Back to School NIght 2nd Semester

1. Mr. Evans
 Calculus

2. Education
 B.S. in Mathematics from the
University of Texas at Austin in 1992
 M.S. in Education from Wilkes
University in 2004
 2013 Stem Fellow
 15th year here at H-H

3. Siemens STEM Fellows 2013

4. Calculus
 Functions (piece-wise)
 Polynomial Functions
 Continuity and Intermediate
Value Theorem
 Derivative
 The Chain Rule,
 General Power Rule
 Implicit Differentiation
 Related Rates
 Integration

5. Example : What dimensions for a one liter cylindrical can will
use the least amount of material?
We can minimize the material by minimizing the area.
2
2 2A r rhπ π= +
area of
ends
lateral
area
We need another
equation that
relates r and h:
2
V r hπ=
( )3
1 L 1000 cm=
2
1000 r hπ=
2
1000
h
rπ
=
2
2
10 0
2
0
2A r r
rπ
π π= + ⋅
2 2000
2A r
r
π= +
2
2000
4A r
r
π′ = −

6. Example : What dimensions for a one liter cylindrical can will
use the least amount of material?
2
2 2A r rhπ π= +
area of
ends
lateral
area
2
V r hπ=
( )3
1 L 1000 cm=
2
1000 r hπ=
2
1000
h
rπ
=
2
2
10 0
2
0
2A r r
rπ
π π= + ⋅
2 2000
2A r
r
π= +
2
2000
4A r
r
π′ = −
2
2000
0 4 r
r
π= −
2
2000
4 r
r
π=
3
2000 4 rπ=
3500
r
π
=
3
500
r
π
=
5.42 cmr ≈
( )
2
1000
5.42
h
π
≈
10.83 cmh ≈
→

7. Sample Problem
Luke and Leia are trapped inside a rectangular trash compactor
on the Death Star. The side walls are moving apart at 0.1 m/sec,
but the end walls are moving together at 0.3 m/sec. If the
volume of liquid inside the compactor is a constant 20 cubic
meters, find the rate at which the height of the liquid is changing
when the side walls are 5 m long and the end walls are 3 m long.

8. Homework Policy
 HW assigned almost every day
 Homework will be checked daily
(2 points per assignment)
 A “best effort attempt” must be made in order to
get any credit for an assignment.
 Homework = Home + Work
 Extra Help always available
 Assignments posted at
http://www.hatboro-horsham.org/hhhs

10. Grades
Quarter Grades
 Total points from
all HW, CW,
Tests and
Quizzes
Semester Grades
 1st and 2nd MP
count 40% each
 Final counts 20%

11. Test Redos
 Students are allowed to retake any test for
full credit.
 They must demonstrate that they have done
work to relearn the material.
 Test retakes will be offered on Thursdays,
students must make an appt with me to
make up a test.
 ReTests will be new tests with different
problems. Might be harder than original.

12. My Style
 Interactive,
participation
encouraged
 Lots of Demos (both in
class and online)
 Work in pairs and
groups daily
 Math need not be
boring