Upload
charles-hancin
View
230
Download
0
Embed Size (px)
Citation preview
7/25/2019 METH - Polynomials, Logs, Exp, Infinite Solutions
1/20
PAST EXAM QUESTIONS: Polynomials, Logarithms,
Exponentials, Innite
sol!tions
"e#ernan $%%& exam $
Question 2
)7(log)2(log3 55 +is closest to
A. 0.08
B. 0.22
C. 1.39
D. 2.32
E. 2.5
Question 3
The solution/s to the equation
xx ee =22is/are
A.
( )2log e
B. 0
C. ( )2log,0 e
D.
2
1log,1 e
E.
22e
Question 5
The complete set o linear actors o the pol!nomial
xxxx 107" 23" +
are
A.
10,1,1 ++ xxx
B.
5,1,2 ++ xxx
C.
5,1,2, ++ xxxx
D.
2,1,5, ++ xxxx
E.10,1,1, ++ xxxx
7/25/2019 METH - Polynomials, Logs, Exp, Infinite Solutions
2/20
"e#ernan $%%' Exam (
Question 2
Solve the following equations forx.
a)
( ) #2 1 =+xe.
*)( ) ( ) 0,13loglog2 55 >= xxx
1 + 2 = 3 marks
"e#ernan $%%' Exam $
Question 3
( )2log 3is closest in $alue to
A. % 0."1
B. 0."1
C. 0.#3
D. 0.#7
E. 1.58
"e#ernan $%%+ Exam $
Question 4
The simultaneous linear equations
5x + (a 3)y =1ax +2y =a
&herea R
, &ill ha$e no solutions or
A.
a = 2
B.
a = 5
C.
a R '(2)
D.
a R '2,5
E.
a (2,5)
"e#ernan $%(% Exam (
7/25/2019 METH - Polynomials, Logs, Exp, Infinite Solutions
3/20
Q!estion &
Consider the system of simultaneous linear equations given by
mx +y = 22x + (m 1)y =m
ind the value!s" of mfor whi#h there is no solution. 3 marks
"e#ernan $%(% Exam $
Question 2
*or the unctionf(x) =ax 3 + bx 2 +cx + d,
3#)3(an+
")1(
10)2(
")1(
====
'f
'f
f
f
matri- equationAX=B is to e use+ to in+ the $alues o a, b, can+ d&here
=
=
3#
"
10
"
an+B
d
c
b
a
X
.
The matri- Ais
A.
3000
0100
0020
0001
B.
13927
1111
12"8
1111
C.
3003
0101
0022
3121
D.
11#81
1123
12"8
1111
7/25/2019 METH - Polynomials, Logs, Exp, Infinite Solutions
4/20
E.
01#27
0123
12"8
1111
"e#ernan $%(( Exam (
Q!estion $
Solvelog e (3) +2log e (x) = log e ("x)
forx. 3 marks
"e#ernan $%(( Exam $
Question 5
The simultaneous linear equations
2x + (k2)y = 2(k+1) x +2y = 1
ha$e no solutions or
A.
k= 2
B.
k= 3
C.
{ }3,2k
D.Rk
E.
k R '2,3
Question 6
$he gra%h of
1an+3 2 +== k xxyxy
do notinterse#t for
A)
k=12 2
-)
12 2
7/25/2019 METH - Polynomials, Logs, Exp, Infinite Solutions
5/20
MA0 $%%1 Exam (
1 mark
& marks
MA0 $%%' Exam (
7/25/2019 METH - Polynomials, Logs, Exp, Infinite Solutions
6/20
2 + 2 = & marks
MA0 $%%' Exam $
MA0 $%%+ Exam (
MA0 $%%+ Exam $
7/25/2019 METH - Polynomials, Logs, Exp, Infinite Solutions
7/20
0.AA $%%& Exam $
0.AA $%%1 Exam (
7/25/2019 METH - Polynomials, Logs, Exp, Infinite Solutions
8/20
2 marks
0.AA $%%1 Exam $
TSSM $%(( Exam $
7/25/2019 METH - Polynomials, Logs, Exp, Infinite Solutions
9/20
Neap $%(% Exam (
Neap $%(% Exam $
7/25/2019 METH - Polynomials, Logs, Exp, Infinite Solutions
10/20
It!te $%%1 Exam (
It!te $%%2 Exam (
Question 3
a) 'ithout using #al#ulator solve02112 = ++ eee xx
forx. 'rite answer ine(a#t form.
3il*aha $%(% Q2
solve2 2 "x xe e = .
INSI4"T $%(% EXAM (
7/25/2019 METH - Polynomials, Logs, Exp, Infinite Solutions
11/20
It!t e $%%1 Exam (
It!te $%%2 Exam (
Q!estion $% $he solution!s" of ( ) ( ) 07log7log =++ xxee
is)are
*. ,- , . / C.25
-25
0.25
E.25
ANS5E6S
"e#ernan $%%& Exam $
2 E 3 * C
"e#ernan $%%' Exam (
Q!estion $
a)
( ) #2 1 =+xe
7/25/2019 METH - Polynomials, Logs, Exp, Infinite Solutions
12/20
( )
( )
( ) 13log
13log
31
=+=
=+
e
e
x
x
x
e
7( mar89
*)
( ) ( )
( ) ( )
15
35
0since,13
log
13
log
13loglog
0,13loglog2
1
5
2
5
52
5
55
=
=
=
=
=
>=
x
x
xx
x
x
xx
xxx
7( mar89
"e#ernan $%%' Exam $
3 C
"e#ernan $%%+ Exam $
& E
"e#ernan $%(% Exam (
Q!estion &
mx +y = 2 (1)2x + (m 1)y =m (2)
or no solutions or innite solutions the determinant of the matri(
121
m
m
equals 4ero.
$hat is-
m 1
2 m 1 = 0
7(
7/25/2019 METH - Polynomials, Logs, Exp, Infinite Solutions
13/20
7( mar89
m(m 1)2 = 0
m2 m 2 = 0
(m 2)(m +1)= 0
m = 2 or m = 1
7( mar89
m = 2,
in (1) 2x +y = 2in (2) 2x +y = 2
$hey are the same equation hen#e there are an innite number of solutions.
5fm = 1
-
in (1) x +y = 2 (3)in (2) 2x 2y = 1 (")
(") 2 x +y = 12
(5)
!3" and !" des#ribe %arallel lines with di6erenty7inter#e%ts so there are no
%oints of interse#tion and hen#e no solutions.
So form = 1
there is no solution.
7( mar89
"e#ernan $%(% Exam $
2 E
"e#ernan $%(( Exam (
Q!estion $
7/25/2019 METH - Polynomials, Logs, Exp, Infinite Solutions
14/20
0)"3(
0"3
"3
)"(log)3(log
)"(log)(log)3(log
)"(log)(log2)3(log
2
2
2
2
==
=
=
=+
=+
xx
xx
xx
xx
xx
xx
ee
eee
eee
x = 0 or x = "3
7( mar89
butlog e (x)
is not dened forx = 0
so
x ="
3
7( mar89
"e#ernan $%(( Exam $
8 C
MA0 $%%& Exam (
7( mar89
7/25/2019 METH - Polynomials, Logs, Exp, Infinite Solutions
15/20
MA0 $%%1 Exam (
MA0 $%%' Exam (
7/25/2019 METH - Polynomials, Logs, Exp, Infinite Solutions
16/20
7/25/2019 METH - Polynomials, Logs, Exp, Infinite Solutions
17/20
MA0 $%%+ Exam (
MA0 $%%+ Exam $
7/25/2019 METH - Polynomials, Logs, Exp, Infinite Solutions
18/20
0.AA $%%& Exam $
& 9
0.AA $%%1 Exam (
0.AA $%%1 Exam $
3 C C 1/ 11 E
TSSM Exam $ $%((
Neap $%(% Exam (
Neap $%(% Exam $
7/25/2019 METH - Polynomials, Logs, Exp, Infinite Solutions
19/20
It!te $%%1 Exam (
It!te $%%2 Exam (
3a02112 = ++ eee xx
-( ) 022 = xx eee
-
( )( 022 = xx eee
-( )( ) 012 =+
xx eee. Sin#e
0eand
01 +xe-
02 = xe-
2=xe-
2log ex =.
3il*aha $%(% Q2
( )1
log 2 52
ex = +
7/25/2019 METH - Polynomials, Logs, Exp, Infinite Solutions
20/20
INSI4"T $%(% EXAM(
:ES$5;< 9
It!te $%%1 Exam (
It!te $%%2 Exam (
2/
( ) ( ) 07log7log =++ xx ee-
( ) ( ) 077log =+ xxe-
( )( ) 077 exx =+-
1"92 =x-
502 =x. Sin#e
07 >x- i.e.
7>x-
2550 ==x E