Be sure this exam has 5 pages including the cover
The University of British Columbia
MATH 308
Midterm Exam II November 2010
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This exam consists of 4 questions worth 10 marks each. No notes nor calculators.
Pr
Math 308
Fall 2010
Assignment 9
1. 5.1
#2 (page 258)
2. 5.1
#3 (page 258)
3. 5.1
Find and sketch the image of the rectangle
R = (x, y) :
1
2
x 3 , |y|
4
1
4
under inversion in the unit circle x2 + y 2 = 1.
4. 5.2
#3 (page 258)
5. 5.2 Find the image of t
Math 308
Fall 2010
Assignment 10
(never due)
1. 5.3
#3 (page 259)
2. 5.3
#4 (page 259)
3. 5.3
#5 (page 259)
4. 5.2
(a) Let t1 (z) be the inversion in the line x + y = 1. Find its formula.
(Hint. It is
an isometry reversing the orientation of angles, thus
Math 308
Fall 2010
Assignment 5
2.3 2.4
1. 2.3
#4 (page 92)
2. 2.4
#4 (page 93)
3. 2.4
#5 (page 93)
4. 2.4
#6 (page 93)
AX
5. Sketch the graph of the function f (x) where, for x R, f (x) is the signed ratio XB
and A, B, and X have coordinates 0, 1, and x.
Math 308
Fall 2010
Assignment 6
2.5 3.2
1. 2.5
#1 (page 93)
Hint: SQ and P R are NOT conjugate diameters.
2. 2.5
#2 (page 93)
3. A line meets the same branch of a hyperbola at points P and Q, and meets its
asymptotes at points A and B. Show that AP = BQ.
Math 308
Fall 2010
Assignment 1
page 14 Problem 8
page 22 Problem 3
page 43 1.1 #5
page 43 1.1 #6(b)
page 43 1.2 #3
page 43 1.2 #6
2
2
Let H denote the hyperbola x2 y2 = 1, and A denote the lines
a
b
that A is the asymptotes of H in the sense that
Math 308
Fall 2010
Assignment 3
(due Oct 13)
page 42 Problem 4 (a,b,c)
page 44 1.4 #2
Hint: Since the coecients for x2 and z 2 are dierent, the intersection of the hyperboloid and the plane y = 1 is an ellipse, not a circle. To use the analysis in the
t
Math 308
Fall 2010
Assignment 4
2.2 2.3
1. page 91 2.2 #1
2. page 91 2.2 #2
3. page 91 2.2 #3(a)
4. Show by example that the magnitude of angle is not an ane property.
5. Can an ane transformation of R2 map 3 non-collinear points to 3 collinear points?
Ex
Math 308
Fall 2010
Assignment 2
page 33 Problem 2(b) without identifying the axes.
page 44 1.3 #1(d) without identifying the axes.
page 39 Problem 2 without identifying the centre nor the axes.
page 44 1.4 #1(b) without identifying the centre nor the
Math 308 Fall 2010 Assignment 3
(due Oct 13)
0 page 42 Problem 4 (a,b,c)
0 page 44 §1.4- #2
Hint: Since the coefcients for :32 and 22 are different, the intersection of the hy-
perboloid and the plane y m 1 is en ellipse, not a circle. To use the analy
Math 308
Fall 2010
Assignment 7
(due Nov 17)
1. 3.2
#4(a) (page 147)
2. 3.2
#5 (page 147)
3. 3.3
#4 (page 148)
4. 3.3
#5(a,b) (page 148)
5. 3.3
#6(a) (page 148)
6. (3.4) Lines V AA , V BB , V CC cut two lines L1 and L2 in A and A , B and B ,
C and C , res
Math 308
Fall 2010
Assignment 7 partial list
(due Nov 17)
3.2
#4(a) (page 147)
3.2
#5 (page 147)
3.3
#4 (page 148)
3.3
#5(a,b) (page 148)
(more will be assigned after second midterm exam)
Midterm Exam II will cover 2.1.23.3.4. A few formulas to be pr
Be sure this exam has 12 pages including the cover
The University of British Columbia
MATH 308, Section 101, Instructor Tai-Peng Tsai
Practice Final Exam December 2010
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No notes nor calculators.
Rules Governi
Math 308
1. 3.5
#2 (page 149)
3. 3.5
Assignment 8
#1(a) (page 149)
2. 3.5
Fall 2010
#3 (page 149)
4. For the collinear Points in #1(a), nd another Point X in the same Line so that
(ABCX) = 2.
5. Investigate the cases where two of the six values of the cro