710
Chapter Thirteen A FUNDAMENTAL TOOL: VECTORS
63. For any vectors v and w , consider the following function of t:
62. Use the following steps and the results of Problems 59
60 to show (without trigonometry) that the geometric and
algebraic denitions of
MATH 308, FIRST WINTER TERM, 2015-2016
1. C ONTACT INFORMATION
The instructor for this course is me, Ben Williams. I may be reached at [email protected]
The course website is http:/www.math.ubc.ca/~tbjw/308/index.html.
O FFICE H OURS :
Monday 1:15-2:45,
T
Math 308
Homework 5
20 November 2015
1. Use the summation formulae for sines and cosines
sin( + ) = sin cos + cos sin ,
cos( + ) = cos cos sin sin
to express each of the following as a sum of powers of sin and cos :
(a) sin(2),
(b) sin(3),
2 tan
(c)
.
1
Math 308
Homework 6
4 December 2015
1. Fix a coordinate system for the Euclidean plane. Any isometric transformation of the plane may be
written as
T (~
x ) = A~
x +~
c
where A is an orthogonal matrix and ~
c is a fixed vector. We say T is orientation pre
Mathematics 308, Euclidean Geometry, Sample Final Exam
The University of British Columbia, 2015/16, Winter Session, Term 1.
There are ten (10) questions, they carry equal weight. Answer all questions. Some questions take up two
page. The exam should be 14
Mathematics 308, Euclidean Geometry, Sample Final Exam
The University of British Columbia, 2015/16, Winter Session, Term 1.
There are ten (10) questions, they carry equal weight. Answer all questions. Some questions take up two
page. The exam should be 14
MATH 308 QUESTIONS
These are some questions which are about the level of a medium to hard final exam question. I may
add to this list. Solutions to selected questions will be made available eventually.
Updated 8 December 2015.
1. C ONSTRUCTIONS & P ROOFS
MATH 308 QUESTIONS
These are some questions which are about the level of a medium to hard final exam question. I may
add to this list. Solutions to selected questions will be made available eventually.
Updated 8 December 2015.
1. C ONSTRUCTIONS & P ROOFS
MATH 308 SAMPLE MIDTERM
B. Williams
There are 5 questions, they carry equal weight. Answer all questions. This exam should be 10 pages
long, and conclude with the symbol .oOo. Please check that this is the case.
Show all your work.
No notes, calculators o
MATH 308 SAMPLE MIDTERM
B. Williams
There are 5 questions, they carry equal weight. Answer all questions. This exam should be 10 pages
long, and conclude with the symbol .oOo. Please check that this is the case.
Show all your work.
No notes, calculators o
Math 308
Homework 2
7 October 2015
In solving these problems, you may use any proposition in the Elements. Whenever I think you might
need a proposition that we have not mentioned in class, I will say so. Please show, in your answers, which
propositions y
Math 308
Homework 3
21 October 2015
In solving these problems, you may use any proposition in the Elements. Whenever I think you might
need a proposition that we have not mentioned in class, I will say so. Please show, in your answers, which
propositions
Math 308
Homework 1
21 September 2015
In solving these problems, you may use any proposition in the Elements. Whenever I think you might
need a proposition that we have not mentioned in class, I will say so. Please show, in your answers, which
proposition
Math 308, Section 101
First Midterm Exam
October 8, 2004
Duration: 50 minutes
Student Number:
Name:
Do not open this test until instructed to do so! This exam should have 8 pages, including
this cover sheet. No textbooks, notes, calculators, or other aids
Math 308, Section 101
Solutions to Study Questions for First Midterm
(in class Wednesday, October 6, 2004)
I. State the three axioms concerning isometries (Axioms 68).
Axiom 6: For any two points P and Q, there exists an isometry f with f ( P) = Q.
Axiom
Math 308
Fall 2010
Midterm Exam I solution
1. Find the focus and directrix of the parabola
y = x2 + 2x.
Answer. Rewrite as y + 1 = (x + 1)2 . It is an upward parabola centered at (1, 1)
and passing through (0, 0) and (2, 0). It is of the form v = 4au2 wit
Be sure this exam has 5 pages including the cover
The University of British Columbia
MATH 308
Midterm Exam I October 2010
Family Name
Given Name
Student Number
Signature
This exam consists of 4 questions worth 10 marks each. No notes nor calculators.
Prob