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7/30/2019 Assign1.U4.Ausama.mechanical Final
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Internal Verification of Assignment
Briefs
Qualification BTEC LEVEL 3 Extended Diploma in Mechanical Engineeringyear 1
Unit No. 4 Title Mathematics for Engineering Technicians
Outcome No. 1 Title Be able to use algebraic methods
Assignment No. 1 Title Algebraic Methods
Part 1 of 1
Assessor Name Ausama Ibrahim Hassan
Internal Verifier Ezz Eldin Hassan
Evaluation criteria
or 1
st
draft
Final
Brief
1 Is the assignment word processed?
2 Is there a title to the assignment?
3Is there reference to the unit and the learning outcomes being
assessed, including outcome statements?
4Is there a suitable scenario/introduction that is appropriate to the
level of the student?
5 Is it clear what evidence the student needs to generate?6 Is the timescale for the assignment appropriate?
7
Do the grading criteria relate to the outcome(s) being assessed and
the P/M/D criteria from the qualification specification? (where
appropriate)
8 Is the assignment appropriate for the level of the students?
9 Is the hand-in date (Completion Date) clear?
10 Overall is the assignment fit for purpose?
Comments
Assessor's Signature Date
IV's Signature Date
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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: 20/11/2011 Completion Date: 4/12/2011 Submitted on: / /
Qualification BTEC LEVEL 3 Extended Diploma in Mechanical Engineeringyear 1
Unit No.: 4 Unit Title: Mathematics for Engineering Technicians
Outcome No. : 1 Outcome Title: Be able to use algebraic methods
Assignment No.: 1Assessment Title: Algebraic Methods
Part: 1 of 1
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
Reference
To achieve the criteria the evidence must show that the
student is able to:
Tick if
met
Page
numbers
P1
Manipulate and simplify three algebraic expressions using the
laws of indices and two using the laws ofLogarithms.
P2
Solve a linear equation by plotting a straight-line graph usingexperimental data and use it to deduce the gradient, intercept andequation 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.
M2
Solve 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 P3 M1 M2
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Internal Verifiers approval to use with students
IVs Name:
Ezz Eldin HassanIVs Signature Date
Front Sheet
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In your work as a mechanical 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 alsoneed 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 algebraicmethods 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:
7/30/2019 Assign1.U4.Ausama.mechanical Final
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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.
2
121
LTMx
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
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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.
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 8Speed, 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 18963232
b. yxyxyx 2232 16872
c.322322 18936 yxyxyx
d. yxyxyx 2233 36954
Group 3
a. bybxyx 2147
b. ayaxyx 2168
c. bybxyx 3279
d. cycxyx 44812
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Task 4: [ M1 ]Applying Kirchoffs current and voltage laws at the junction and the two loops of the electriccircuit below produces the following linear simultaneous equations:
121311 VIIRIR (1)
221322VIIRIR
(2)
Where :
21R
42R
53RChoose only one from below:
A.
VV 61
VV 22
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
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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
0v
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:
020100 22 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
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Assessment Feedback Form
(This feedback sheet mu st be completed by the ASSESSOR where appropriate)
Students Name:
Unit No.: 4
Assessment Title: algebraic methods
Criteria Achieved
P1 P2 P3 M1 M2
Grading Criteria Achieved:
Unit Title: Mathematics for Technicians
Outcome No.: 1
Outcome Title: Be able to use algebraic methods
Assignment No.: 1
Part: 1 of 1
Criteria
Reference Assessment Criteria Achieved Evidence Comments/feedback
P1
Manipulate and simplify three algebraic expressions using thelaws of indices and two using the laws of Logarithms. Yes/No
P2
Solve a linear equation by plotting a straight-line graph usingexperimental data and use it to deduce the gradient, intercept andequation of the line.
Yes/No
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.
M2
Solve one quadratic equation by factorization and one by theformula method. Yes/No
Assessors General Comments:
Assessors Name: Ausama I. HassanSignature:
Date:
Students Comments:
Students Name: Signature: Date
Student's Work has been Internally Verified
7/30/2019 Assign1.U4.Ausama.mechanical Final
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IVs Name:Ezz Eldin Hassan
IVs Signature Date
Feedback Sheet
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