = 5x - 1 X Y Part 2: Operations with Real Numbers Use the Order of Operations to evaluate each expression. 1. 2. 3. 4. 5. (7 + 32) – 2 · 4 187 – 34 ÷ 17 42 · 2 + [7 – (32 – 5)] 3(2 + 7 – 8) + 16 4[(3 + 2 · 3) – 5] + 7 Perform the indicated operation. 6. 7. 8. 9. -39 + 68 -23 + (-25) 9 – (-15) -23 – (-72) 10. 11. 12. 13. (-12)(-5) 54 ÷ (-18) 45 [8 + (-8)] (-3)(4 – 7) ADDING AND SUBTRACTING WITH LIKE DENOMINATORS 1 3 4 (1) Add + = numerators 7 7 7 (2) Keep denominator MULTIPLYING FRACTIONS 2 4 8 4 (1) Multiply = = across top and 3 6 18 9 across bottom (2) Reduce Perform the indicated operation. 14. 15. ! ! ! ! + ! 18. ! + − ! ! ! 16. − ! − ! ! ! 19. 9 ! 17. − ! + − ! 20. !" ! 21. − ! ! ! ! ! ! ! ÷ −3 ÷ !" ! ! Combine Like Terms Add like terms with the same variable & exponent Distribute Multiply outside term by every part inside ( ) Simplify the expressions. (2x + 3) + (5x – 6) = (2x + 5x) + (3 – 6) = 7x – 3 (4d – 2) – (5d – 3) = (4d – 5d) + [-2 –(-3)] = -1d + ( -2 + 3) = -d + 1 2(3x – 6) = 2· 3x – 2 · 6 = 6x – 12 3x (2x – 4) = 3x · 2x – 3x · 4 = 6x2 – 12x 8𝑥 − 12 8𝑥 12 = − = 2𝑥 − 3 4 4 4 22. (3x + 4) + (2x – 1) 23. (4a + 3b) – (2a + 5b) 24. (-4x + 3) – (-6x + 3) 25. (2q + 3) – (-4q + 5) + (6q – 7) 26. 8(5x -9) 27. 3x(-5x – 4) 28. (5x – 7) – 3(2x – 1) 29. 30. !! ! !! ! !"!!!" !" Part 3: Solving Equations CHECK: Solve. 1. 5x + 9 = 39 2. 6 – 2d = 42 ! 3. 15 = ! – 2 4. 9p + 20 = -7 5. 5.2 + 1.3x = -1.3 6. ! !" – 5 = -17