Summer Review Packet 10

Name: _______________________________________________________

AP CALCULUS AB 2008 - SUMMER REVIEW PACKET

Sunlake High School

AP Calculus AB Summer Review Packet

The problems in this packet are intended to review what you should already know from previous classes, not to teach you new information. The skills selected are those frequently used in calculus. You should attempt every problem. Spread the work out over the summer. If you get stuck you might try an algebra 2 or precalculus review book. You may also email me, Mrs. Marotte at [email protected], type APCALC in the subject line and please identify yourself by name in the email. This is due the first day of class. 1.

Write an equation of the line a. with a slope of 2 and a y-intercept of -3 b. with a slope of -2/3 and passing through (-1,4) c. passing through (3,5) and (6,2) d. parallel to 2x – 4y = 8 passing through the point (1, -2). e. perpendicular to 2x – 4y = 8 passing through the point (1, -2). h. which is the perpendicular bisector of the line segment joining (2,6) and (8,0)

2.

Simplify the following:

x3 a. −5 x 3.

€ 4.

x2 − 4x − 5 b. 2 x + 2x + 1

2 € x −2 a. = x +1 2

1€ c. +x=4 x

€ b. x − 9x + 9 = 0 2

(x −1)

e.

1 3

x x

3 5

€ d.

e.

x −1 −

Graph without a calculator: a) y = (x − 3) + € 2

b) y = (x + 1)

e) y = ln(x − 1)

f)

g) y = 2sin x

i) y = tan x + 1

j) y = 2x − 3

k)

3

Graph and label all asymptotes of

6.

Graph (x − 2) + y = 5 and (y + 2) − x = 16.

7.

Which relations are functions?

2

2

a) xy = 3 2

2

c)

€

5.

e) x + (y − 2) = 4 8.

d.

3

Solve

2

€

x−4 c. 4−x

2

x

€

d) y = e −

h) y = cos πx

2

2

b)

c) xy = 7

f)

g) y = x + 3

Find the domain, range, and inverse of the graph.

2

2

d) x + 3y = 5

5 =0 x −1

9.

If

and

10.

Solve the following. 3

11.

2

, find

a) 4t − 12t + 8t = 0

b)

e)

f) 4e

.

c) 2x

=5

d) 2

g)

Solve algebraically .

h) 2sin x = sinx + 1; 0 ≤ x ≤ 2π

12.

Solve using matrices

.

13.

Factor 3

3

a) 3x + 192 14.

2

b) 2x − 11x + 12x + 9

d) 9x − 3x − 2

Simplify the following. a)

b)

a) i

27

c)

15.

Simplify

16.

Find each summation. a)

17.

Find the area and perimeter (or circumference) of each figure.

b) (7+3i)(5 − i)

a)

2
in


b)

b)

6
in


c)

4
ft


2
in


8
in
 18.

2

c)

7
cm
 100°
 12
ft


Find x.

7
 x


13


19.

Find the following.

a) 20.

b) cos120°

c)

d) csc60°

e)

f) cot(−135°)

Simplify. 2

a) 4sin2x cos2x

b) 1 − sec x

2

c)

2

2

d) cos x − sin x

2

e) cos x + sin x

21.

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

22.

Solve the following for the principal values of the indicated variable. a) 3cosx – 1 = 2

23.

€ 25.

sin 2 x + cos 2 x =

b)

tan 2 x + 1 =

e)

c) If log w = ½ log x + log y, then w =

b) sin0

c) tan π /2

d) cos π/4

e) sin π/2

f) sin π

g) arctan1

Solve for x. x

b) ln e = 4

c) ln x + ln x = 0

d) e

ln5

=x

e) ln 1 – ln e = x

g) ln (x + 5) = ln (x-1) – ln (x + 1)

Evaluate the limit a)

d)

g)

€

d)

Evaluate: Answer must be in radians.

f) ln 6 + ln x – ln 2 = 3

€

sin 4 x − cos 4 x =

€

-7

b) log6 (36 x 6 )

3

€

c)

€

a) log2 64 =

a) ln e = x

27.

c) tan x – 1 = 0

Solve

a) cos0 26.

2

=0

Complete the following trig identities. a)

24.

b) 2sin(2x) -

limx →3 (x 2 + 2)

limx →−2 limx →8

x−4 2 x − 2x − 8 1 x −8

limx →3

e)

limx →−3

h)

limx →5

€

€

€

(x + 3)(x − 4) (x + 3)(x + 1)

b)

x 2 + 2x − 3 x 2 + 7x + 12€

x −5 | x −5 |

€

c)

limx →25

f)

limx →2

5 −5 x − 25

x3 + 8 x+2