assign1.u4.ausama.mechanical final

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:


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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


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IVs Name:Ezz Eldin Hassan

IVs Signature Date

Feedback Sheet


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