Math 11100
Important Concepts for Test 3
(Sections 7.4-9.2)
Fall 2012
ANSWERS
Example #1
x | x 2,0, 2
Example #2
a.
Example #3
Equation of vertical asymptote: x = -3
Example #4
B7
Example #5
r
Example #6
Ryan will need 8 more gallons of gas.
Example #7
Th
Math 11100
Important Concepts for Test 4
(Sections 9.3-10.6)
ANSWERS
Example #1
116 , 1912
Example #2
64, 3438
Example #3
Stacy's canoe speed was 7 miles per hour.
Example #4
It would take Greg about 3.58 hours and Dax about 2.58 hours.
Example #5
t
Examp
Math 11100
Important Concepts for Test 4
(Sections 9.3-10.6)
Fall 2012
Section 9.3
Know how to solve equations that are quadratic in form by making a substitution
Example #1
Example #2
Solve: 8(3x 5)2 2(3x 5) 1 0
Solve: 2 x
2
3
1
x 3 28 0
Know how to use
MATH 11100
TEST 4 Practice Problems
2
Sections 9.3-10.6
1
1.
Solve for x:
x 3 3x 3 4
2.
Solve for a:
q
3.
Solve for x:
2x
x
8 0
x 1 x 1
4.
Solve for x:
4 x 2 x 1 5
5.
Solve for t:
S at 2 abt
6.
Elise drove at a constant speed for 160 miles on a grave
Math 11100
Important Concepts for Test 3
(Sections 7.4-9.2)
Fall 2012
Section 7.4
Know how to determine the domain of the variable in a rational equation.
Example #1
4
x
1
2
x 2x x 4 x
2
Know how to solve rational equations.
Example #2
Find the domain of
r_
MATH 11100 In-Class Quiz 06 Class Identier (Check One): Print Last Name
Sections 7.1 and 7.2 C] MW 3:00 PM 4:50 PM Print First Name
And Pre-Reading of 7.3 CI MW 6:00 PM 7:50 PM
Note the domain of the following functions in the speaed notation:
Math 11100
Important Concepts for Test 4
(Sections 9.3-10.6)
ANSWERS
Example #1
116 , 1912
Example #2
64, 3438
Example #3
Stacy's canoe speed was 7 miles per hour.
Example #4
It would take Greg about 3.58 hours and Dax about 2.58 hours.
Example #5
t
Examp
MATH 11100 in~Class Quiz 04 Class Identier (Check One): Print Last Name
Sections 5.1, 32, 5.3 [3 MW 3:00 PM a 4:50 PM Print First Name i Sr 1 f . A
And PreReading of5.4, 5.5 8 MW 6:00 PM 7:50 PM
, 4-; z
7 _l 2,3 33
1) Simplify. Remember the required
Notes Outline:
9.6 (Wrap-Up) More Applications of Quadratics
3 Maximum/Minimum Values of Quadratic Applications
34)
Find the pair of numbers whose sum is 60 and whose product is a maximum.
38)
A Projectile Problem. A projectile on Earth is fired straight
Notes Outline:
7.4 Rational Expression Equations and Rational Function Graphs
0 To Recall: Domain of the Rational Equation Terms
QUESTION:WhatisthedomainoftheRationalExpressionEquation(insetnotation)?
8
18)
28)
1 Solve Rational Equations
28)
TheSteps
D
Homework 26-30 and pg 151 Problems
Dominique Dec
October 5, 2014
HW #26 b) Show that H =Spancfw_x1 , x2 mx3 is a subspace of R3
i) x1 = 0, x2 = 0, x3 = 0
H = cfw_0, 0, 0 (0, 0, 0) H.
ii) u : cfw_s1 v1 + s2 v2 + s3 v3 H
v : cfw_t1 v1 + t2 v2 + t3 v3
u +
Homework Week 12 #45-48 and Book
Dominique Dec
November 16, 2014
3a c
b 3c
; a, b, c in R be a subspace of R4 . 1) Find a basis for the subspace,
HW #45 Let H =
7a + 6b + 5c
3a + c
2) State the dimension.
1
0
3
c
0b
3a
3
1
0
0a b 3c
7a
Homework Week 9 and Book Work
Dominique Dec
October 26, 2014
w1
v1
u1
w2
v2
u2
HW #35 Show that Rn is a vector space: u = . , v = . , w = .
.
.
.
.
.
.
u1 + v1
v1
u1
u2 v2 u2 + v2
V : . + . =
.
.
. .
.
.
.
wn
vn
un
1. u + v
Rn
Homework for Week 7 with book work
Dominique Dec
October 11, 2014
4 0 0 0
7 1 0 0
#12 pg 168 Use codeterminants and cofactors to nd det
2 6 3 0
5 8 4 3
- 4(11+1 ) det [A1,1 ] = 4(1)(3)(3) = 36
6 3
2 4 0
9 0 4 1 0
#14 pg 168 Use codeterminants and cofacto
Homework #14-18, and book problems
Dominique Dec
September 20, 2014
#16 pg 60 Determine by inspection whether the vecors are linearly independent. Justify the answer.
2
3
2 , 6
8
12
No, vectors are linearly dependent because v2 is 3 v2 .
2
#18 pg 60 De
Homework 5, 6, 7, and 8 with extra Problems
Dominique Dec
September 3, 2014
#2 pg. 22 Determine which matrices are in reduced echelon form and which others are only in echelon
form.
a
b
c
d
reduced row echelon form
echelon form
reduced row echelon form
re
Homework 9, 10, 11, 12, 13 and Book Problems
Dominique Dec
September 10, 2014
#12 pg 40 Write the augmented matrix for the linear system that corresponds to the matrix
equation Ax = b. Then solve the system and write the solution as a vector.
1 2 1 1
1
2
Homework 1,2,3, and 4 with extra Problems
Dominique Dec
August 25, 2014
Homework #1 Show that (1, 1, 2) is a solution for the system of linear equations:
x1 2x2 + 3x3 =9
x1 + 3x2 =4
f (x) =
2x1 5x2 + 5x3 =17
1. 1 2(1) + 3(2) = 9
1 + 2 + 6 = 9 T rue
2. (1
Sections 1.3 and 1.5
Dominique Dec
January 15, 2015
1.3 Homework
2 Conjecture a formula for the sum of the rst n even postive integers. Prove by using mathematical
induction.
S(n) = n 2k
k=1
=
2(1) + 2(2) + 2(3) + . . . + 2(n) = n(n + 1)
1 2k
k=1
n+1 2k
k
Homework for Section 9.2 and 9.3
Dominique Dec
March 29, 2015
Section 9.2
5 Find a complete set of incongruent primitive roots of 13.
- There will be (13) = (12) = 4 incongruent roots. We must rst show that ord13 2 = 12 and that
it must be a divisor of 12