**[3]**implies three marks.

*of exam grade.*If you have any questions please do not hesitate to use the comment function on the bottom

*:*

# Exercise Sheets

http://euclid.ucc.ie/pages/staff/wills/teaching/ms2001/exercise1.pdf

— *Qns. 2,4,7 — 9*

http://euclid.ucc.ie/pages/staff/wills/teaching/ms2001/exercise2.pdf

— *Qns. 1, 5, 6 (but not the questions on singularities), 8, 9*

http://euclid.ucc.ie/pages/staff/wills/teaching/ms2001/exercise3.pdf

— *Qns. 3 ( especially the part on where they are differentiable), 5, 9, 10, 11, 14*

http://euclid.ucc.ie/pages/staff/wills/teaching/ms2001/exercise4.pdf

— *Qns. 10 (also consider vertical asymptotes (well, vertical asymptotes *are *singularities), the domain (where the function is defined), roots, -intercepts. Examine the local maxima & minima using both the second and first derivative tests. Examine concavity by using the method of split points.), 11 — 17*

# Past Papers

http://booleweb.ucc.ie/ExamPapers/exams2010/MathsStds/Autumn/MS2001Aut2010.pdf

*— except Q. 1(d)*

*http://booleweb.ucc.ie/ExamPapers/exams2010/MathsStds/MS2001Sum2010.pdf*

*— except Q. 1(d)*

*http://booleweb.ucc.ie/ExamPapers/exams2009/MathsStds/Autumn/MS2001A09.pdf*

*— except Q. 1(d)*

*http://booleweb.ucc.ie/ExamPapers/exams2009/MathsStds/MS2001s09.pdf*

*— except Q. 1(d)*

*http://booleweb.ucc.ie/ExamPapers/Exams2008/MathsStds/MS2001a08.pdf*

*http://booleweb.ucc.ie/ExamPapers/exams2008/Maths_Stds/MS2001Sum08.pdf*

*— except Q. 2*

*http://booleweb.ucc.ie/ExamPapers/exams2007/Maths_Stds/MS2001Aut07.pdf*

*— except Q. 1(d)*

*http://booleweb.ucc.ie/ExamPapers/exams2007/Maths_Stds/MS2001Sum2007.pdf*

*— except Q. 1(d),(e)*

**For these older papers the layout is different to ours:**

http://booleweb.ucc.ie/ExamPapers/exams2006/Maths_Stds/Autumn/ms2001Aut.pdf

http://booleweb.ucc.ie/ExamPapers/exams2006/Maths_Stds/MS2001Sum06.pdf

http://booleweb.ucc.ie/ExamPapers/Exams2005/Maths_Stds/MS2001Aut05.pdf

http://booleweb.ucc.ie/ExamPapers/Exams2005/Maths_Stds/MS2001.pdf

*— except Q. 6(c)*

*http://booleweb.ucc.ie/ExamPapers/exams2004/Maths_Stds/MS2001aut.pdf*

*http://booleweb.ucc.ie/ExamPapers/exams2004/Maths_Stds/ms2001s2004.pdf*

*http://booleweb.ucc.ie/ExamPapers/exams2003/Maths_Studies/ms2001aut.pdf*

*http://booleweb.ucc.ie/ExamPapers/exams2003/Maths_Studies/MS2001.pdf*

*http://booleweb.ucc.ie/ExamPapers/exams2002/Maths_Stds/ms2001.pdf*

— *except Q. 2(b)*

*http://booleweb.ucc.ie/ExamPapers/exams/Mathematical_Studies/MS2001.pdf*

*— except Q. 6(a)*

# New Material

The material that was additional to previous years was:

- Closed Interval Method (note that Wills does define Critical points – however we define critical points on closed intervals and include the endpoints)
- First Derivative Test
- Asymptotes
- Concavity

Past paper questions on maxima and minima *on closed intervals* can (in general) be answered using the Closed Interval Method.

Past paper questions on maxima and minima on more general sets (including the entire real line) can (in general) be answered using the First Derivative Test.

Finally we use asymptotes to help in curve sketching.

Section 4 from Problems has examples of questions on this new material.

**In particular, questions 4 and 5 are of exam grade.**

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