MATH 2551-G MIDTERM 1
VERSION B
SUMMER 2025
COVERS SECTIONS 12.1-12.6, 13.1-13.4, 14.1-14.2
Full name: GT ID:
Honor code statement: I will abide strictly by the Georgia Tech honor code at all times. I
will not use a calculator. I will not reference any website, application, or other CAS-enabled
service. I will not consult with my notes or anyone during this exam. I will not provide aid to
anyone else during this exam.
( ) I am initialing to the left to attest to my integrity.
Read all instructions carefully before beginning.
• Print your name and GT ID neatly above.
• You have 75 minutes to take the exam.
• You may not use aids of any kind.
• Please show your work.
Question Points
1 2
2 2
3 2
4 4
5 10
6 10
7 10
8 10
Total: 50
, MATH 2551-G Midterm 1 Version B - Page 2 of 9 June 2, 2025
For problems 1-3 choose whether each statement is true or false. If the statement is always
true, pick true. If the statement is ever false, pick false. Be sure to neatly fill in the bubble
corresponding to your answer choice.
1. (2 points) If u, v, and w are vectors in R3, then u · (v × w) = u · (w × v).
√
© TRUE FALSE
2. (2 points) If the speed of a particle is zero, its velocity must be zero.
√
TRUE © FALSE
3. (2 points) If two lines are parallel to the same plane, then these two lines must intersect.
√
© TRUE FALSE
4. (4 points) Which of the following is true of the quadric surface z = 4x2 + y2 − 2y?
© A) It is a plane, because all of its cross-sections in the x = k, y = k, and z = k
planes are straight lines.
© B) It is a sphere, because all of its cross-sections in the x = k, y = k, and z = k
planes are circles.
√
C) It is an elliptical paraboloid, because its cross-sections are ellipses
in the z = k planes and parabolas in the x = k and y = k planes.
© D) It is a hyperbolic paraboloid, because its cross-sections are hyperbolas in the
z = k planes and parabolas in the x = k and y = k planes.
© E) It is a cone, because its cross-sections are circles in the z = k planes and
straight lines in the x = k and y = k planes.
VERSION B
SUMMER 2025
COVERS SECTIONS 12.1-12.6, 13.1-13.4, 14.1-14.2
Full name: GT ID:
Honor code statement: I will abide strictly by the Georgia Tech honor code at all times. I
will not use a calculator. I will not reference any website, application, or other CAS-enabled
service. I will not consult with my notes or anyone during this exam. I will not provide aid to
anyone else during this exam.
( ) I am initialing to the left to attest to my integrity.
Read all instructions carefully before beginning.
• Print your name and GT ID neatly above.
• You have 75 minutes to take the exam.
• You may not use aids of any kind.
• Please show your work.
Question Points
1 2
2 2
3 2
4 4
5 10
6 10
7 10
8 10
Total: 50
, MATH 2551-G Midterm 1 Version B - Page 2 of 9 June 2, 2025
For problems 1-3 choose whether each statement is true or false. If the statement is always
true, pick true. If the statement is ever false, pick false. Be sure to neatly fill in the bubble
corresponding to your answer choice.
1. (2 points) If u, v, and w are vectors in R3, then u · (v × w) = u · (w × v).
√
© TRUE FALSE
2. (2 points) If the speed of a particle is zero, its velocity must be zero.
√
TRUE © FALSE
3. (2 points) If two lines are parallel to the same plane, then these two lines must intersect.
√
© TRUE FALSE
4. (4 points) Which of the following is true of the quadric surface z = 4x2 + y2 − 2y?
© A) It is a plane, because all of its cross-sections in the x = k, y = k, and z = k
planes are straight lines.
© B) It is a sphere, because all of its cross-sections in the x = k, y = k, and z = k
planes are circles.
√
C) It is an elliptical paraboloid, because its cross-sections are ellipses
in the z = k planes and parabolas in the x = k and y = k planes.
© D) It is a hyperbolic paraboloid, because its cross-sections are hyperbolas in the
z = k planes and parabolas in the x = k and y = k planes.
© E) It is a cone, because its cross-sections are circles in the z = k planes and
straight lines in the x = k and y = k planes.
