MTH4103 Geometry I 2009/10

Week-12 Test information update

• Now that the week-12 test has been held, this test and sample solutions for this test appear below with the previous in-term tests.
• After the test has been marked, you will be emailed your mark in the usual way (probably in the New Year).
• You can collect your test, and get feedback about any errors you made, by visiting me during an Office Hour in Semester B. If you have not already collected your mid-term (week-7) test, you can also collect this test and get feedback on it, at the same time. (Please remember to bring your student ID card, which you should carry with you at all times in College.)

Revision and final exam information

• I expect there to be a Geometry I revision lecture scheduled during the College's Revision Week (26-30 April 2010), although you should start your revision well before then. In addition, I will have a limited number of Office Hours in April and May (before the Geometry I exam) for students to ask questions. The times for these will be posted on this web-page in due course.
• The 2006/07, 2007/08 and 2008/09 final exams are available below to help with your revision. Sample solutions are not provided for these, since it is best to work out the solutions for yourself and to understand the concepts involved. See also your lecture notes and courseworks and their solutions for help. Once you have worked out a solution to an exam question, you should think about how to check it, as this will be important on the final exam. If you have any questions about a solution that you have worked out and checked, I will be very happy to answer these questions during an Office Hour.
• The 2009/10 Geometry I final exam will have the same rubric and a similar structure to the 2008/09 exam (but of course, you should not expect exactly the same topics to be covered). You are responsible for all the material covered in the online lecture notes, up to and including week 12, as well as all the courseworks and solutions. Check out the Key Objectives below, stating the basic material you should study and understand first, before studying the more advanced material. Starting in 2006/07, the structure and content and some of the notation of the Geometry I module changed, so you should not take too much notice of the Geometry I exams previous to 2006/07.
• Some questions on the final exam will be similar to coursework questions. There will certainly be definitions asked for on the final exam, which you should be able to reproduce accurately. There will certainly be proofs asked for on the final exam, some of which may be from the lecture notes, and some may be similar to proofs asked for in the courseworks.
• When taking the final exam, please read each question carefully, and answer the question that is actually asked! Include your working out, as this will usually be considered for partial marks, but also make sure you perform your calculations accurately, and clearly indicate your final answer in any computation.

Key Objectives

The following is a list of basic material you should study and understand first, before studying the more advanced material. If you master these Key Objectives then you should be reasonably sure of at least passing the final examination. A good proportion of these Key Objectives will be covered on the final examination, as well as more advanced material. If you wish to obtain a B or an A grade, you should be familiar with all the material in the Geometry I online lecture notes.

1. Vectors in 3 dimensions: know the definitions of sum, scalar multiple, position vector, scalar product, vector product, and triple scalar product, and be able to do calculations using coordinates to be able to apply all this to find distances, areas, volumes, and equations of lines and planes given information about them.
2. Systems of linear equations in 2 and in 3 variables: know how to perform Gaussian elimination to echelon form, and back substitution, in order to be able to find all solutions of a system of linear equations in 2 or in 3 variables.
3. Matrices, especially 2x2 and 3x3: know the definitions and methods to be able to find: sums, scalar multiples, products, determinants, whether invertible, eigenvalues and eigenvectors.
4. Linear transformations: know the definition of a linear transformation, know how to obtain a matrix representing a linear transformation, know the matrices representing rotations and reflections in the (x,y)-plane.

About coursework

• Each week (except week 7 and week 12) on Thursday by 14:00 a new coursework will be available to download.
• The whole purpose of coursework is to help you learn the mathematics and so to help you do well on the tests and examination. When working on the coursework questions, you should constantly refer to your lecture notes and make sure you understand them.
• Each coursework will consist of a Feedback Question together with Practice Questions. Read each question carefully, make sure you understand it and the concepts involved, and answer the question that is actually asked! Think about the tools which may apply to the question, such as definitions, theorems and techniques, and use your lecture notes to help you understand these tools. Combine tools if necessary. Be creative! Be precise! Check your answer.
• In Geometry I, your solution to the Feedback Question must be handed in first thing at your exercise class the following Monday or Tuesday. It is important that you do this question and that it is your own best work, in order to be able to get effective written feedback to help you. You should also attempt to do as much as you can of the Practice Questions, but you should not hand in your solutions to these. You can ask for help with the Practice Questions in your exercise class.
• Also on Thursday afternoons (except in week 7), the following will be available: scanned copies of that week's lecture notes; sample solutions to all the previous week's coursework questions, so that, in particular, you can check your answers to the Practice Questions.

Notes

• The definitive content of this module is contained in the lecture notes, and so the module text is not essential. However, you may find the module text useful in supplying some additional examples, diagrams and explanations. The module text is less useful for the theoretical aspects of this module.
• Students are expected to be quiet during lectures. Mobile phones must be switched OFF in lectures and in exercise classes.
• Exercise classes start in week 2. There are no exercise classes during the consolidation and test week (week 7).
• Use of calculators is not permitted in either the final examination or the in-term tests.

Useful material

• The Phrase Book (of basic words and symbols of higher mathematics)
• Prof. Cameron's excellent list of mathematical notation (including the Greek alphabet)
• Prof. Chiswell's excellent lecture notes on Matrices and Geometry (but beware of content differences, as well as some notational and method differences, from Geometry 1)

Previous in-term tests

• 2009 week-12 test 2009 week-12 test solutions
• 2009 mid-term test 2009 mid-term test solutions
• 2008 mid-term test 2008 mid-term test solutions
• 2007 mid-term test 2007 mid-term test solutions
• 2006 mid-term test 2006 mid-term test solutions

Previous examinations

• 2008/09 final exam
• 2007/08 final exam
• 2006/07 final exam

Examination Rubric

Assessment Profile

• Week-7 mid-term test: 10%
• Week-12 end-of-term test: 10%
• Final examination: 80%