Summer Assignment for Students Entering August 2019
Transcript of Summer Assignment for Students Entering August 2019
Pre-AICE Mathematics 3 Summer Assignment for Students Entering August 2019
Students who are currently scheduled for Pre-AICE Mathematics 3 in the 2019 β 2020 school
year. It is important that you complete each section of problems in its entirety. The goal of this
assignment is not merely completion, but completion with excellence. These are topics and
skills that need to be mastered by the time you come to school on August 12, 2019. Students
who have not mastered these topics will experience extraordinary difficulty in Pre-AICE
Mathematics 3 as these topics will not be taught as part of that class. You are also welcome to
work with a friend, but make sure that you understand the material. During the first week of
school, we will briefly review these topics. Following the review, there will be an exam
covering this material.
IMPORTANT: This assignment is OPTIONAL. However, if you complete it properly, you will
receive 15 percent extra credit on your first exam grade.
Teacher: Matthew Preston
Email: [email protected]
If you need to email me with a question:
1.) Include your name in the email.
2.) Try to send a photo of the problem youβre working on.
3.) State clearly which part you are experiencing difficulty with.
4.) I will only be checking my email occasionally. So, please try all other avenues of getting your questions
answered first. Thank you.
Helpful Websites:
www.khanacademy.org
www.kutasoftware.com
www.learnzillion.com
www.math-drills.com
www.youtube.com
Section 1: Simplifying Expressions
Directions: Simplify each of the following expressions.
1. 4(π + 2) + 3(2π β 3) 2. 2(3π + 2) + 3(2π β 3)
3. 3π(2π β 5) β 2(3π β 3) 4. 2π(π2 + 2) + 3π(2π β 3)
5. 3π(π β 2) + 2π(3π β 2) 6. 2π(π β 3) β 3π(3π β 2)
7. π₯(π₯2 β 2π¦) + 3π₯2(π₯ + 2π¦)
8. π(π β π + π) β π(π β π + π)
9. π(π + 2π β 3π) β 2π(π β π β 3π) 10. 3π₯π¦(4π§ β 12) β 5π₯π§(2π¦ + 4)
11. 2π₯2(4π₯π¦ β 5) β 8π¦π₯3 + 9π₯2 12. 1
3(27π₯ + 18) β
2
7(28π₯ β 42)
13. π₯(π₯2 β 2π¦) β 3π₯2(π₯ + 2π¦) 14. 3π(π β 2π + 3π) β 2π(π β π β 5π)
Section 2: Graphing Linear Equations
Directions: Graph each of the following linear equations on the coordinate plane. You may use
any method you wish. However, I recommend choosing a specific method based upon the way
the equation is presented.
15. π¦ =7
2π₯ β 2
16. π¦ = β6π₯ + 3
17. π¦ = β5
18. π¦ =6
5π₯ + 1
19. π¦ =1
4π₯ + 2
20. π₯ = 5
21. π¦ =5
3π₯ 22. π¦ = β
1
3π₯ + 3
23. π¦ =1
5π₯ β 4
24. π¦ = β1
2π₯ β 2
25. π¦ = 2π₯ + 5
26. π₯ β 2π¦ = 6
27. 3π₯ β 2π¦ = β2 28. 3π₯ + 2π¦ = 4
29. π₯ + 4π¦ = 4
30. 4π₯ + π¦ = β1
31. 5π₯ + 2π¦ = β10
32. π₯ + 5π¦ = 10
Section 3: Writing Equations of Lines
Directions: Write the equation of the line that passes through the following points in slope
intercept form. Reminder: Find the slope first
33. (0,1) πππ (7,14) 34. (β13, β4) πππ (1, 4)
35. (β3,5) πππ (2, β13) 36. (11,31) πππ (25,36)
37. (β41,12) πππ (β10, β2) 38. (12,18) πππ (26,31)
39. (13, β17) πππ (β3,11) 40. (β5, β16) πππ (6,17)
41. (β4, β9) πππ (9, 18) 42. (19, β2) πππ (β4, 14)
Directions: Write the equation of each of the following lines using the given slope and point.
Write your final equation in standard form.
43. π‘βπππ’πβ: (1, 2) π ππππ = 7 44. π‘βπππ’πβ: (3, β1) π ππππ = β1
45. π‘βπππ’πβ: (β2, 5) π ππππ = β4 46. π‘βπππ’πβ: (3, 5) π ππππ =5
3
47. π‘βπππ’πβ (2, β4) π ππππ = 0 48. π‘βπππ’πβ (2, 5) π ππππ = π’ππππππππ
49. π‘βπππ’πβ (3, 1) π ππππ =1
2 50. π‘βπππ’πβ (β1, 2) π ππππ = 2
Section 4: Solving Equations
Find the solution to each of the following equations. Remember, some equations may have no
solution or infinite solutions.
51. 4(π₯ + 10) = 50 + 2π₯ 52. β12π + 39 = 11(π + 14)
53. β13π β 53 = β2(2π β 14) 54. 8 + 10(6 β 11π₯) = β54 + 12π₯
55. 5(π₯ + 10) β 6π₯ = π₯ + 66 56. β11π + 11(6π + 4) = 44 + 10π
57. 6π + 5(1 β 6π) = 2(1 β 13π) + 13 58. 3(2π₯ β 14) = β3(β13 + π₯)
59. 2(5 β 8π) β 13 = 9(1 β π) β 12 60. 8(5 + 4π) + 11 = β5(3 β 7π)
61. 7π₯ β 3π₯ = β6(π₯ + 10) + 5(β3 β 3π₯) 62. β9π + 10(π + 3) = β7(π β 10)
63. β32 β 8π = β4(2π + 8) 64. β2π₯ + 12 = β2(π₯ β 6)
65. β4(π£ β 2) = 2(β2π£ + 7) 66. 3(π β 7) = β9 + 3π
Answer Key for Selected Problems
1. 10π β 1 2. 12π β 5
3. 6π2 β 21π + 6 4. 2π3 + 6π2 β 5π
5. 9π2 β 10π 6. β7π2
7. 4π₯3 + 6π₯2π¦ β 2π₯π¦ 8. 0
9. π2 + 2π2 β 3ππ + 6ππ 10. 2π₯π¦π§ β 36π₯π¦ β 20π₯π§
11. βπ₯2 12. π₯ + 18
13. β2π₯3 β 6π₯2π¦ β 2π₯π¦ 14. 3ππ + 4ππ + 9π2 + 2π2 β 2ππ
*** Answers to #15 β 32 not included ***
33. π¦ =7
3π₯ + 1 34. π¦ =
4
7π₯ +
3
7
35. π¦ = β18
5π₯ β
29
5 36. π¦ =
5
14π₯ +
379
14
37. π¦ = β14
31π₯ β
202
31 38. π¦ =
13
14π₯ +
204
7
39. π¦ = β7
4π₯ +
23
4 40. π¦ = 3π₯ β 1
41. π¦ =27
13π₯ β
9
13 42. π¦ = β
16
23π₯ +
258
23
43. β7π₯ + π¦ = β5
44. π₯ + π¦ = 2
45. 4π₯ + π¦ = β3 46. β5
3π₯ + π¦ = 0
47. π¦ = β4 48. π₯ = 2
49. β1
2π₯ + π¦ = β
1
2 50. 2π₯ + π¦ = 4
51. 5 52. -5
53. -9 54. 1
55. -8 56. 0
57. 5 58. 9
59. 0 60. 22
61. -3 62. 5
63. All Real Numbers 64. All Real Numbers
65. No Solutions 66. No Solutions