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21Nov2018

Leaving Certificate Examination 1961 Honours Applied Mathematics

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Question 1

ABC is a triangle in which BC=8", \cos B = \frac{1}{2}, \cos C = \frac{11}{14}. Forces of 3, 12, 7 lb. wt. act along BA, BC, CA, respectively. How far from B does the line of action of their resultant cut BC?.

Find the magnitude of the resultant in lb. wt., correct to one place of decimals, and find the angle which its line of action make with BC, correct to the nearest degree.

Question 2

Explain the terms “limiting friction,” “coefficient of friction.”

When a truck is ascending an incline of 28 in 100 with a uniform acceleration of 1.6 ft. per sec. per sec., a box on the floor of the truck is just about to slide backwards. Show by diagram the forces acting on the box, and find the coefficient of friction between the box and the floor of the truck.

Question 3

A man is cycling at 10 m.p.h. in a steady wind. When he cycles in a direction 30^\circ north of east the wind appears to him to blow directly from the east. When he cycles due east the wind appears to him to blow from the south-east. Find the velocity of the wind in magnitude and direction.

Question 4

Two bodies, of mass 50 gm. and 350 gm. respectively, are lying on a smooth horizontal bench which is 10\frac{1}{2} feet high. The 50 gm. body is at the edge of the bench and the 350 gm. body is 4 feet away in a direction perpendicular to the edge, the bodies being connected by a light inextensible string 8 feet long. If the 50 gm. body is pushed gently over the edge, find how many seconds later it will reach the ground.

Question 5

Derive an expression for the total time of flight of a projectile in terms of its initial velocity and angle of projection.

A, B, C, are three collinear points on a horizontal plane. A projectile fired from A passes over B at a height of 21 feet and reaches its greatest height as it passes over C. If BC=48 feet and the total time of flight of the projectile is 2\frac{1}{2} seconds, find its initial velocity.

Question 6

A mass of 4 lb. suspended from a fixed point by a light inextensible string 2 feet long acts as a conical pendulum, the mass describing a horizontal circle at a uniform rate of 60 revolutions per minute. Find the tension in the string, in lb., wt., and the inclination of the string to the vertical.

Question 7

A particle is moving along a straight line so that is distance x (cms.) from a fixed point O at the time t (secs.) is given by the formula

    \[x=5\sin2t\]

.

Show that the motion is simple harmonic and find the periodic time and the maximum velocity.

If the velocity of the particle at P is 6 cm. per sec., find its acceleration at P, and find the least time the particle takes to travel to P from O.

[See Tables, p. 30].

Question 8

A triangular lamina ABC is immersed in a liquid of specific gravity 0.9 so that the vertex A is at the surface and the sides AC is vertical. If AB=5", BC=3", CA=4", find the thrust of the liquid on ABC in ounces.

P is a point on AC such that the thrust of the liquid on ABP is give-ninths of the thrust on ABC. Find the length of AP.

[A cubic foot of water weights 62\frac{1}{2} lb.]

Question 9

ABCD is a quadrilateral lamina in which AB=10", AC=6", BC=8", AD=DC=5". Find the perpendicular distance of the centre of gravity of ABCD from AC.

Find, also, the perpendicular distance of the centre of gravity of BCD from AB.


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

 

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