Leaving Certificate Examination 1952 Honours Applied Mathematics
Question 1
A light string hangs from two fixed points
,
which are in the same horizontal line. The string carries a weight of
lb. at
and weight of
lb. at
. The angles
,
,
are
,
,
, respectively. Find, graphically or otherwise, the value of
.
Question 2
A uniform ladder, of weight lb. and length
ft., rests with one end in contact with a smooth vertical wall and the other end in contact with a rough horizontal plane, the inclination of the ladder to the horizontal being
. A man of weight
lb. can ascend just
ft. up the ladder without causing the ladder to slip. Find
, the coefficient of friction between the ladder and the plane.
Question 3
A uniform wiere, weighing ounces, is bent so as to form an isosceles triangle
in which
inches, and
inches. Find the position of the centre of gravity.
What weight must be attached at so that
will be horizontal when the triangle is suspended at
?
Question 4
A train which is being uniformly retarded covers two successive stages, each mile in length, in
seconds and
seconds, respectively. Find the uniform retardation and find how much farther the train will travel before it comes to rest.
Question 5
A car weighing one tone is ascending an incline of in
and is accelerating uniformly at the rate of
rate per sec
. If the frictional resistance to motion are equivalent to
lb. weight, find the horse-power at which the car is working when its speed is
m.p.h.
Question 6
A railway engine weighing tons travels at
m.p.h. round a curve of
yards radius on a level track. The distance between the rails is
feet, and the centre of gravity of the engine is
feet above the rails and midway between them. Find the vertical pressure upon each of the rails.
What is the maximum speed at which the engine could travel round the curve without losing contact with one of the rails?
Question 7
A particle is projected from ground level so as just to clear a vertical tower feet high which is standing on a horizontal plane. As the particle passes over the tower its velocity is
feet per second in a direction making an angle of
above the horizontal. Find the horizontal distance from the foot of the tower (a) to the point where the particle hits the ground, (b) to the point of projection.
Question 8
What is Simple Harmonic Motion?
A particle is moving with Simple Harmonic Motion. When it is feet from its mean position its velocity is
feet per second and its acceleration is
feet per second
. Find the amplitude and the period of the motion.
Where would the particle be two-thirds of a second after passing through its mean position?
Question 9
A rectangular dock-gate is feet in width. The water on one side of it is
feet deep and on the other side it is
feet deep. Find the resultant thrust on the gate, in tons.
To what height must the level of the water on the lower side be raised so that the thrust on that side may be equal to half the thrust on the deeper side?
[One cubic foot of water weighs lb.]
Citation:
State Examinations Commission (2018). State Examination Commission. Accessed at: https://www.examinations.ie/?l=en&mc=au&sc=ru
Malone, D and Murray, H. (2016). Archive of Maths State Exams Papers. Accessed at: http://archive.maths.nuim.ie/staff/dmalone/StateExamPapers/
Licence:
“Contains Irish Public Sector Information licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) licence”.
The EU Directive 2003/98/EC on the re-use of public sector information, its amendment EU Directive 2013/37/EC, its transposed Irish Statutory Instruments S.I. No. 279/2005, S.I No. 103/2008, and S.I. No. 525/2015, and related Circulars issued by the Department of Finance (Circular 32/05), and Department of Public Expenditure and Reform (Circular 16/15 and Circular 12/16).
Note. Circular 12/2016: Licence for Re-Use of Public Sector Information adopts CC-BY as the standard PSI licence, and notes that the open standard licence identified in this Circular supersedes PSI General Licence No: 2005/08/01.
Links:
https://circulars.gov.ie/pdf/circular/per/2016/12.pdf
https://creativecommons.org/licenses/by/4.0/legalcod