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Sharjah Institute of TechnologyAssessment Activity Front Sheet
(This front sheet must be completed by the STUDENT where appropriate and included with the work submitted for assessment)
Students Name:Assessors
Name:Ausama I.Hassan
Date Issued: 30/10/2011Completion
Date:20/11/2011 Submitted on: / /
Qualification BTEC LEVEL 3 Extended Diploma in Electrical and Electronic Engineering -Group A (EBD1A)
Unit No.: 4 Unit Title:Mathematics for Engineering
Technicians
Outcome No. : 1 Outcome Title: Be able to use algebraic methods
Assignment No.: 1
Assessment Title: Algebraic MethodsPart:
1 of
In this assessment you will have opportunities to provide evidence against the following criteria.
Indicate the page numbers where the evidence can be found
Criteria
Refer
ence
To achieve the criteria the evidence must show that the
student is able to:
Tick if
met
Page
numbers
P1Manipulate and simplify three algebraic expressions using the
laws of indices and two using the laws of Logarithms.
P2
Solve a linear equation by plotting a straight-line graph using
experimental data and use it to deduce the gradient, intercept
and equation of the line.
P3 Factorize by extraction and grouping of a common factor fromexpressions with two, three and four terms respectively.
M1Solve a pair of simultaneous linear equations in two
unknowns.
M2Solve one quadratic equation by factorization and one by the
formula method.
Declaration
I certify that this assignment is my own work, written in my own words. Any other persons work
included in my assignment is referenced / acknowledged.
Students Name: Students Signature: Date:
Criteria Achieved
P1 P2 P3M1
M2
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Internal Verifiers approval to use with students
IVs Name:Waleed IVs Signature Date
Front Sheet
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BTEC LEVEL 3 Extended Diploma in Electrical and Electronic Engineering
Unit 4: Mathematics for Engineering Technicians
In your work as a telecommunication technician, you may have to deal with a variety of
calculations and manipulations that need a knowledge of indices, logarithms,factorizations and quadratics . You may also have to deal with a variety of experimental
data that when you graph them you end up with a linear relationship between them and
you have to decide the gradient and the intercept. You will also need to know how to
solve linear simultaneous equations with two unknowns. As part of your course you are
required to prove your abilities to do such algebraic methods of calculations,
manipulations and graphing through solving the following tasks:
Task 1: [ P 1 ]
A. When doing engineering problems, you'll often be required to determine
the numerical value and the units of a variable in an equation. The
numerical value usually isn't too difficult to get, but for a novice, the
same can't be said for the units. Dimensional analysis, is a useful method
for determining the units of a variable in an equation. Another use of
dimensional analysis is in checking the correctness of an equation which
you have derived after some algebraic manipulation. Even a minor error
in algebra can be detected because it will often result in an equation
which is dimensionally incorrect.
Most physical quantities can be expressed in terms of combinations of
five basic dimensions. These are mass (M), length (L), time (T),
electrical current (I), and temperature, represented by the Greek
letter theta (). These five dimensions have been chosen as being basic
because they are easy to measure in experiments. Dimensions aren't the
same as units. For example, the physical quantity, speed, may be
measured in units of metres per second, miles per hour etc.; but
regardless of the units used, speed is always a length divided a time, so
we say that the dimensions of speed are length divided by time, or simply
L/T. Similarly, the dimensions of area are L2 since area can always be
calculated as a length times a length
Dimensional analysis depends mainly on the rules of indices.
Now use the rules of indices to find the dimensions of the physical
quantity (x). Choose only one from each of the following:
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1.
a.12
1
.
.
=LTL
LMLTx
b.L
TLTMLx
1311 . =
c.112
2
.
.
=TMLL
LMLTx
2.
a. ( )[ ]221= LTMx
b. ( )[ ]321= LTMx
c. ( )[ ] 21
21= LTMx
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3.
a.
2
13
3
2
2
1
2
=
TL
M
M
LTx
b.
2
1
3
2
2
1
13
=
LT
M
M
TLx
c.
2
1
34
2
1
=
LT
M
M
LTx
B. Two hypothetical physical quantities(y) and (a) have the following
hypothetical logarithmic relationships. Find the value of (y) . (Choose only
one group):
Group 1
1.
34 log)log2(loglog aaay =
2.
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aaay ln3)3ln29(lnln 32 =
Group 2
1.
45 log)log6(loglog aaay +=
2.
aaay ln6)5ln225(lnln 25 =
Group 3
1.
324 log2)log3(loglog aaay +=
2.
229 ln2)2ln416(lnln aaay =
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Task 2: [ P 2 ]
A ball is ejected vertically up and the following data were recorded(choose one):
Group(a)
Time, t (s) 2 4 6 8
Speed, v (m/s) 79.8 60.1 39.9 20.2
Group(b)
Time, t (s) 4 8 12 16
Speed, v (m/s) 159.1 119.5 80.7 40.9
Group(c)
Time, t (s) 8 16 24 32
Speed, v (m/s) 321.2 238.9 161.3 79.4
1. The relationship between speed and time is expected to be linear. Show that
it is so by plotting the speed against time.
2. Write the general equation of the straight line in terms of the gradient and y-
intercept.
3. Calculate the gradient from the data given. What does it represent?
4. Calculate the y-intercept from the data given. What does it represent?
5. Write the equation of the straight line for this particular case in terms of the
gradient and
y-intercept.
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Task 3: [ P3 ]
Factorize by extraction and grouping of a common factor from the following expressions (choose only one from each group):
Group 1
a. zxxy 11121 +
b. axay 12144 +
c. bxby 981 +
d. cxcy 1149 +
Group 2
a. xyyxyx 18963 232 ++
b. yxyxyx 2232 16872 ++
c. 322322 18936 yxyxyx ++
d. yxyxyx 2233 36954 ++
Group 3
a. bybxyx 2147 +++
b. ayaxyx 2168 +++
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c. bybxyx 3279 +++
d. cycxyx 44812 +++
Task 4: [ M1 ]Applying Kirchoffs current and voltage laws at the junction and the two loops of the electric circuit below produces thefollowing linear simultaneous equations:
( ) 121311 VIIRIR =++ (1)( )
221322 VIIRIR =++ (2)
Where :
=21R
=42R
=53R
Choose only one from below:
A.
VV 61 =
VV 22 =
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B.
VV 81 =
VV 32 =
C.
VV 91=
VV 52 =
With the above given equations (1) and (2) and the given data calculate algebraically the currents
21 .. IandI
Task 5: [ M2 ]
The vertical distance, )(s , in meters, covered by a particle thrown vertically up with an initial speed )(u, in meters per
seconds, is given by:2
2
1atuts +=
(1)
Where:
t= time (in seconds) taken to cover the distance.
210)(
= msnalgravitatioondeceleratia
asuv 222+=
0=v
20
2us
Equation (1) reduces to:
22
520
tutu
=
The final equation which gives the time taken to cover the maximum height the particle
reaches is hence given by the following quadratic equation:
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02010022=+ uutt (2)
Required to solve equation (2) to find the time (t) by:
1. Factorization
2. The formula.
Use only one value of (u) from the list below:
A. smu /50=B. smu /80=C. smu /90=D. smu /100=
Assessment Feedback Form
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(This feedback sheet must be completed by the ASSESSOR where appropriate
Students Name:
Unit No.: 4Assessment Title:
Algebraic Methods
Grading Criteria Achieved:
Unit Title: Mathematics for Engineering Technicians
Outcome No.: 1
Outcome Title: Be able to use algebraic methods
Assignment No.: 1
Part: 1o
f1
Criteria
ReferenceAssessment Criteria
Achieve
dEvidence Comments/feedback
P1
Manipulate and simplify three algebraic
expressions using the laws of indices and two
using the laws of Logarithms.Yes/No
Task1:
P2
Solve a linear equation by plotting a straight-
line graph using experimental data and use it to
deduce the gradient, intercept and equation of
the line.
Yes/NoTask2:
P3
Factorize by extraction and grouping of a
common factor from expressions with two,
three and four terms respectively.Yes/No
Task3:
M1Solve a pair of simultaneous linear equations
in two unknowns.
M2Solve one quadratic equation by factorization
and one by the formula method.
Assessors General Comments:
Assessors Name: Ausama I.Hassan Signature: Date:
Students Comments:
Students Name: Signature: DateStudent's Work has been Internally Verified
IVs Name: Waleed IVs Signature Date
Feedback Sheet
Criteria Achieved
P1P2
P3M1
M2
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