Solutions

Berkeley preliminary exams

• Berkeley prelim exam archive

• Fall 2020 online graduate preliminary exam, Part A, with solutions

• Spring 2021 online graduate preliminary exam, Part A, with solutions

• Fall 2003 preliminary-exam solutions

General practice packets

• Multivariable-calculus practice

• Selected calculus practice from GRE Mathematics Test Form GR8767 – multiple-choice calculus questions from the GRE Mathematics Test form GR8767, with the answer key and item difficulty worksheet for the form.

• Week 1: Calculus I practice solutions

• Week 2: Calculus II, part 1 practice solutions

• Week 3: Calculus II, part 2 and Calculus III practice solutions

• Week 4: Differential equations and linear algebra practice solutions

• Week 5: Abstract algebra and complex analysis practice solutions

• Week 6: Miscellaneous analysis, topology, and probability practice solutions

Harvard Math 21b, Spring 2018

• Course exam archive

• Final exam with solutions

• Practice final 1 with solutions

• Practice final 3 with solutions

• Practice final 4 with solutions

• Practice final 5 with solutions

• Practice final 6 with solutions

• Practice final 7 with solutions

• Practice final 8 with solutions

• Practice final 9 with solutions

Topology

• Point-set topology midterm with solutions