2023/2024 Examinations
MAS 102 Calculus II : Final Exam
MAS 102
Full Name :
Student Number:
Do not
Instruction
• No items other than pen, pencil, eraser and your id are allowed. Yo
belongings that are not allowed at the designated area in the front of
• Before you start, fill out the identification section on the title page an
page with an inerasable pen.
• Show your work for full credit and write the final answer to each prob
You are encouraged to write in English but some Korean is acceptable
each page as scratch spaces but anything written there will not be gra
• The exam is for three hours. Ask permission by raising your hand if y
need to go to toilet. You are not allowed to go to toilet for the first 30
minutes.
• Any attempt to cheat or a failure to follow this instruction lead to ser
not limited to failing the exam or the course.
, MAS 102 Name:
10(a) / 10 10(b) / 10 11(a)
11(b) / 15 Total
–1–
1. (a) Calculate √ √ Z πZ π x2 sin(x2)dxdy.
0 y
Ans:
where B is the solid lying between the spheres x2 + y2 + z2 = 1 a
the xy-plane and below the cone z = px2 + y2.
MAS 102 Calculus II : Final Exam
MAS 102
Full Name :
Student Number:
Do not
Instruction
• No items other than pen, pencil, eraser and your id are allowed. Yo
belongings that are not allowed at the designated area in the front of
• Before you start, fill out the identification section on the title page an
page with an inerasable pen.
• Show your work for full credit and write the final answer to each prob
You are encouraged to write in English but some Korean is acceptable
each page as scratch spaces but anything written there will not be gra
• The exam is for three hours. Ask permission by raising your hand if y
need to go to toilet. You are not allowed to go to toilet for the first 30
minutes.
• Any attempt to cheat or a failure to follow this instruction lead to ser
not limited to failing the exam or the course.
, MAS 102 Name:
10(a) / 10 10(b) / 10 11(a)
11(b) / 15 Total
–1–
1. (a) Calculate √ √ Z πZ π x2 sin(x2)dxdy.
0 y
Ans:
where B is the solid lying between the spheres x2 + y2 + z2 = 1 a
the xy-plane and below the cone z = px2 + y2.
