TO:

FROM:Ms. Attia and Ms. Mohler

You have signed up to take AP Calculus AB next school year.

Attached you will find your summer packet. This packet is meant to help you refresh all the algebra you will need to succeed in AB Calculus. Completed packetsare due the FIRST DAY OF SCHOOL. If you lose this copy, go to the Wakefield website for another copy.

We will work these problems during SUMMER BRIDGE. So we encourage you to attend the AP Summer Bridge Program .

We are looking forward to a wonderful year with you! If you need to reach us over the summer you can email Ms. Mohler at or Ms. Attia at .

Have a great summer!

Ms. Attia and Ms. Mohler

AB Calculus Summer Assignment - 2015Name:______

These problems are representative of the kinds of algebra, geometry, and pre-calculus topics that you must be proficient at in order to be successful in calculus. This packet is due THE FIRST DAY OF SCHOOL. We will be happy to help you with this during Summer Bridge.

  1. Simplify:

Simplify each of the following. That includes distributing and adding like terms, rationalizing the denominator, simplifying fractions by factoring and canceling common factors, simplifying complex fractions (combine to single numerator and single denominator before multiplying by reciprocal!), simplifying radicals, and simplifying using the properties of exponents.

1) / 2) Rationalize denominator:

3) / 4)
5a)
b) / 6a)
b)
7) / 8)
  1. Evaluate:

Evaluate each of the following.

9) / 10a)
b)
11a)
b)
c) / 12a)
b)
c)
13) If , find / 14) If , find
15) If , find / 16) If , find
  1. Solve Equations:

Solve each of the following. Check all solutions! (Remember extraneous solutions?)

Try factoring polynomials first. Use quadratic formula or graph zeros if necessary.

17) / 18) / 19)
20) / 21) / 22)

Solve Equations - continued:

23) / 24) / 25)
26) / 27) / 28)
29) / 30) / 31)
32)
Graph zeros, use synthetic division to depress polynomial and solve last 2 zeros. / 33)
34) / 35) / 36)
37) / 38) / 39)

Solve Equations - continued:

40) / 41) / 42)
43) / 44) / 45)
46) / 47) / 48)
  1. Solve Inequalities:

Rewrite as one of two types of compound inequalities. Solve and graph on number line.

49)
Graph: / 50)
Graph:
51)
Graph: / 52)
Graph:
  1. Solve Systems:

Solve each system of equations. Check by graphing with calculator.

53) / 54)
55) / 56) Use calculator & round solution to 3 decimal places.

  1. Modeling:

Write an equation for the function that models the given information.

57)Write the point-slope form equation for a line that has a slope of 3 and passes through the point (-2, 5) / 58) Write a quadratic equation for a parabola that has a vertex at (2, -4) and passes through the point (4, 8)
59) Write the equation of a sinusoid that has an amplitude of 5, a period of , and passes through the point / 60) Write a model for a quantity that grows exponentially. It has an initial quantity of 10 and passes through the point (3, 1250).
  1. Functions:

Sketch a graph of #61 and 63 by graphing the parent function (with dashed line) and then using transformations to draw the given function. Identify the domain and range, asymptotes (label on the graph), the intervals where the function is increasing and the end behavior (both ends!) of each function.

61)
/ 62)
63)
/ 64)
65)
/ 66) Make your own axes with scale!

Functions – continued:

67)
/ 68)

  1. Area:

Find the area of each figure. These require the area formulas that you are expected to know. (There is NO formula sheet for the AP exam!)

69)
/ 70)

71)
/ 72)


  1. Slope:

73) Find the slope between the points (-4, 9) and (2, 4).
74) Estimate the slope at given the table of values.
/ 0 / 2 / 5 / 6 / 10
/ 4 / 7 / 12 / 12 / 15
  1. Know thy unit circle!

Complete the following unit circle. Show both degrees and radians for angle measures and fill in the ordered pairs as trigonometric ratios.

1