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28 Sep 2018

Leaving Certificate Examination 1943 Honours Applied Mathematics

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Question 1

Two ships quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds and quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds are quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds miles apart, quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds being due west of quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds and steaming due East at quicklatex.com-ed5decd492fdc6648538222379ceaf27_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds miles per hour. quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds is steaming due North at quicklatex.com-ced9adf500abe3e625f021cf18429a9e_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds miles per hour. When will they be nearest one another and what will be their distance apart at that time?

Question 2

A particle slides down a smooth inclined plane quicklatex.com-ed5decd492fdc6648538222379ceaf27_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds feet long in quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds seconds : find its acceleration and the inclination of the plane to the horizontal.

How far from the bottom should a second particle be started on the plane one second after the first had started from the top so that the two particles will reach the bottom together?

Question 3

On a rectangular sheet of iron, quicklatex.com-ed5decd492fdc6648538222379ceaf27_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds inches by quicklatex.com-3883c8dfa7e1fd380cd2fa2674d982e2_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds inches, marks are made on two adjacent edges at a distance of quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds inches from one corner. These marks are joined by a straight line and the sheet folded down along this line. Find the centre of gravity of the sheet so folded.

Question 4

Describe any method by which the acceleration due to gravity may be determined experimentally. Mention the causes of error likely to affect the result.

Question 5

An object of quicklatex.com-ced9adf500abe3e625f021cf18429a9e_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds lb. wt. is placed upon a sheet of glass resting on a horizontal table and a string attached to the object passes horizontally over a pulley at the end of the table. When a weight of quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds lb. is hung on the free end of the string, the object is drawn from rest through a distance of quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds feet in quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds seconds. Find the coefficient of friction between the object and the glass and also the tension in the string.

Question 6

A uniform iron bar quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds, quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds ft. long, weighs quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds lb., has a quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds lb. weight fixed to it at a point quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds ft. from quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds, and is supported by means of cords attached to its ends from a peg quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds. The cord quicklatex.com-c703974f82fa531d93879bbfbfb6c9cb_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds is quicklatex.com-6024d8b1a86917dc3144686a41ea70aa_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds ft. long and the cord quicklatex.com-156c32c8826a40241f75e66f5f0ad483_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds is quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds ft. long. Find the inclination of the bar to the horizontal in the position of equilibrium and find the tensions in the cords.

Question 7

The height of a lift from the ground quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds seconds after starting is quicklatex.com-63ab7de62920c09a3246a8ce084ab3ce_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds feet, given by the following table :-

quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds quicklatex.com-edeca52e97715225ceecec173423f15e_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds quicklatex.com-2b18fa15a2f284d990fd81b9cae524ce_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds quicklatex.com-3883c8dfa7e1fd380cd2fa2674d982e2_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds quicklatex.com-0d7f64ee36de9328eff9d1e69ba1ac35_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds quicklatex.com-ed5decd492fdc6648538222379ceaf27_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds
quicklatex.com-63ab7de62920c09a3246a8ce084ab3ce_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds quicklatex.com-e37a7ce3683aa7c32967f8f4105807da_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds quicklatex.com-0b6795a8859b2dbce2c767cd70071030_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds quicklatex.com-1e3189a3cddbe9fbce4fee1e2860c5a8_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds quicklatex.com-992e140b7d785a48a391703d540c0fec_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds quicklatex.com-62c3d43e954ab68daef1e02c388929d5_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds quicklatex.com-f7fec9c181a67bd5545e7c7427db2121_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds quicklatex.com-03a099fb35686761d3247ea18a036180_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds quicklatex.com-cb3af3dc88e7960c9d2f809c44de100c_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds quicklatex.com-43263fef7ad1c19ea5448bafe13da4af_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds quicklatex.com-916f0d604ec884175937e8c38eeeff28_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds quicklatex.com-f705f27a978d01fea9bd54966f324228_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds quicklatex.com-b90cbf34e19a25067a4d43bd71e8f98a_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds

Draw the distance-time graph for the lift. Find the greatest velocity of the lift.

Draw a rough velocity-time graph, and use it to give a short account of the variation in the acceleration throughout the journey.

Question 8

An inverted cone, of angle quicklatex.com-43254279a766115b4c8c77b4f9e086ff_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds, has a smooth inside surface and rests with its axis vertical. A smooth particle moves in a horizontal circle on the inside of the cone with a uniform speed of quicklatex.com-2b18fa15a2f284d990fd81b9cae524ce_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds feet per second. Find the distance of the particle from the vertex of the cone.

Question 9

A particle is moving in a straight line with Simple Harmonic Motion. When it is quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds ft. and quicklatex.com-ed5decd492fdc6648538222379ceaf27_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds ft. from the centre of its path, its speed are quicklatex.com-4c8846d90c9db2c7945bc56cc2df5c3f_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds ft./sec. and quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1943 Honours Applied Mathematics | Maths Grinds ft./sec. respectively. Find the period and the amplitude of the motion. Find also the maximum speed and the maximum acceleration of the particle.

 


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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