MCV4U Assignment: Derivatives of Exponential and Trigonometric Functions
Name:_______
Follow the instructions for each question on the question pages. Write your responses using proper
mathematical notation, terminology, and full sentences. Your overall grade will be a combination of the
scoring (for K,A, and T combined) on the questions and the rubric (C).
Mathematical
Notation
(ie: exponential,
trigonometric,
limit, & derivative
notation, etc)
Mathematical
terminology
(ie: exponent,
base, logarithm,
period, maximum,
minimum, critical
numbers and
points, points of
inflection, etc)
Organization
(ie: use of equal
signs, headings,
spacing, etc)
Language
Communication
Level 1
The student...
rarely uses proper
mathematical
notation in
solutions
Level 2
Level 3
Level 4
sometimes uses
proper
mathematical
notation in
solutions
usually uses
proper
mathematical
notation in
solutions
always uses
proper
mathematical
notation in
solutions
rarely uses proper
mathematical
terminology in
solutions
sometimes uses
proper
mathematical
terminology in
solutions
usually uses
proper
mathematical
terminology in
solutions
always uses
proper
mathematical
terminology in
solutions
rarely uses
headings and
descriptions to aid
clarity of solutions
sometimes uses
headings and
descriptions to aid
clarity of solutions
usually uses
headings and
descriptions to aid
clarity of solutions
always uses
headings and
descriptions to aid
clarity of solutions
rarely uses equal
signs properly in
solutions
sometimes uses
equal signs
properly in
solutions
usually uses equal
signs properly in
solutions
always uses equal
signs properly in
solutions
rarely uses full
sentences in
solutions
sometimes uses
full sentences in
solutions
usually uses full
sentences in
solutions
always uses full
sentences in
solutions
Grading:
Marks Earned:
/40 from solutions
/100 from rubric
Weighted Marks:
/80
/20
Total Grade:
MCV4U Assignment: Derivatives of Exponential and Trigonometric Functions
1. A population of deer in a specific location is given by the equation below,
population in 1000s of deer and is the time in years.
a)
Name:_______
, where
is the
What is the initial population?
/2
b)
/4
Use limit laws and your knowledge of exponential and trigonometric functions to determine
. Explain in sentences any part that does not follow directly from a limit law.
MCV4U Assignment: Derivatives of Exponential and Trigonometric Functions
c)
What does your answer for #2 represent in terms of the scenario?
/2
d)
/4
How fast is the population changing after one year?
Name:_______
MCV4U Assignment: Derivatives of Exponential and Trigonometric Functions
2. Your mark on the Calculus exam in percent,
a)
Name:_______
, depends on how many hours you study, .
If after one hour of studying your mark would be 45%, determine the value of .
/3
b)
What is your maximum mark (local max, no need to use the optimization algorithm), and how long
do you need to study to achieve that mark?
/5
c)
Relating back to the context of the question, why does it make sense for
to have a local
maximum (as opposed to having either a local minimum or no local extrema)?
/3
3. Use the curve sketching algorithm to sketch a graph of
.
/17
on the interval