Concepts of Calculus for Middle Level Teachers
Homework List
Unless otherwise indicated, all problems are taken from Calculus Connections, by
Harcharras & Mitrea.
PS 0: Linear Functions and Polynomials Revisited
PS 1: Limits
PS 2: Average Rate of Change
p. 114-115 # 1, 2, 3
p. 115-116 Classroom Discussion 3.1.2 # 1, 2
p. 117 # 2
p. 78 – 79 #19, 20, 21abc
p. 81 # 4
PS 3: The Slope Function
PS 4: Instantaneous Rate of Change and the Derivative
p. 123 Classroom Discussion 3.2.2 # 5
PS 5: Derivatives of Polynomials
p. 127 # 1, 2, 3, 4
p. 127 # 6 (and sketch both the curve and the tangent line)
p. 136 # 4 (Habits of Mind)
p. 137 # 5
PS 6: Understanding Derivatives
p. 124 Classroom Discussion 3.2.4 #1-7, 9
p. 127 # 9
p. 133 # 1 (first read all parts of the problem to sketch the picture for part e, then
work parts a, b and finish part e).
p. 134 # 2 (read section 3.3 to learn about acceleration)
PS 7: Derivatives of Exponential Functions
p. 176-177 Classroom Connections 4.3.1 Paper Folding (also estimate how many
times you would have to fold the paper so that the folded paper would reach
the sun; the distance to the sun is 92,955,820.5 miles and the thickness of the
paper is .004 inches)
p. 179 Classroom Discussion 4.3.2 Exponential Versus Linear # 1-5
p. 182 – 184 Classroom Connection 4.3.2 Savings Accounts
p. 189 #7
Handout: Differences and Derivatives
PS 8: Roots of Polynomials
p 134 #4
PS 9: Increasing and Decreasing
p. 129 #12 (Habits of Mind)
PS 10: Maximums and Minimums
For this section you should take note of the summary of steps on page 163.
p. 153 -155 Classroom Discussion 4.1.1 # 1- 5 (you will need to use graph paper)
p. 156 # 2, 3
p. 161 # 1
p. 164 # 7, 8 (for #8 note that profit = revenue – production cost)
p. 165-166 # 9, 13 (use the graph of the cost function to minimize it)
Handout: Regression Lines (Habits of Mind)
Handout: Making a Can (Habits of Mind)
PS 11: Velocity Graphs
PS 12: Area under the Curve
p. 218 Classroom Connection 6.2.2 Area of a Foot. Here are special instructions:
a) Ask Michelle and Kristie for a copy of the foot from page 219.
b) Work problems #1 and #2 from page 218.
c) The error is the difference between the actual area and the
approximation to the area. The magnitude of the error is the
absolute value of the error. So, as an example, if the actual area is
73 and your estimate is 78, then the magnitude of the error is 5
square units. Using your answers to #1 and #2, find an upper
bound for the magnitude of the error in approximating the actual
area of the foot by either of your estimates; that is, find a number
that is at least as large as the magnitude of the error.
d) How can you use your answers to #1 and #2 to find a better
estimate of the area of the foot?
p. 235 # 1abc
Also write each using summation notation. The notation Rn and Ln stand
for right-hand and left-hand sums, respectively, with n rectangles. For
part c, determine Rn and Ln only for n=100, 200, 400, using the calculator
instructions provided. For part #1d, write the first three decimal places of
A, the actual area, based on your results from part c.
p. 271 # 13, 14
PS 13: Definite Integrals
p. 271 #35
PS 14: Distance and Velocity
p. 82 #5 – 8, also estimate the distance traveled by the car
PS 15: Anti-derivatives of Polynomials
p. 196 # 1-22, 25, 26 (Note rules of integration 1-5 identified on page 196.)
p. 195 Classroom Discussion 5.1.8: Motion and Antiderivatives (Habits of Mind)
Note that h' ' ( t ) denotes the second derivative of h, and represents
acceleration.
p. 197 #32
PS 16: Area Functions
PS 17: Fundamental Theorem of Calculus
p. 239 – 240 # 1, 2, 3 (You do not need to reference Section 6.1 in #1, 2, this
simply refers to standard area formulas in geometry.)
Read Example on pp 241-242, and determine the area bounded by the graphs of
y  x 2 , y = 9, y = 0 and x = 5. Can you write an integral(s) to represent
this area?
pp. 242 – 244, Classroom Discussion 6.3.2 # 1, 2, 3, 4ab
p. 244 # 7, 9, 10, 11
p. 259 Classroom Discussion 6.5.1 # 2e, 3abd
p. 261 # 2, 3
PS 18: Using your Calculator to Compute Integrals
PS 19: Applications