CORK INSTITUTE OF TECHNOLOGY
INSTITIUID TEICNEOLAIOCHTA CHORCAI
Semester 3 Examinations 2008
Module Title: Automotive Maths
Module Code:
MATH 6001
School:
School of Mechanical and Process Engineering
Programme Title:
Bachelor of Arts in Transport Management & Technology – Stage 1
Programme Code:
TTMAT_7_Y1
External Examiner(s):
Internal Examiner(s):
Instructions:
Dr. P. Robinson
Mr Michael ORiordan
Answer question one and any three other questions.
All questions carry equal marks.
Duration:
2 Hours
Sitting:
Autumn 2008
Requirements for this examination: Graph Paper, Statistical Tables
Note to Candidates: Please check the Programme Title and the Module Title to ensure that you have received the
correct examination paper. If in doubt, please check with an invigilator.
Q. 1
(a) Evaluate (33 ×34) ÷ 36
2.5 marks
(b
2.5 marks
)
Transpose 2adc= d to make c the subject
(c) Evaluate 5.71 × 104+ 7.77 ×104
2.5 marks
(d
2.5 marks
)
(e)
(f)
Convert 8653 ×10 −6 meters to mm
Evaluate
Sin 30 ο
Cos 30 ο
Evaluate 36
1
2.5 marks
2.5 marks
2
(g) Express in standard form 0.0065
2.5 marks
(h
Given a castor angle tolerance as 6°20΄± 40, state the minimum and maximum allowable
)
castor angle
2.5 marks
(i)
Convert 130º to radians
2.5 marks
(j)
Convert 2.5 radians to degrees
2.5 marks
An engine has an original bore of 86 mm and a stroke of 72 mm and has a compression ratio 8.2
Q. 2
If the engine cylinder bore is increased by 1.5 mm oversize, then calculate:
(a)
(b
)
(c)
The original capacity.
5 marks
The capacity after being rebored
5 marks
Percentage increase in capacity
5 marks
Compression ratio after reboring
5 marks
The percentage increase in compression
5 marks
(d
)
(e)
Page 2 / 5
Q3
(a) Solve for x and y
5 marks
2x + 3y = 11
4x + 2y = 10
(b
)
Solve for x and y
5 marks
8x – 3y = 39
7x + 5y = -4
(c)
Solve : A copper wire of length l = 2km has a resistance of 4 Ω and
a resistivity ,p of 17.2 × 10 – 6 Ω mm. Find the cross –sectional area,
5 marks
of the wire given that
R=
(d
)
(e)
pl
a
Solve for x: 3(2 x − 6 ) + 2(x + 3) = 4( x − 5)
Transpose the equation to make v the subject: s =
Page 3 / 5
5 marks
1
(u + v ) t
2
5 marks
Q4
12 marks
(a) Draw a histogram, frequency polygon for the data given below
Cass Intervals
Frequency
Cumulative Frequency
1.24 -1.26
2
2
1.27 - 1.29
4
6
1.30 - 1.32
4
10
1.33 - 1.35
10
20
1.36 -1.38
11
31
1.39 – 1.41
5
36
1.42 – 1.44
3
39
1.45 – 1.47
1
40
(b
7 marks
)
The diameters of some of copper pipes are measured and recorded to the nearest tenth of a millimetre,
as shown in the table below.
Calculate the mean diameter of the copper pipes.
Diameter of copper pipe
Frequency
36.5 mm
4
37.7 mm
4
35.8 mm
5
36.9 mm
7
(c)
3 marks
Calculate the median of following data:
3, 1, -1, 6, 9, 7, 1
(d
3 marks
)
Calculate the mode of following data
4, 5, 1, 4, 6, 2, 4, 3, 6
Page 4 / 5
Q. 5
(a)
10 marks
A vehicle engine is running at 3500 RPM. The road wheel has an effective diameter of 0.868m, the
pinion has 19 teeth and the crown wheel has 78teeth.
The gearbox ratio is 3.45.
Calculate the speed of the vehicle.
(b
15 marks
)
A certain vehicle has a wheelbase of 4 meters and a track of 1.6 meters. When the vehicle is turning
on a certain radius the steering angle of the inner wheel is 22 degrees.
Calculate
(i)
The angle of the outer wheel.
(ii
The length of the radius (measured to the centre of the axle).
)
Q6
(a)
7 marks
On measuring a camber angle of a road wheel a 520mm long vertical line drawn through the centre
point of the top of the wheel meets the road surface 35mm from the centre of the tyre thread as shown
in diagram. Calculate the camber angle.
(b
9 marks
)
If the area of a circle is the same as that of a square with sides of 9.2 cm.
Calculate the diameter of the circle.
(c)
9 marks
A measurement taken around the circumference of an engine flywheel of a diameter 360mm shows
Page 5 / 5
that the inlet valve opens 40mm before top dead centre (t .d .c). What angle does this measurement
represent?
Q. 7
(a)
14 marks
The velocity of a body at various times is given in the table below:
Velocity
(m/s)
7.7
10.5
13.3
15.5
20.5
23
Time
(sec)
1
2
3
4
6
7
(i)
Plot the graph
(ii)
From the graph, determine the velocity at 5 seconds
(iii)
Calculate the acceleration rate (slope of the line)
(b)
11 marks
Calculate the speed of rotation in revolutions per minute of the driven wheels of a motorcar
travelling in straight linen at a speed of 24.05 km/hr, if the overall diameter of the wheel and tyre
assembly is 420mm. π = 3.142
.
Page 6 / 5