4.3
The First Derivative Test
SETTING THE STAGE
A small rocket is launched as part of an atmospheric study. The onboard digital
sensor sends back these measurements of the rockets height at 5s intervals.
Time (s)
Height (m)
0
5
1.5
754.0
10
15
20
25
1261
MAM1000W 2015 Test 5 Comments and Common
Mistakes
Once youve collected your script, you might notice the markers have written some
mysterious codes like PM2, DE3, or PA1 next to your answers. We have used these
codes to indicate common errors, and this do
DEPARTMENT
AND APPLIED MATHEMATICS
OF MATHEMATICS
Mathematics loo  MAMIO0.W
CLASS TEST
Tuesday 1 April 2O03
2
1
Time: 1; Hours (5:30  7:OOpm)
F\rll Marks: 1OO
Marks Available: 1OO
MARKING
No Answer
Correct Answer
5
0

l
Wtong Answer
1
,
No calcalators
MAM1000W
Class Test 5, Page 1 of 2
22 August 2012
University of Cape Town
Department of Mathematics and Applied Mathematics
MAM1000W Class Test 5
22 August 2012
Time: 1 hour 30 minutes
Your student number and your answer to each question must be carefully
3)
UNIVERSITY OF CAPE TOWN
Department of Mathematics and Applied Mathematics
Mathematics 100 MAMlOOW (Paper 2)
OCTOBER/NOVEMBER EXAMINATION 2003
Mathematics MAMIOOW
6. A curve is given by the parametric equations 1: = sin1 t, y : ln(1 + 2t). Find the sl
UNIVERSITY or CAPE TOWN
University Examinations October/November 2001
Department of Mathematics and Applied Mathematics
MAMlOOW
Paper 1
Time: 3 hours Full marks: 100
;: Marks available : 100
Note: (i) Full answers are expected. Marks Will be deducted for
University of Cape Town
Department of Mathematics and Applied Mathematics
MAM1000W Final Exam Paper 2
15 November 2006
Time: 2 hours
Calculators may not be used during this test. Your student number
and your answer to each question must be carefully shade
University of Cape Town
Department of Mathematics and Applied
Mathematics
MAM 1000W Supplementary / Deferred
Exam Paper 2
January 2013
Time: 3 hours
NOTES
There are 4 pages (not including this cover page), with a total of 35
questions.
Your student number
Student Number:
Surname:
First Name(s):
Department of Mathematics and Applied Mathematics
MAM1000W
Examination: Paper 2
27 November 2015
Time : 2 hours
Full marks: 100
This question paper consists of 17 pages (including this one).
Answer all questions i
University of Cape Town
Department of Mathematics and Applied Mathematics
MAM1000W Final Exam Paper 1
30 October 2008
Time: 2 hours
Answer the questions in the spaces provided on the question sheets. If you
run out of room for an answer, continue at the b
Student Number:
Surname:
First Name(s):
Department of Mathematics and Applied Mathematics
MAM1000W
Test 5
30 September 2015
Time : 18h00 20h00
Full marks: 80
This question paper consists of 15 pages (including this one).
Answer all questions in the spac
MAM1000W third period
Class Test 2, Page 1 of 2
23 March 2009
University of Cape Town
Department of Mathematics and Applied Mathematics
MAM1000W Class Test 2
23 March 2009
Third period
Time: 45 minutes
Calculators may not be used during this test. Your st
UNIVERSITY OF CAPE TOWN
Department of Mathematics and Applied Mathematics
Mathematics 100 MAMIOOW
Final Examination October / November 2004
Paperl
Time: 3 Hours , Full Marks: 100
This paper consists of two pages Marks Available: 100
Calculators are not al
Student Number:
Surname:
First Name(s):
Department of Mathematics and Applied Mathematics
MAM1000W
Supplementary Examination: Paper 1
January 2016
Time : 2 hours
Full marks: 100
This question paper consists of 17 pages (including this one).
Answer all q
INATION
EXAM
2002
ocToBER/NOVEMBER
MAM100W
Mathematics
OF CAPE TOWN
UNIVERSITY
Department of Mathematics and Applied Mathematics
Mathematics 1OO MAM10OW (PAPER 1)
Time:
MARKS AVAILABLE
3 Hours
1OO
FULL MARKS: 10O
Only calculators approued'by the D eportm
?
!
i
ot
+
g.
 : ,
e.
c^
l i
1
t s o
= ' t s
i i i ; i s i i i f i + f ljf+$l li*
: g t H; 5 [ ] e c q
g#
coa
+
s
!e
g Y i Fi l F l ; f 3 c e e rF; :
a r g f g 3 $ r F H * " *$Fi ii
^<
+
a
s,r
@
oe6
a
s
:1
s
r i * tg g i j 'r
F [i f i i
F F '[fs, i e
ir
University of Cape Town
Department of Mathematics and Applied Mathematics
MAMIOOOW Final Exam Paper 1
30 October 2012 Time: 2 hours
Answer the questions in the spaces provided on the question sheets, or at the
back of the exam. Show all your work; answers
UNIVERSITY OF CAPE TOWN
of Mathematics
Department
and Applied Mdthematics
Mathematics 100  MAM100W
Thursday 12 May 20oE
F\rll Marks: 50  100%
CLASS TEST 3
1
Time: 1i Hours (5:30  7:00pm)
Calculators are not allowed,
1. State and prove the formula for
UNIVERSITY or CAPE TOWN
DEPARTMENT OF MATHEMATICS AND APPLIED MATHEMATICS
Mathematics 100 MAMlDOW
SUPPLEMENTARY EXAMINATION  PAPER 1 _ JANUARY 2002
Time: 3 Hours , I . Marks Available: 100
Full Marks : 100
Only calculators approved by the Department may
University of Cape Town
Department of Mathematics and Applied Mathematics
MAM1000W Class Test 1
10 March 2008
First period
Time: 45 minutes
Answer the questions in the spaces provided on the question sheets. If you
run out of room for an answer, continue
MAM1000W
June test, Page 1 of 8
23 May 2012
University of Cape Town
Department of Mathematics and Applied Mathematics
MAM1000W June test 23 May 2012
Time: 2 hours
Marks: 100
Student Number:
Surname:
First Name:
This test is in two sections. Section A cons
s
; 3 Fq
'l
:
:l O
l=l . rE ; "
n
f
:
i 3 :; '
sa J 6  G
q = = = =
:.^!.:
P
'
G J
9
e,
"3
3
=
>
:"r6
gr H':oFcF
c I t c 
e *
g
ir lo Ed e 3 "  : s
5
i : i e e
E
s
t
;3 f3 qt E
i
e
B
B 3
6
E , 6 .
l
^
.
5
=
"i E
E
P
*
^
le"
I
!.*
63
T
sr r:i
o
= :
Student Number:
Surname:
First Name(s):
University of Cape Town
Department of Mathematics and Applied Mathematics
MAM1000W
Supplementary Exam (Paper 2)
January 2014
Full marks: 100
This question paper consists of 15 pages (including this one).
Answer al
Student Number:
Surname:
First Name(s):
Department of Mathematics and Applied Mathematics
MAM1000W
Test 5
30 September 2014
Time : 18h00 19h30
Full marks: 80
This question paper consists of 12 pages (including this one).
Answer all questions in the spac
MAM1000W first period
Class Test 2, Page 1 of 2
23 March 2009
University of Cape Town
Department of Mathematics and Applied Mathematics
MAM1000W Class Test 2
23 March 2009
First period
Time: 45 minutes
Calculators may not be used during this test. Your st
MAM1000W first period
Class Test 6, Page 1 of 3
12 October 2006
University of Cape Town
Department of Mathematics and Applied Mathematics
MAM1000W Class Test 6
12 October 2006
First period
Time: 45 minutes
Calculators may not be used during this test. You
IIIIIIIII
IIIIIIIIIMIIIHEII
_IIIIIIIIIIIIIIII
University of Cape Town
Department of Mathematics and Applied Mathematics
MAMlODOW
Final Exam (Paper 1) 31 October 2013
rFime : 17h00 19h00 Full marks: 100
o This question paper consists of 16 pages (includi
2LA Linear Algebra
2016
Tutorial 3: Subspaces
1. Prove or disprove: Every line through the origin is a subspace of R2 .
Solution: Let m R. Then the straight line through the origin with slope m is
the set of points
W = cfw_(x, y) : y = mx.
(Note: not cfw_
2LA Linear Algebra
2016
Tutorial 10
Determinants, eigenvalues, eigenvectors, and diagonalization
1. Find the determinant of each of the following matrices. Hence determine whether
each matrix is invertible.
a. A = 6 .
Solution:
det A = 6.
b. B =
1 3
.
2 2