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4 Oct 2018

Leaving Certificate Examination 1947 Honours Applied Mathematics

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Question 1

A body moving in a straight line travels distances quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds, quicklatex.com-3675ba693016b80ac93fbf734e15678b_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds, quicklatex.com-090252563a7d95933f4046a6c256de5b_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds of quicklatex.com-0354b226ba45875d1147019432d962a0_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds ft., quicklatex.com-ddf864dcedfcfd79bbf9fb8c1a17a8de_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds ft., quicklatex.com-fef5d9bb0bd664dfe03d2ae1a00c063d_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds ft. respectively in three successive intervals of quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds secs., quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds secs., and quicklatex.com-2b18fa15a2f284d990fd81b9cae524ce_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds secs. Show that these facts are not inconsistent with the hypothesis that the body is moving with uniform retardation. On this hypothesis that the body is moving with uniform retardation. On this hypothesis find the distance from quicklatex.com-e24826b0fac28861acd034428af346f0_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds to the point where the velocity vanishes and the time occupied in describing this distance.

Question 2

A body weighing quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds lb. is placed on a rough plane inclined at quicklatex.com-93b8c92075274f0cf41c5863defa1c92_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds to the horizontal. The angle of friction is quicklatex.com-209c1958604e9f7d31e020b608033e83_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds. Find (a) the least force parallel to a line of greatest slope; (b) the least horizontal force, that will move the body up the plane.

Question 3

A uniform rod quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds, of weight quicklatex.com-054ef36c6e54f65ccdd586c0869b4fb0_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds lbs., is suspended in a vertical position by a string attached to it at quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds. It is now drawn from the vertical by a force acting horizontally on quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds, and equal to one-third the weight of the rod. Find the tension of the string and the angle it makes with vertical when the rod is in the position of equilibrium. Find also the inclination of the rod to the vertical.

Question 4

The parallel sides of a trapezium are of lengths quicklatex.com-84fdf06eaf2b99889abd1c8acdc13d5f_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds and quicklatex.com-91dc9a245a0f25a550d41a6feb58273f_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds respectively and are a distance quicklatex.com-63ab7de62920c09a3246a8ce084ab3ce_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds apart. Find the distance of the centroid from the side quicklatex.com-84fdf06eaf2b99889abd1c8acdc13d5f_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds.

A trapezium quicklatex.com-e0fa8e17620a5116a336a68e895abd4f_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds is part of a rectangle quicklatex.com-0bc2407dfe67fc49000363238a97afd0_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds. The co-ordinates of quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds, quicklatex.com-6ce7c226153d55058c10348c6739a4c5_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds, quicklatex.com-b90475b22ab5c52e8edfa41828a34159_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds, quicklatex.com-e0f17e01fb67b2164e7656895346ce8b_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds are respectively quicklatex.com-ba19c8bef108591c27db142ad7f752af_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds ; quicklatex.com-daa12f56fac5c816dc4ca6e92800d4de_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds ; quicklatex.com-ac4aeb14314fb0debc0b62b1881fa5e6_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds ; quicklatex.com-cdd2aab186c0b37aa49cfedfd539a6f6_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds and those of quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds, quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds. quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds, quicklatex.com-e24826b0fac28861acd034428af346f0_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds are respectively quicklatex.com-75437422d0c9d959e079c63c8136a436_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds ; quicklatex.com-60d4a6786937cf6259aa54977082a403_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds ; quicklatex.com-18c678387fb4be0ede40e6ae0af8c8fd_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds ; quicklatex.com-5bc4dfd6ce2d5be3fbf5d3f7c4e25e95_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds. Find the centroid of the figure obtained when the trapezium quicklatex.com-e0fa8e17620a5116a336a68e895abd4f_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds is removed from the rectangle quicklatex.com-0bc2407dfe67fc49000363238a97afd0_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds.

Question 5

A place quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds is situated quicklatex.com-0a7d1908dc17ba7c399644cfaecdaeba_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds miles north-west of quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds. An aeroplane has a maximum speed of quicklatex.com-fef5d9bb0bd664dfe03d2ae1a00c063d_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds miles per hour in still air and a south-west wind of quicklatex.com-5710ac6ade182d0ad850e6efd2e4a189_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds m.p.h. is blowing at the level at which the plane is flying. Find the shortest time needed to fly from quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds to quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds and the compass course which the navigator must steer.

Question 6

An engine weighs quicklatex.com-5710ac6ade182d0ad850e6efd2e4a189_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds tons, of which quicklatex.com-66bafba23129fa8ab0a7d7fd2fc25d52_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds tons is borne by the driving wheels. The engine is coupled to a carriage weighing quicklatex.com-cbbca562b8a27132c102a81b44b1362d_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds tons. The resistance to the motion of the engine is quicklatex.com-3c4de7b9ce82b47f9788dc2416e4c750_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds lb. per ton and to the motion of the carriage quicklatex.com-ed5decd492fdc6648538222379ceaf27_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds lb. per ton. If the coefficient of friction between the driving wheels and the rails is quicklatex.com-61cb8bf66d4f8d9b7f43c80c50913760_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds, find the maximum acceleration (i.e., when the driving wheels are on the point of slipping), and the tension in the coupling between the engine and the carriage.

Question 7

A metal cube of side quicklatex.com-2b18fa15a2f284d990fd81b9cae524ce_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds cm. is suspended in a liquid of density quicklatex.com-f606a0f1a08ecde4089491100dafd003_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds grm. per c.c. so that a pair of faces are horizontal and the upper face quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds cm. below the surface of the liquid. The atmospheric pressure is quicklatex.com-a33d8c40b0dac0e5cb6f7788ea10224d_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds cm. of mercury (density of mercury quicklatex.com-b4a3222b53a62e3f2494ccd3d0875c9f_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds grm. per c.c.). Find the resultant upward thrust on the cube due to the liquid and the total thrust on a vertical face of the cube.

Question 8

Two small blocks, of weights quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds lb., and quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds lb., are suspended from the same point by equal strings each quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds ft. long. The quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds lb. block has a small spike in  it so that when it collides with the quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds lb. block the two adhere together. The quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds lb. block is raised till the string to which it is attached is horizontal, and then let go.

Find its velocity (i) just before, (ii) immediately after it strikes the quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds lb. block. Find in foot-pounds the decrease in kinetic energy due to the collision and the sum of the tensions in the strings immediately after the collision.

Question 9

Prove the formula

    quicklatex.com-9ec91cfde9707658bdab006bde9b37aa_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds

for a point moving in a straight line with simple harmonic motion. If the period is quicklatex.com-165ae8e53b023536cd30bc2f6a21fa2f_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds sec. find the amplitude if the acceleration is not greater than quicklatex.com-6ab7528844bb1b8da4d6cf570bdbb6ab_l3 | Leaving Certificate Examination 1947 Honours Applied Mathematics | Maths Grinds.

 


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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