Math 11: Resources
- FALL 2010
Practise questions for exams, and the exam solutions
- Midterm 1
- Fall 2010 midterm 1 with solutions and grading scheme.
These are not model solutions, but enable you to check answers and see how we broke down the grading of points.
- Fall 2008 midterm 1. Notes: solutions are written in, so cover them to test yourself! We will not have as many multiple choice as this. #1a we didn't do; #5 is quite hard.
- Practise problems from Fall 2007/2008 and their solutions. Notes: #1,2 are thought-provoking and non-standard, so save for after you've done the other ones; #10 uses symmetric form of line equation, we didn't do; #13 we didn't do distance between planes so only try if need amusement; skip #18. #22 the solution is wrong: n should be <6,4,-1> with consequence for plane eqn.
- Fall 2004 midterm 1
Notes: ours will not be all multiple choice format like this.
But we may have True/False questions. (Answers: dddbbccdcc)
- NYU Spring 2003 practise problems
Notes: #2 not needed; #4 is a little 2D for us, so don't worry about it.
- NYU Spring 2003 midterm 1,
Notes: distance in #3 not needed; #4 not needed.
- Midterm 2
- Fall 2010 final
with rough solutions and grading
- Practise problems for Fall 2007/2008, and solutions. Notes: 1c and 12 you can ignore. 4 is nice (sketch the surface first).
- Practise exams from 2005:
Midterm 2, and
- Fall 2004 final.
Notes: Looks like some great questions.
We won't have a multiple-choice format like this.
For # 3 we'd remind you of the definition of Laplace operator.
# 4 can skip since we haven't done constructing f from its grad in 3D.
1. b, 2. d, 3. d, 4. d, 5. c, 6. b, 7. c, 8. c, 9. c, 10. a, 11. b, 12. d, 13. a, 14. d, 15. d, 16. b, 17. a, 18. c, 19. a, 20. c, 21. d, 22. c, 23. b, 24. a, 25. a
- Practise NYU Spring 2003 final,
Notes: skip 7, or maybe find the total mass instead of the center of mass?
- NYU Spring 2003 final, with
- NYU Spring 2002 midterm.
- NYU Fall 2002 final.
- NYU Fall 2002 midterm.
- Another NYU Fall 2002 midterm.
Notes: skip the last question on probability.
Graphing / visualization tools
MATLAB: entirely optional, but a great plotting/computing package that will serve you well in the future
- Download the software from
we have 100 or so on-campus licenses (to work you must be online in
- Susan A. Schwarz
(email her if you have
Mac OS 10.2 or earlier for install CDs) can help with
- M. Pilant's Matlab examples
- Bent Petersen's Matlab starter page
- Robert Higdon's nice
- My 1-page
intro53.m code, and
intro code from Linear Algebra (shows more matrix stuff)
- Guide from
Cambridge University Engineering Department.
- Simple intro from Utah, Hany Farid's intro reference, and Gilbert Strang's
intro at MIT.
- Self-guided courses from Dartmouth academic computing:
Introduction to Matlab,
Programming in Matlab, and
Introduction to Matlab Graphics
- Matlab codes from our class demos:
- showplane, plots a plane as a panel in 3D.
- earlydemos, some simple plots of lines,
planes, their intersection, and parametric curves, from Ch. 13-14.