Solutions to Tutorial 9 Section D: Self-Practice Questions
1(i)
y = sec 2 x
dy
= 2sec 2 x tan 2 x
dx
d2 y
= 2 ( 2sec 2 x tan 2 2 x + 2sec3 2 x )
2
dx
d2 y
When x = 0 , y = 1,
= 2 ( 2sec3 ( 0 ) ) = 4 (shown)
dx 2
(ii)
When x = 0 ,
dy
=0
dx
By Maclaurins Th
As a bookkeeper, you complete your work by completing the tasks of the
accounting cycle. Its called a cycle because the accounting workflow is
circular: entering transactions, manipulating the transactions through the
accounting cycle, closing the books a
OXFORD BROOKES UNIVERSITY
PROGRAMME: MASTER IN BUSINESS ADMISTRATION
COURSE: QUANTATIVE
TAKE AWAY ASSISGNMENT
STUDENT NAME : JUDY O. CARO
QUESTION ONE
Drivers are classified by an insurance company as low, average or high risk drivers.
The company estimat
Raffles Institution Mathematics 9740 Year 5 2011
_
Online Assignment S1: Permutations and Combinations
1
Find the number of different arrangements of all the letters of the word
ABRACADABRA.
Solution
There are 11 letters comprising 5 As, 2 Bs, 2 Rs, 1 C &
Raffles Institution
H2 Mathematics 9740
Year 6 2012
Tutorial S7 Correlation and Regression
12 Optional (N98/2/8)
(i)
(ii)
13 Optional (N96/4/9)
The sample correlation coefficient is calculated using
data from a sample (a subset of the population) which
ma
2012 Tutorial S6
Suggested Solution for Q12:
Let X be the number of people who appear, out of 40 passengers.
Then X ~ B(40, 0.85) .
P(X > 36) = 1 P( X 36) 0.13017 = 0.130 (3 s.f.)
Note: P( X > 36) = 0.130 if
p1 = 0.15
and P( X > 36) decreases if p1 > 0.15
Tutorial S4: Normal Distribution
Section D (Self Practice) Solutions
1 Let X be the mass of an apple in grams. Then X ~ N( , 2 ) .
P( X > 125) = 0.10
125
= 0.10
PZ >
125
PZ
= 0.90
125
= 1.2816 (5 s.f.)
P( X < 75) = 0.13
75
PZ <
= 0.13
75
= 1.
Tutorial S3 (Suggested Solutions)
Binomial and Poisson Distributions
Section D (Self-Practice Questions)
1
(i) Let X be the number of vehicles, out of 5, which turn right.
X ~ B (5, 0.9)
P(X3)
=
1P(X 2)
=
10.00856
=
0.9914
=
0.991 (3s.f.)
(ii) P(X = 4X 3)
Tut S3A Binomial Distribution
Solution to Q12
Let X be the number of defective items.
X B(6, p)
Probability that we have exactly 2 defective items in a sample of 6 is
P = P( X = 2) = 6C2 p 2 (1 p) 4
We are looking for value of p that gives P as a maximum.
Raffles Institution
H2 Mathematics 9740
Year 6 2012
_
S2: Probability
Challenging Questions / Extensions Solutions
k
r k
r
13 (a) m n and
k m + n m + n
m n
k r k
m + n
r
(b) To require k draw before 1st white means previous k-1 all black hence
m
Tutorial 12B: Complex Numbers II
6
On a single Argand diagram, sketch the loci given by
(i) z 3 = 4 ,
(ii) z 3 3i = z .
Hence, or otherwise, find the exact values of all the complex numbers z that satisfy both (i)
and (ii).
Answer
Im
z 3 = 4
3
4
O
4 cos
7
Tutorial 12B: Complex Numbers II
Section C (Extension / Challenging Questions) Solutions
12
On an Argand diagram, sketch the locus of the point representing the complex number z
where z + i = 2 z 2i . [Hint: Find the Cartesian equation of the locus]
Hence
Tutorial 12A : Complex Numbers I
Section D (Self-Practice Questions) Solutions
1(i) Find the exact values of x, y R such that
3
5
+
= 4.
x + iy 2 + 6i
[3]
(ii) The complex number z is given by 3 + i .
Find the modulus and argument of z .
k
1
is real.
*
z
Tutorial 11A2: Vectors I Equations of Straight Lines
Section C (Solutions)
_
Tutorial 11A2: Vectors I Equations of Straight Lines
Page 1 of 10
Raffles Institution H2 Mathematics 9740 Year 6 2012
_
_
Tutorial 11A2: Vectors I Equations of Straight Lines
Pag
Raffles Institution
H2 Mathematics 9740
Year 6 2012
_
Tutorial 11A1: Vectors I Ratio Theorem and Scalar Product
Section C Extension/Challenging Questions (Solutions)
9
CB =
1
1
AB, BD =
AB
m +1
m 1
CD = CB + BD
1
1
AB +
AB
m +1
m 1
2m
=2
AB
m 1
2m
=
BA
1
Chap 10: Differential Equations
Comments on Section B Challenging Questions
Q11
x
x
x
Assuming that the other function is y, the DE is y'.2xe = y.2xe + y'.e which
2
o
2
2
2xy
, a variable separable DE. The solution to this, assuming that the
2x 1
student
TRUE/FALSE
1. Information is a business resource.
ANS: T
PTS: 1
2. An information system is an example of a natural system.
ANS: F
PTS: 1
3. Transaction processing systems convert non-financial transactions into financial transactions.
ANS: F
PTS: 1
4. Th