Math 2D Section A Midterm Practice Exam
Spring 2025
Name of student:
Problem Score
1
2
3
4
5
Total
Calculators and any notes are NOT allowed during the exam. Any violations of the UCI Code
of Student Conduct will be reported. Please make sure that your answers are legible.
1
, Problem 1. (20 points) True or false (No justification needed):
1
(a) lim(x,y)→(0,0) xy sin x2 +y 2
does not exist.
(b) Two distinct lines in R3 either intersect at one point or are parallel.
(c) proj⃗a ⃗b is always parallel to ⃗a.
(d) There is a unique plane in R3 containing the points (1, 2, 1), (2, 3, 0), and (4, 5, −2).
(e) In polar coordinates, the point (r, θ) = (−100, π6 ) is the same as (r, θ) = (100, 7π
6
).
2
Spring 2025
Name of student:
Problem Score
1
2
3
4
5
Total
Calculators and any notes are NOT allowed during the exam. Any violations of the UCI Code
of Student Conduct will be reported. Please make sure that your answers are legible.
1
, Problem 1. (20 points) True or false (No justification needed):
1
(a) lim(x,y)→(0,0) xy sin x2 +y 2
does not exist.
(b) Two distinct lines in R3 either intersect at one point or are parallel.
(c) proj⃗a ⃗b is always parallel to ⃗a.
(d) There is a unique plane in R3 containing the points (1, 2, 1), (2, 3, 0), and (4, 5, −2).
(e) In polar coordinates, the point (r, θ) = (−100, π6 ) is the same as (r, θ) = (100, 7π
6
).
2
