Math 200 T01 Instructor: T. Thompson
Summer 2026 Midterm 1 VA
June 3 Time Limit: 45 Minutes
• DO NOT open the exam booklet until you are told to begin. Write your name and
student number above and read the instructions below. This exam is out of 20 points.
• Cell phones and headphones are not allowed on you. Put your cell phones turned off and
your headphones in your backpack. If you have your cell phone or headphones on your body (in
your pocket, et cetera), you will receive a zero.
• The only approved calculator is the Sharp EL-510 R models. All other calculators will be
confiscated.
• There is a bubble sheet at the back of the exam. Do not rip it out. Circle your answers to
the multiple choice in the booklet AND fill in your answer at the back of the exam. No part marks
are given for multiple choice.
• Use the method requested. There may be more than one way to solve a problem, but if you’re
asked to use a certain method then you must do so. If you are not asked to use a certain method,
use any method in the course.
• Organize your work in a reasonably neat and coherent way in the space provided below each
question. Work scattered over a page without a clear ordering will receive little credit. Mysterious
answers will not receive full credit.
, Math 200 T01 Midterm 1 June 3
Multiple Choice
Recommended Total Time: 15 minutes; Average: 3 minutes 45 seconds per question
Read all directions carefully. Circle your answers to the question below AND shade your
answer on the bubble sheet at the back of the exam. Do not rip out the bubble sheet.
1. (2 points) Determine the radius of the sphere
x2 + y 2 + z 2 − 4x + 6y − 8z + 4 = 0
(A) 1; (B) 3; (C) 5; (D) 7; (E) 9
Complete the square in each variable:
x² − 4x = (x − 2)² − 4; y² + 6y = (y + 3)² − 9;
z² − 8z = (z − 4)² − 16.
(x − 2)² + (y + 3)² + (z − 4)² = 4 + 9 + 16 − 4 = 25.
Standard sphere form: (x − h)² + (y − k)² + (z − l)² = r².
Radius: r = √25 = 5. Answer: (C).
2. (2 points) Consider the quadric surface with cross sections given below
y z z
x y x
z = 1 x = 0 y = 0
Determine the equation of the quadric surface which best corresponds to these cross sections.
(A) z = x2 + y 2 ; (B) z = y 2 − x2 ; (C) z 2 = x2 + y 2 ; (D) x2 + y 2 − z 2 = 1;
(E) z 2 − x2 − y 2 = 1
At x = 0: z = y²; the yz-section opens upward.
At y = 0: z = −x²; the xz-section opens downward.
Thus z = y² − x²; at z = 1, y² − x² = 1 (a hyperbola).
All three sections match the diagrams. Answer: (B).
Summer 2026 Midterm 1 VA
June 3 Time Limit: 45 Minutes
• DO NOT open the exam booklet until you are told to begin. Write your name and
student number above and read the instructions below. This exam is out of 20 points.
• Cell phones and headphones are not allowed on you. Put your cell phones turned off and
your headphones in your backpack. If you have your cell phone or headphones on your body (in
your pocket, et cetera), you will receive a zero.
• The only approved calculator is the Sharp EL-510 R models. All other calculators will be
confiscated.
• There is a bubble sheet at the back of the exam. Do not rip it out. Circle your answers to
the multiple choice in the booklet AND fill in your answer at the back of the exam. No part marks
are given for multiple choice.
• Use the method requested. There may be more than one way to solve a problem, but if you’re
asked to use a certain method then you must do so. If you are not asked to use a certain method,
use any method in the course.
• Organize your work in a reasonably neat and coherent way in the space provided below each
question. Work scattered over a page without a clear ordering will receive little credit. Mysterious
answers will not receive full credit.
, Math 200 T01 Midterm 1 June 3
Multiple Choice
Recommended Total Time: 15 minutes; Average: 3 minutes 45 seconds per question
Read all directions carefully. Circle your answers to the question below AND shade your
answer on the bubble sheet at the back of the exam. Do not rip out the bubble sheet.
1. (2 points) Determine the radius of the sphere
x2 + y 2 + z 2 − 4x + 6y − 8z + 4 = 0
(A) 1; (B) 3; (C) 5; (D) 7; (E) 9
Complete the square in each variable:
x² − 4x = (x − 2)² − 4; y² + 6y = (y + 3)² − 9;
z² − 8z = (z − 4)² − 16.
(x − 2)² + (y + 3)² + (z − 4)² = 4 + 9 + 16 − 4 = 25.
Standard sphere form: (x − h)² + (y − k)² + (z − l)² = r².
Radius: r = √25 = 5. Answer: (C).
2. (2 points) Consider the quadric surface with cross sections given below
y z z
x y x
z = 1 x = 0 y = 0
Determine the equation of the quadric surface which best corresponds to these cross sections.
(A) z = x2 + y 2 ; (B) z = y 2 − x2 ; (C) z 2 = x2 + y 2 ; (D) x2 + y 2 − z 2 = 1;
(E) z 2 − x2 − y 2 = 1
At x = 0: z = y²; the yz-section opens upward.
At y = 0: z = −x²; the xz-section opens downward.
Thus z = y² − x²; at z = 1, y² − x² = 1 (a hyperbola).
All three sections match the diagrams. Answer: (B).
