Advanced Placement Calculus AB and AB/BC

Advanced Placement Calculus AB and AB/BC

2016-2017

Summer Assignment

Congratulations! You are enrolled in Advanced Placement Calculus AB or AB/BC for the next school year. This course will count as both a math credit at Northeast as well as college credit if you pass the national AP Calculus AB/BC exam on May 9, 2017.

Remember that by enrolling in the course, you are making a commitment to excellence in daily work. Successful students in AP Calculus possess the following characteristics:

• Daily review of the new content material taught in class
• Diligent completion of homework on a daily basis
• Participation in study groups or working with a study buddy
• Understanding concepts vs. cramming details
• Proficient in translating mathematical expressions into necessary and sufficient justifications

The problems in this packet are designed to help you review topics from previous mathematics courses that are important to your success in AP Calculus AB/BC. DO ALL PROBLEMS WITHOUT A CALCULATOR. Show all work that leads to each solution. You may use your notes, go online and search review videos, etc., but you must do all the work on your own. All work should be completed and ready to turn in on the first day of school. This will be part of your first quarter grade. You will have a quiz on this material the first week that we return to school. The entire packet should take less than 3 hours of your time this summer. I would recommend not starting too early in the summer as you need to remember the material for your quiz.

If you have any questions, please email us at or

We look forward to working with you next year!

J. Lebowitz and C.Braun

I. Simplify. Show the work that leads to your answer.

1. 2. 3.

II. Complete the following.

4. 5. 6.

7. 8. 9.

10. 11.

III. Simplify each expression (Show your work.)

12. 13. 14.

15. 16. 17.

IV. Given ,determine each of the following:

18. 19. 20.

21. 22. 23.

V. Simplify (remember…no calculators).

24. 25. 26.

27. 28. 29.

30. 31. 32.

33. 34. 35.

VI. Using point-slope form , write an equation for each line described below.

36. slope , containing the point (2,3)37. containing the points (1, -3) and (-5,2)

38. slope 0, containing the point (4,3)39. Perpendicular to the line in #36 containing the point (3, 4)

VII. For each function, determine its domain and range (remember…no calculators).

Function Domain Range

40. ______

41. ______

42. ______

43. ______

VIII. Solve for x, show your work.

44. 45. 46.

47. 48. 49.

50.

IX. Graph each function and label the axes with an appropriate scale.

1. 2.

3. 4.

5. 6.

X. Solve the following for all real values of x.

1. 2. 3.

4. 5.

XI. Trigonometry Review

6. A 20 foot ladder rests against a building 15 feet from the floor. How far does the ladder extend from the base of the wall? What angle does the ladder make with the ground?

Solve the following for the principal values of the indicated variable.

7. 3cosx – 1 = 28. 2sin(2x) -= 09. tan2x – 1 = 0

Complete the following trig identities.

10. 11. 12.

13. 14. 15.

Find the length of the missing side. Leave answers in simplified radical form.

16. 17.18.

XII. Determine whether the functions represent even functions, odd functions or neither.

1. 2. 3. 4.

5. 6. 7. 8.

Determine whether the following functions are even, odd, or neither. Show your work.

9. f(x) = x5 – x10. f(x) = x6- 8x2 + 411. f(x) = 3x3 – 1

XIII. Find the average rate of change (slope) for the following functions on the indicated intervals.

1. f(x) = x3 -2x; [0, 4] 2. f(x) = ; [4, 25]

3. A car travels 420 miles in a period of 210 minutes. Find the average velocity of the car in miles per hour over this time period,

4. On January 1st 2003, the value of a stock was $135 a share. By December 1st 2003, the value of the stock had fallen to $38 a share. What is the average rate of change in the value of the stock in dollars per month?

5. In 1984, the Fizzy Cola company sold 23 million gallons of soda. By 2003, the company was selling 127 million gallons of soda. What is the average rate of change in the number of gallons of soda per year.

6. During a recent trip to the store, a car's velocity went from 0 to 60 mph in 20 seconds. What is the average acceleration of the car in mile per hour per hour?

XIV. Complete the Unit Circle. You must have this memorized upon return to school. Fill in the Sine, Cosine, Radian, and Degree measures.