IB Math Studies I Summer Assignment This assignment is due the second day of class in Fall and will be checked. A quiz will be given on this material. Everything in this assignment should be review of select skills learned in Algebra and Algebra II. Please use your time this summer wisely to make sure you have mastered the following:
• Simplifying radicals • Order of operations • Laws of Algebra (distributive law, factoring, and expansion) • Laws of Exponents • Linear Equations
Though it is not included in this packet, it is expected that students understand how to add, subtract, multiply and divide fractions. Please e-‐mail me if you have any questions over the summer: [email protected] Simplifying Radicals
1. 75
2. 36
3. 80
4. 8
5. 32
6. 64
7. 30
8. 108
9. !"!"
10. 175
Order of Operations Reminder
Simplify the expression.
11. 5 ∙ 4 + 9 −7 + 5 =
12. (−10) ÷ 2 + 3 2 + 4 ! =
13. −5! ∙ 2 ∙ 9 − 2 (−2) =
14. (– 5)! ∙ 2 ∙ 39 − 2 (−2) =
15. !!+ 5 − !
!∙ !!=
16. 2! ∙ 3 ÷ 6 − (−2) =
17. 5𝑥 − (𝑥 + 2)! =
18. 8𝑥 − 17𝑥 + 𝑥 4𝑥 2𝑥 − 𝑥! =
How do you remember order of operations … ? PEMDAS!
P Parentheses first E Exponents (i.e. powers and square roots) MD Multiplication and Division (left to right) AS Addition and Subtraction (left to right) After you have done “P” and ”E”, just go from left to right doing any “M” or “D” as you see them. Then go from left to right doing any “A” or “S”.
Laws of Algebra Factor completely.
19. 𝑥! − 9𝑥
20. 27𝑚! − 75𝑚
21. 𝑥! + 4𝑥 + 3
22. 𝑚! − 25
23. ℎ! − 25
24. 𝑥! − 3𝑥 − 54
25. 2𝑥! + 6𝑥! − 18𝑥 + 4
26. 3𝑥! + 12𝑥 + 9
27. 2𝑥! + 5𝑥 + 2
28. 4𝑥! + 8𝑥! + 4𝑥
Expand or distribute completely (don’t forget PEMDAS!).
29. 𝑥 + 3 𝑥 − 9
30. 2 𝑥! + 1 + (𝑥 + 1)
31. 5 + 𝑥 !
32. 3𝑥 𝑥! + 11
33. 5 4𝑥 + 1 − 7(4𝑥 + 1)
34. 𝑥 + 9 ! − (𝑥! + 18𝑥 + 81)
35. − 8𝑚 + 9𝑛 − 3𝑝
36. 𝑟 + 4 𝑟 − 4
Laws of Exponents Reminder (must remember these laws!!) Simplify. 37. 𝑥! × 𝑥! 38. 2!! ! 39. 𝑎𝑏! ! 40. !"!!
!
!!! 41. !
! × !!
!!! 42. !"!!!!
!" !" ! Write without negative exponents.
43. 3!! 44. 𝑥!!𝑦 45. !!
!!
Linear Equations Graph the following lines. 46. 𝑦 = !
!𝑥 + 5 47. 2𝑦 − 3 = −2𝑥 − 1
48. a. Find the slope of the line that goes through points A(−1, 5) and B(3, 1). b. What is the slope of the line that is perpendicular to the original line in part (a.)? 49. Line m and line n intersect at a point P. Find the coordinates of P. Line m: 𝑦 = −4𝑥 + 7 Line n: 𝑦 − 1 = 0.5𝑥 − 2