Center for Academic Resources in Engineering (CARE)
Peer Exam Review Session
Math 241 − Calculus III
Midterm 1 Worksheet
The problems in this review are designed to help prepare you for your upcoming exam. Questions pertain
to material covered in the course and are intended to reflect the topics likely to appear in the exam. Keep
in mind that this worksheet was created by CARE tutors, and while it is thorough, it is not comprehensive.
In addition to exam review sessions, CARE also hosts regularly scheduled tutoring hours.
Tutors are available to answer questions, review problems, and help you feel prepared for your
exam during these times:
Session 1: Feb. 13, 5-7pm Aditya, Jesse, Sean
Session 2: Feb. 14, 5-7pm Anjali, David, Nidhi
Can’t make it to a session? Here’s our schedule by course:
https://care.grainger.illinois.edu/tutoring/schedule-by-subject
Solutions will be available on our website after the last review session that we host, as well as
posted in the queue during the session.
Step-by-step login for exam review session:
1. Log into Queue @ Illinois
2. Click “New Question”
3. Add your NetID and Name
4. Press “Add to Queue”
Good luck with your exam!
, Math 241 − Calculus III Midterm 1 Exam Review
1. Find →u × →v if →u = ⟨3, −4, 1⟩ and →v = ⟨5, 2, −6⟩
2. Find an equation for the plane that passes through the point P = (1, 2, 3) and contains the line L
given by the parametric equation:
x(t) = 1 − 3t y(t) = 3
for −∞ < t < ∞ z(t) = 6 + 2t
3. For each equation below, write the corresponding letter in the box next to the picture of the surface
it describes
(A) x2 + y2 − z2 + 1 = 0 (B) 4x2 + y2 + 4z2 − 1 = 0
2 of 4
, Math 241 − Calculus III Midterm 1 Exam Review
4. Consider two points A and B.
A = (0, 7, 2)
B = (1, 2, 0)
(a) Find the vector that represents the displacement between the points (vector drawn from A to B)
(b) What is the projection of this vector onto →r = ⟨5, −2, 7⟩?
(c) What is the projection of the vector from part (a) onto the plane represented by the equation
5x − 2y + 7z = 10
3 of 4
Peer Exam Review Session
Math 241 − Calculus III
Midterm 1 Worksheet
The problems in this review are designed to help prepare you for your upcoming exam. Questions pertain
to material covered in the course and are intended to reflect the topics likely to appear in the exam. Keep
in mind that this worksheet was created by CARE tutors, and while it is thorough, it is not comprehensive.
In addition to exam review sessions, CARE also hosts regularly scheduled tutoring hours.
Tutors are available to answer questions, review problems, and help you feel prepared for your
exam during these times:
Session 1: Feb. 13, 5-7pm Aditya, Jesse, Sean
Session 2: Feb. 14, 5-7pm Anjali, David, Nidhi
Can’t make it to a session? Here’s our schedule by course:
https://care.grainger.illinois.edu/tutoring/schedule-by-subject
Solutions will be available on our website after the last review session that we host, as well as
posted in the queue during the session.
Step-by-step login for exam review session:
1. Log into Queue @ Illinois
2. Click “New Question”
3. Add your NetID and Name
4. Press “Add to Queue”
Good luck with your exam!
, Math 241 − Calculus III Midterm 1 Exam Review
1. Find →u × →v if →u = ⟨3, −4, 1⟩ and →v = ⟨5, 2, −6⟩
2. Find an equation for the plane that passes through the point P = (1, 2, 3) and contains the line L
given by the parametric equation:
x(t) = 1 − 3t y(t) = 3
for −∞ < t < ∞ z(t) = 6 + 2t
3. For each equation below, write the corresponding letter in the box next to the picture of the surface
it describes
(A) x2 + y2 − z2 + 1 = 0 (B) 4x2 + y2 + 4z2 − 1 = 0
2 of 4
, Math 241 − Calculus III Midterm 1 Exam Review
4. Consider two points A and B.
A = (0, 7, 2)
B = (1, 2, 0)
(a) Find the vector that represents the displacement between the points (vector drawn from A to B)
(b) What is the projection of this vector onto →r = ⟨5, −2, 7⟩?
(c) What is the projection of the vector from part (a) onto the plane represented by the equation
5x − 2y + 7z = 10
3 of 4
