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3Oct2018

Leaving Certificate Examination 1946 Honours Applied Mathematics

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Question 1

A train travelling at quicklatex.com-03a099fb35686761d3247ea18a036180_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds feet per second is brought to rest, its speed after quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds secs. being given by the table :

quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds secs.quicklatex.com-76ca4871224b050607ca9fa7e541ebb1_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grindsquicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grindsquicklatex.com-8a0f60b8ca3ec09a3984d53508863c9a_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grindsquicklatex.com-66bafba23129fa8ab0a7d7fd2fc25d52_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grindsquicklatex.com-6fa002e1799dcb54bc79a06dc47ef0af_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grindsquicklatex.com-cbbca562b8a27132c102a81b44b1362d_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grindsquicklatex.com-7260fe4f20eb47e11e44b79da133e21c_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds
quicklatex.com-8bafe7d16e660869fc203e8bffd77abc_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds ft./sec.quicklatex.com-03a099fb35686761d3247ea18a036180_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grindsquicklatex.com-55947b5971ee17c162024320bb0d3a09_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grindsquicklatex.com-4c8846d90c9db2c7945bc56cc2df5c3f_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grindsquicklatex.com-3c93d87eeccffc684ed16ac57c3e9f0f_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grindsquicklatex.com-2b18fa15a2f284d990fd81b9cae524ce_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grindsquicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grindsquicklatex.com-76ca4871224b050607ca9fa7e541ebb1_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds

Draw the velocity-time graph. Find, approximately, (i) how far the train travelled in the quicklatex.com-7260fe4f20eb47e11e44b79da133e21c_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds secs., (ii) the retardation when quicklatex.com-e8c5059557266924f5e8d868ecdf0c0c_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds.

Question 2

A gate weighing quicklatex.com-fef5d9bb0bd664dfe03d2ae1a00c063d_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds lb. has its centre of gravity quicklatex.com-6024d8b1a86917dc3144686a41ea70aa_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds‘ from the line of hinges which are quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds‘ apart. A boy weighing quicklatex.com-4fbb80c3d7c3c9bdfaf780287e19f597_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds lb. stands on the gate so that his weight acts at a distance of quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds ft. from the line of hinges. If the force on the upper hinge is horizontal, find its magnitude and the reaction at the lower hinge in magnitude and direction.

Question 3

A uniform beam quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds of weight quicklatex.com-4fbb80c3d7c3c9bdfaf780287e19f597_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds lb. and of length quicklatex.com-3c4de7b9ce82b47f9788dc2416e4c750_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds‘ rests with the end quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds on a rough horizontal plane, the end quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds being connected by means of a light wire with a point quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds‘ vertically above quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds. The beam is inclined at an angle quicklatex.com-d6ffefedf9d4e7e4f42ba65b9f3b9416_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds to the vertical. By taking moments about quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds and quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds find the horizontal and vertical components of the reaction at quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds. If the coefficient of friction is quicklatex.com-c1202576eb6006ba366f3dcac824fc44_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds, find the greatest value of quicklatex.com-d6ffefedf9d4e7e4f42ba65b9f3b9416_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds so that slipping may not occur at quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds.

Question 4

A uniform rectangular board quicklatex.com-0bc2407dfe67fc49000363238a97afd0_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds has quicklatex.com-4578cc8ab679d17f11038ed4141b0c3a_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds, quicklatex.com-3960c36edd8b2218b0c14c3389994f68_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds“. A square hole of side quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds“, the distances of whose centre from quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds and quicklatex.com-7eb8f30e99944d2a38f0872981ee6aa3_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds are quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds” and quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds” respectively, is cut in the board. The hole is filled to the same thickness as the original board with metal whose specific gravity is quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds times that of the material of the board. Find the position of the centre of gravity.

Question 5

A coach is slipped from a train travelling at quicklatex.com-5710ac6ade182d0ad850e6efd2e4a189_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds m.p.h. The resistance due to brakes etc., being quicklatex.com-5710ac6ade182d0ad850e6efd2e4a189_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds lb. per ton, find what distance it travels before coming to rest and the time taken.

Question 6

A man projects a ball from a height of quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds ft. above the ground at an angle of quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds with the horizontal and with a velocity of quicklatex.com-0d5b79f8c98c15cb8ee4648dd054b6a0_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds ft./sec. The ball is caught by another man when it is at a height of quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds ft. from the ground. How far apart are the two men? Find also the magnitude and direction of the velocity of the ball when caught by the second man.

Question 7

A ship quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds is sailing due North at a speed of quicklatex.com-ed5decd492fdc6648538222379ceaf27_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds miles per hour. A ship quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds, quicklatex.com-2b18fa15a2f284d990fd81b9cae524ce_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds miles due west of quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds, is sailing due East at the rate of quicklatex.com-3883c8dfa7e1fd380cd2fa2674d982e2_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds miles per hour. Find (i) the relative velocity of quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds with respect to quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds, (ii) how far the ships are apart when quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds is due South of quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds, (iii) after what time the ships are closest to one another.

Question 8

An engine with weighs quicklatex.com-3883c8dfa7e1fd380cd2fa2674d982e2_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds tons passes round a curve of radius quicklatex.com-9dcc9664e46b37b81e768c60d821762c_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds ft. with a speed of quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds miles per hour. What horizontal pressure in lb. wt. must be exerted by the outer rail if both rails are on the same level? If the distance between the rails is quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds ft. find to the nearest inch the height of the outer rail above the inner so that the lateral thrust may be avoided.

Question 9

A body is moving in a straight line with simple harmonic motion, the amplitude being quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds” and the period quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds secs. Find the velocity and the acceleration quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1946 Honours Applied Mathematics | Maths Grinds sec. after passing the mid-position.

 


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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