AP Calculus AB & AP Calculus AB/BC

Information & Summer Assignment

What you will need in class on a daily basis:

2” 3-Ring binder with dividers

Loose leaf paper

Composition Book

Pencils

Eraser

Highlighters

Graphing Calculator: TI-84 Plus CE orTI-Nspire CX

(If you are in the market for a new calculator, these are the two I recommend. However, if you already have a TI-84 Plus or TI-84 Plus Silver, you do not need to buy a new calculator. Both will be sufficient for what we will do in AP Calculus.)

What You Can Expect:

  • While some of each class period will be directed teaching, studentproblem-solving will be a key component of each day’s activities.
  • Assignments will be given on a daily basis. (Regular assignments will not be checked or collected but questions will be taken the following class day on a limited basis.)
  • 1-2 quizzesper unit.
  • You will be expected to keep up with your work and seek help from your peersin addition to seeking help from your instructor.
  • In AP Calculus you are expected to understand every concept numerically, graphically, analytically, and verbally---so you will be assessed accordingly. You cannot just be able to arrive at a numerical answer; you must be able to explain in words what the answer means.
  • Everything we do in this class is to prepare you for the AP Calculus Exam. But you have to do your part to reach that goal.
  • This course is taught as a college course. Expect it to be challenging!

Ways to Succeed in this Class:

  • Keep up with your notes on a daily basis (be sure to review them before attempting the assignment).
  • Do your homework, do your homework, do your homework! (Check the answers on ItsLearning.)
  • Form a study group early in the year and set up regular meeting times outside of school hours.
  • When you enter the room, put the assignment #’s of those problems you struggled with on the board.
  • When you come into the room, ask other students for clarification on any problems you did not understand.
  • Keep TTK’s (Things To Know) up to date from day one and study them on a regular basis.
  • Actively participate in ALL class discussions.

AP Calculus Summer Assignment

The assignment will be due Monday, August 7th. I highly recommend that you work on and complete this assignment the week before the start of school, NOT EARLY IN SUMMER. This will result in a smoother transition into this course. You will be given daily homework starting on the first day of the course. This assignment will be in addition to daily homework. It is to your benefit to complete this right before school starts.

DIRECTIONS: Each of the following questions are pre-calculus concepts. For each question give your complete work on separate paper. YOU MAY NOT USE A CALCULATOR.

  1. Simplify:
  1. Rationalize the denominator: (a) (b)
  1. Simplify: (a) (b) (c)
  1. Simplify: (a) (b) (c)
  1. Solve the following equations for the indicated variable:

(a)V = 2(ab + bc + ca) for a

(b)2x – 2yd = y + xd for d

  1. Factor completely: (a) (b) (c) (d)
  1. Find all real solutions: (a) (b) (c) (d)
  1. Without a calculator, evaluate the following:

(a) (b) (c)

(d) arctan( –1) (e) arcsin (–1) (f) arcos (–1)

  1. Solve the inequalities: (a) (b) (c)
  1. Solve: (a) (b) (c)
  1. Determine the equation of the following lines. Report your answer in point-slope form.

(a)the line through (–1, 3) and (2, –4)

(b)the line through (–1, 2) and perpendicular to the line 2x – 3y + 5 = 0

  1. State the domain of the function in interval notation:
  1. State the domain and range of the function.: (a) (b)
  1. Simplify , where: (a) (b) (c)
  1. Let . Show that . State the domain and range of f(x).
  1. Write the following functions as a piecewise function. Then sketch each graph.

(a)

(b)

(c)

  1. Graph the following piecewise functions:

(a)

(b)

(c)

  1. Given and , find:

(a)

(b)

(c)

(d)

(e)

(f)

  1. A water tank has the shape of an inverted cone (like an ice cream cone without ice cream). The tank is 10m high and has a radius of 3m at the top. If the water is 5m deep (in the middle), what is the surface area of the top of the water?
  1. Two cars start moving from the same point. One travels south at 100km/hr, the other west at 50 km/hr. How far apart are they two hours later?
  1. A kite is 100m above the ground. If there is 200m of string out, what is the angle between the string and the horizontal? (Assume the string is perfectly straight.)
  1. Study the following trig identities and natural logarithm properties

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)ln 1 = 0

(k)ln e = 1

(l)

(m)

(n)

(o)