AP Calculus AB Summer Packet 2017

Summer Problem Packet

The following pages contain approximately 180 problems divided into the following categories: graphing, lines, factoring and simplifying, solving equations, negative and fractional exponents, trigonometry, and geometry. These are the skills that we will use most often throughout the course. It is absolutely essential to master these skills in order to have success in calculus.

Directions:

• Solve the problems on separate loose-leaf paper. Label each problem clearly. Show all of your work. Provide written explanations when needed. Draw a rectangle around your final answer. All problems should be done without the use of a calculator. Your solutions are to be handed in on the first day of class and this assignment will count as a grade. Also the answers will be posted on my webpage.

• There are other formula sheets provided on my webpage. Please memorize these formulas and make yourselves familiar of parent functions and their graphs. http://www.gmsdk12.org/APCalculusAB.aspx

Other Required Materials

1 bound composition book, 1 1” 3 ringer binder, notebook filler paper, pencil, eraser, TI-84 calculator (any model of TI-84 is acceptable).

I. GraphingDescribe the graphs of each of the following functions using only one of the following terms: line, parabola, cubic, hyperbola, semicircle.

II. Lines (Use point-slope as much as possible)

Find the equation of the line with the given properties.

III. Factoring and Simplifying

Factor each of the following completely.

Simplify each of the following expressions.

Rationalize each of the following expressions.

Factor each of the following.

Find a formula for the average rate of change of each function from x = 1 to some number x = c. Simplify as much as possible.

Simplify the following expressions.

For the following functions, find the domain and the y-intercepts.

IV. Solving Equations

Solve each of the following equations.

Find all real zeros of the following functions.

V. Negative and Fractional Exponents

Rewrite each expression with fractional exponents and simplify.

Rewrite each expression with radicals and simplify.

Rewrite and simplify each of the following so that only positive exponents are used.

VI. Trigonometry

Evaluate each of the following expressions without the use of a calculator.

Find exact solutions to each of the following equations over the interval [0,2π ) .

VII. Geometry