+
City&
09
Guilds
4 01 111
9209-401 NOVEMBER 2018
Level 4 Diploma in Electrical and Electronic Engineering
Level 4 Diploma in Mechanical Engineering
Engineering mathematics
Monday
provided, stick your candidate
12 November 2018
09:30-12:30
barcode label here.
Candidate name (first, last)
First
LLIIILILIILELLLT
Last
Candidate enrolment number
Gender (M/F)
Date of birth (DDMMYYYY)
LILILLI
ASsessment date (DDMMYYYY)
Centre number
Candidate signature and declaration*
in this bOx.
If additional answer sheets are used, enter the additional number of pages
label is in
barcode
their
that
check
must
candidates
Before taking the examination, all
the appropriate box. Incorrectly placed barcodes may cause delays in the markingprocess.
Please ensure that you staple additional answer sheets to the back of this answer booklet, clearly labelling
and qualification number in BLOCK CAPITALS.
these with your full name, enrolment number, centre number
unless otherwise instructed.
a
All candidates need to use a black/blue pen. Do notuse pencil or gel pen,
to City & Guilds, and will be
returned
be
will not
If provided with source documents, these documents
shredded. Do not write on the source documents.
in this examination and that I will
*I declare that I had no prior knowledge of the questions
ot divulge to any person any information about the questions.
examination
fou should have the following for this
non-programmable scientific calculator
General instructions
drawing only.
Use black ball-point pen. Use pencil
clear for scanning purposes.
and
bold
be
must
Any pencil drawings
brackets.
in
shown
The marks for questions are
Answer allquestions.
for
.Write all of your working out and
answers
in this booklet.
Answer the questions in the spaces provided.
cannot be marked.
AnswerS written in margins or on blank pages
marked.
to
be
do
Cross through any work you
not want
Round final answers to three significant figures unless otherwise stated.
Show all calculations. If you usea calculator, show sufficient steps to justify
your answer.
The City and Guilds of London Institute 2018
STOO054052 A4 PO4500136893 1038%682
418072384350116
+
12 Novernber 2018
a
Cnange the subject of the formula from A
to x.
(5 marks)
AT
**
b)
be simplified to
Show that the formula for x may
(3 marks)
rA-TtA +37t)
AA + 21)
*******
*********
*
***************
(Total marks 8)
T
12 November 2018
9200-401
a
Obtain the real number ranges for which the following inequalities hold.
4
b)
(3 marks
(4 marks)
x-1
(Total marks 7)
-
-
X-1
+
3
See next page
1214yernher 91
401
Solve the simultaneous equations
3-2y 10
+
Xy +2y = 50
(/rmark
(Total marks 7)
1Nveniler )1
-401
Show that
cos 20+2sina =(cos
sin )*
sin 28
(/maka)
(otal marks 7)
418072384350516
eenex page
+
12 November 2018
Obtain all of the angles
2cos0 Cose
in the
interval (0, 2 t] that satisfy the
equation
(11 marks)
(Total marks 11)
6
A01
12Novermer 2014
dy
d'y
Derive
expressions
for
the
lirst
derivativeand
second
derivativeyof
the function
y=eSin2x
(6 rmarks)
(Total marks 6)
7
418072384350716
See next page
12 November 2014
401
A horizontal beam of length /carries a uniformily distributed load ol w NI. llhe bean
is rigidly fixed at both ends so that the slope of the beam is horlzontal at eachod. The
downward deflection yat a distance.r from one end is givern by
w24E
where E and I are constants.
a)
Determine
the position of the maximum deflection in the beam
i)
i)
an equation for the maximum deflection in terms of the given data.
***
******
8
(6 rrarks)
2 rnarks)
F
12 November 2018
9-401
b)
Obtain the position(s) of any points of inflection in the loaded beam.
5 marks)
(Total marks 13)
9
See next page
+
12 November 2018
401
Evaluate the following integrals.
a) r2sin r3 dr
b)
(2 marks)
(8 marks)
d
(Total marks 10)
+
10
1n7202E101.
12 November 2018
9-401
Calculate the area enclosed by the curves
y
6x+
(6 marks)
xandy2 =*+ 10x
(Totalmarks 6).
11
See next page
he brakes of a vehicle are
vehicle speed v satisfies theapplied when the vehicle speed is V
m/s)Subsequently, the
equation
12 Novemb
2018
do23
where
a)
a
is
a
constant and x is the distance travelled
after
braking.
Obtain an expression for the total
distance d travelled after the brakes are
applied until the vehicle has comes to a
complete stop.
Calculate the stopping distance when V 25 m/s and a
=
-
(5 marks)
2
(2 marks)
***
e*****
(Total marks7)
12
2
101
+
12 November 2018
401
Express the complex number z=-+3
a
(6 marks)
polar form
(2 marks)
b)
Cartesian form (a + jb).
(Total marks 8)
13
418072384351316
See next page
12 November 2018B
d
the
values of real numbers x and y that satisfy the equation
(10 marks)
E1-J
+ ,2x +/y 51 +)
2-i
(Total marks 10)
14
418072384351416
End of examination