Exam I Hints and Answers
Math 126 B Autumn 2014
Version 1: In Problem 1, a = h2, 5, 7i:
1
3
, 0, 10
i
1. (a) projb a = h 10
1
(b) cos = 780
(c) v =
2.
4 h5, 23, 15i
779
74
3. (a) 3, 3 ; (b) 3, 2
3
4. 5x + 15y + 7z = 15
5. L = 14 e20 +
19
4
6. x = 2t, y =
Exam I Answers
Math 126 E Autumn 2016
7 11 9
1. R , ,
4 2 4
2. (a) = ; (b)
3
9
0, 0,
5
3. (a) BC = h10, 0, 0i; (b) area = 40; (c) F (3, 11, 15)
4. i. D
ii. C
iii. B
iv. A
5. (a) x = 1, y = 1 + t, z = 1 2t; (b) (1) =
1
18
53/2
MATH 126 LECTURE EXAMPLES
1. Your current grade in this course is given by a two-variable function G(h, m), where
h is your homework percentage and m is your first midterm score out of 50 points.
Possible values of G are given in the table below. (NOTE: I
MATH 126 E
Exam I
Autumn 2016
Name
Student ID #
Section
HONOR STATEMENT
I affirm that my work upholds the highest standards of honesty and academic integrity at the
University of Washington, and that I have neither given nor received any unauthorized assi
Exam I Answers
Math 126 E & F Spring 2017
Version 1: In #1, A is the point (3, 0, 4).
1. (a) area of the parallelogram is 137.
(b) One possible set of parametric equations for the line through A and C:
x = 3, y = 3t, z = 4 5t.
2. a = 2, b = 65 and a = 2,
Name:
Student Number:
Math 126 E
Quiz 2. 07/26/2011
Problem 1. [10 points] Find and classify all critical points of the function
f (x, y ) = 2x2 3xy + 2y 2 .
Problem 2. [10 points] The n moles of any ideal gas obey the law
pV = nRT,
where R = 8.314JK 1 mo
Exam I Hints and Answers
Math 126 A & B Spring 2012
20
20
1. (a) (4 points) w = 3, 4, 2 or w = 3, 4, 2
29
29
1
(b) (4 points) = cos1
175
(c) (1 point) (3, 3 )
(d)
i. (1 point) circle
ii. (1 point) hyperbola
iii. (1 point) cone
2. x + 4y + z = 87
3. (a) (
Math 126, Section C, Autumn 2012, Solutions to Midterm I
1. Answer the following question regarding the picture below
We know AC = 2, 6, 2, BD = 4, 0, 2 and A = (0, 2, 1).
(a) (4 points) Compute the two vectors u= AB = DC and v= AD = BC . From v+u= AC =<
Math 126 E
Quiz 2. 07/26/2011
Problem 1. [10 points] Find and classify all critical points of the function
f (x, y ) = 2x2 3xy + 2y 2 .
Solution. First, let us nd all critical points. Let us solve the system of two equations
fx = fy = 0. Since
fx = 4x 3y,
Name:
Student Number:
Quiz 1
Math 126 E. 07/05/2011
Problem 1. [10 points] Find the plane that passes through the point P = (1, 0, 0) and the line
x = t, y = t, z = t 1.
Problem 2. [10 points] Consider the following three points:
A = (0, 0, 0), B = (2, 0,
Quiz 1
Math 126 E. 07/05/2011
Problem 1. [10 points] Find the plane that passes through the point P = (1, 0, 0) and the line
x = t, y = t, z = t 1.
Solution. We already have a point P on this plane; let us nd a normal vector n. To nd it,
let us nd the two