ASSESSMENT ACTIVITY FRONT SHEET Learner name Course title BTEC Higher...

Question

ASSESSMENT ACTIVITY FRONT SHEET

Learner name
Course title	BTEC Higher National Diploma in Mechanical Engineering -VT720
Assessor name
Internal Verifier name		Date	15/11/’12
Unit number and title	1. Analytical Methods for Engineers – A/601/1401
Assignment title	A02: ‘ Calculus’ ‘ Statistics and Probability’
Group work	NO
Outcome number(s) and statement(s)	3 Analyse and model engineering situations and solve problems using calculus. 4 Analyse and model engineering situations and solve problems using statistics and probability.
Date set		Hand-in date
Review dates	1	2	3

Learner declaration

I confirm that the work submitted for this assignment is my own.
Learner signature	Date

Introduction

Purpose/aims	This assignment provides the student with the opportunity to acquire knowledge of a range of mathematical techniques such as techniques of calculus, statistics and probability for the analysis, modelling and solution of realistic engineering problems.
Background or scenario	You are a new employee in an auto manufacturing company working as a trainee. Your employer has asked you to do the following tasks and to prepare a computer – processed assignment report showing all intermediate steps. No hand-written work will be accepted.

Tasks

Task #

Task

Criteria covered

1

1.1 Differentiate algebraic and trigonometric functions using
the product, quotient and function of function rules.
a)
b)
c)
1.2 Determine the first and the second derivative for algebraic,
logarithmic, inverse trigonometric and inverse hyperbolic
functions:
a)
b)
c)
d)
1.3 Integrate functions using the rules, by parts, by
substitution and partial fractions.
a)
b)
c)
d)
1.4

a) Solve the following engineering problem using calculus:
Find the acceleration of an object oscillating in a straight
line whose displacement is given by s = a cos?t + b sin?t,
where ?, a, b are constants.
b) Analyze the following engineering situation:
In the case where a = 0 find when
(i) the velocity is zero,
(ii) the acceleration is zero.

P3.1, P3.2, P3.3, P3.4

2

2.1 The thickness of 20 samples of steel plate are measured and
the results (in mm) to two significant figures are as follows:

7,4 7,2 6,5 7,1 7,8 7,3 7,5 6,2 6,9 6,8
6,5 6,7 7,3 7,4 6,5 6,8 7,3 7,6 7,0 6,9.
a) Arrange the engineering data in 6 equal classes between
6,2 and 7,8 mm. Represent engineering data in tabular
form determining the frequency distribution.
b) Represent the same data in graphical form using
histogram.
2.2 For the engineering data given in Task 2.1 determine:
i) measures of central tendency (Mean, Median, Mode)
ii) measures of dispersion ( Range, Standard Deviation, IQR)
2.3 Consider the following engineering situations (I and II).
For each situation(I and II) :

Apply the Pearson product moment correlation coefficient.

Apply the equation of the regression line.

(I) An auto manufacturing company wanted to investigate how the price of one of its car models depreciates with age. The research department at the company took a sample of eight cars of this model and collected the following information on the ages (in years) and price (in hundreds of dollars) of these cars.

Age	8	3	6	9	2	5	6	3
Price	19	92	51	22	146	43	37	97

(II) The following data give information on the ages (in years) and the number of breakdowns during the past month for a sample of seven machines at a large company.

Age	12	7	2	8	13	9	4
Number of breakdowns	10	5	1	4	12	7	2

2.4 Use the normal distribution and confidence intervals to estimate the quality of the following engineering system.
The mean diameter of a sample of 500 rollers is normally
distributed, it is 23,50 mm and the standard deviation 0,5
mm. Rollers are acceptable with diameters 23,36±0,54 mm.
a) Estimate the probability of any one roller being within the

acceptable limits, using the fact that the mean diameter is
normally distributed.
b) Using the confidence intervals, estimate the limits
between which all the diameters are likely to lie.

P4.1, P4.2
P4.3, P4.4

M1

Using your regression model (Task 2.3 I), produce forecast of
a) the price of a 7-year-old car.
b) the price of an 18-year-old car.
Comment on your findings.

M2

Analyze the answer obtained in Task 1.4 by using an
accurate graph of the current function.

M3

Use spreadsheet to present a scatter diagram for the data in Task 2.3. Plot the regression line on the scatter diagram. Coherently present and communicate work using technical language accurately.

005_ojjc5k-g0bou2nb.docx

Robert · Accepted Answer

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ASSESSMENT ACTIVITY FRONT SHEET Learner name Course title BTEC Higher National Diploma in Mechanical Engineering -VT720 Assessor name Internal Verifier name Date 15/11/’12 Unit number and title 1....

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