Summer 2009 - Intro to Calculus
The Johns Hopkins University
Instructor: Mike Limarzi
Wednesday, July 15th, 2009
Name:
Midterm
Please show all of your work, and justify your answers completely. A correct answer with no work
shown does not guarantee full p
Name:
Grade:
out of 20
Intro to Calculus - Summer 2009
Instructor - Mike Limarzi
Daily Quiz 7 - Thursday, July 9, 2009
1. (5 points) Find a polynomial with real coecients that has the given roots: 1, 4 2i. Expand
completely.
2. (5 points) State the degree
Name:
Grade:
out of 20
Intro to Calculus - Summer 2009
Instructor - Mike Limarzi
Daily Quiz 8 - Monday, July 13, 2009
1. (5 points) Find all real solutions: x2/3 + 10 = 7x1/3 .
Let w = x1/3 . Now we can rewrite our equation as:
w2 7w + 10 = 0. Factoring,
Name:
Grade:
out of 20
Intro to Calculus - Summer 2009
Instructor - Mike Limarzi
Daily Quiz 8 - Monday, July 13, 2009
1. (5 points) Find all real solutions: x2/3 + 10 = 7x1/3 .
2. (5 points) Find all real solutions: |x2 x 6| = 6.
3. (5 points) Find all x-
Name:
Grade:
out of 20
Intro to Calculus - Summer 2009
Instructor - Mike Limarzi
Daily Quiz 9 - Tuesday, July 14, 2009
1. (5 points) Find the domain of
x1
. Is there a vertical asymptote or a hole when x = 1?
x2 1
x1
x1
=
.
x2 1
(x + 1)(x 1)
This means th
Name:
Grade:
out of 20
Intro to Calculus - Summer 2009
Instructor - Mike Limarzi
Daily Quiz 9 - Tuesday, July 14, 2009
1. (5 points) Find the domain of
x1
. Is there a vertical asymptote or a hole when x = 1?
x2 1
2. (5 points) Find equations of all horiz
Name:
Grade:
out of 20
Intro to Calculus - Summer 2009
Instructor - Mike Limarzi
Daily Quiz 10 - Thursday, July 16, 2009
1. (5 points) Rewrite as a sum or dierence of multiples of logarithms.
3 xy
.
ln
t4/3
2. (5 points) Rewrite as a single expression.
3
Name:
Grade:
out of 20
Intro to Calculus - Summer 2009
Instructor - Mike Limarzi
Daily Quiz 12 - Tuesday, July 21, 2009
1. (5 points) Sketch at least one cycle of the following function. Determine its period and label
key points.
y = sin(2x).
The period i
Name:
Grade:
out of 20
Intro to Calculus - Summer 2009
Instructor - Mike Limarzi
Daily Quiz 12 - Tuesday, July 21, 2009
1. (5 points) Sketch at least one cycle of the following function. Determine its period and label
key points.
y = sin(2x).
2. (5 points
Name:
Grade:
out of 20
Intro to Calculus - Summer 2009
Instructor - Mike Limarzi
Daily Quiz 7 - Thursday, July 9, 2009
1. (5 points) Find a polynomial with real coecients that has the given roots: 1, 4 2i. Expand
completely.
Since we know this function ha
Name:
Grade:
out of 20
Intro to Calculus - Summer 2009
Instructor - Mike Limarzi
Daily Quiz 6 - Wednesday, July 8, 2009
1. (5 points) Find vertex, axis of symmetry, y-intercept, x-intercepts, and intervals when function is increasing or decreasing: y = x2
Name:
Grade:
out of 20
Intro to Calculus - Summer 2009
Instructor - Mike Limarzi
Daily Quiz 2 - Wednesday, July 1, 2009
1. (5 points) Solve for x: |3x + 4| = 12.
2. (5 points) Determine the center and radius of the circle: x2 3x + y 2 + 2y = 3 .
4
3. (5 p
Name:
Grade:
out of 20
Intro to Calculus - Summer 2009
Instructor - Mike Limarzi
Daily Quiz 3 - Thursday, July 2, 2009
1. (5 points) State the quadratic formula.
Let ax2 + bx + c = 0 be a quadratic equation with a = 0. Then, the solutions to this
equation
Name:
Grade:
out of 20
Intro to Calculus - Summer 2009
Instructor - Mike Limarzi
Daily Quiz 3 - Thursday, July 2, 2009
1. (5 points) State the quadratic formula.
2. (5 points) Which of the following graphs represent functions? Check all that apply.
3. (5
Name:
Grade:
out of 20
Intro to Calculus - Summer 2009
Instructor - Mike Limarzi
Daily Quiz 4 - Monday, July 6, 2009
1. (5 points) Let f (x) = 3x2 x. Find and simplify f (x + h) f (x).
2. (5 points) State
graph with axes
x
f (x) =
x
the domain and range o
Name:
Grade:
out of 20
Intro to Calculus - Summer 2009
Instructor - Mike Limarzi
Daily Quiz 5 - Tuesday, July 7, 2009
1. (5 points) Determine if f (x) = x4 x2 + 2 is odd or even. Is it symmetric over an axis? If
so, which?
Even: f (x) = f (x).
f (x) = (x)
Name:
Grade:
out of 20
Intro to Calculus - Summer 2009
Instructor - Mike Limarzi
Daily Quiz 5 - Tuesday, July 7, 2009
1. (5 points) Determine if f (x) = x4 x2 + 2 is odd or even. Is it symmetric over an axis? If
so, which?
2. (5 points) Let f (x) = x2 and
Name:
Grade:
out of 20
Intro to Calculus - Summer 2009
Instructor - Mike Limarzi
Daily Quiz 6 - Wednesday, July 8, 2009
1. (5 points) Find vertex, axis of symmetry, y-intercept, x-intercepts, and intervals when function is increasing or decreasing: y = x2
Name:
Grade:
out of 20
Intro to Calculus - Summer 2009
Instructor - Mike Limarzi
Daily Quiz 13 - Wednesday, July 22, 2009
1. (5 points) Simplify the following expression:
(cos tan + 1)(sin 1)
.
cos2
sin
(cos cos + 1)(sin 1)
(cos tan + 1)(sin 1)
=
2
cos
c
Name:
Grade:
out of 20
Intro to Calculus - Summer 2009
Instructor - Mike Limarzi
Daily Quiz 13 - Wednesday, July 22, 2009
1. (5 points) Simplify the following expression:
(cos tan + 1)(sin 1)
.
cos2
2. (5 points) Show that the following equation is not a
Name:
Grade:
out of 20
Intro to Calculus - Summer 2009
Instructor - Mike Limarzi
Daily Quiz 14 - Thursday, July 23, 2009
1. (5 points) Use an identity to nd the exact value:
sin
.
+
3
4
Since sin(A + B ) = sin A cos B + sin B cos A, we get:
sin
+
= sin
co
Calculus III 110.202 Final Exam
Johns Hopkins University, December 11, 2009
Name:
Signature:
Circle your section number:
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9
Instructions:
1. Not including this cover page, there are 17 pages in this exam. The last
three pages are left blank