EBD1A Unit4 Ass.1 2011-2012.Ausama.border

7/30/2019 EBD1A Unit4 Ass.1 2011-2012.Ausama.border

1/13

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


2/13

Internal Verifiers approval to use with students

IVs Name:Waleed IVs Signature Date

Front Sheet


3/13

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:


4/13

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


5/13

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.


6/13

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 =


7/13

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.


8/13

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 +++


9/13

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 =


10/13

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:


11/13

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


12/13

(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


13/13

Date post:	14-Apr-2018
Category:	Documents
Upload:	osama-hassan
View:	216 times
Download:	0 times

EBD1A Unit4 Ass.1 2011-2012.Ausama.border

Documents