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5 Oct 2018

Leaving Certificate Examination 1948 Honours Applied Mathematics

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Question 1

A liner proceeding on a course quicklatex.com-c2d3e63fb43e42bdf77a4f1bb094291d_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds North of East appears to be moving N.E. as seen from a tug moving at quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds knots in an easterly direction. Find the speed of the liner.

How much must the tug increase its speed so that the liner will now appear to be moving due North?

Question 2

A piece of uniform wire is bent so as to form three sides quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds, quicklatex.com-3675ba693016b80ac93fbf734e15678b_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds, quicklatex.com-090252563a7d95933f4046a6c256de5b_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds of a square quicklatex.com-0bc2407dfe67fc49000363238a97afd0_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds. Find the position of the centre of gravity.

If a particle of mass equal to that of the wire is attached at the point quicklatex.com-e24826b0fac28861acd034428af346f0_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds, and the whole is freely suspended at quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds, find the inclination of quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds to the vertical.

Question 3

An engine pulls a train at a uniform speed of quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds miles per hour up an incline of quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds of quicklatex.com-4fbb80c3d7c3c9bdfaf780287e19f597_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds. If the couplings between the train and the engine break, how far will the train continue to run up the incline, if the resistance to its motion is quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds lb. wt. per ton?

Question 4

A football is kicked from a spot on the ground with a velocity of quicklatex.com-5710ac6ade182d0ad850e6efd2e4a189_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds feet per second and strikes a vertical wall quicklatex.com-5710ac6ade182d0ad850e6efd2e4a189_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds feet away at a point quicklatex.com-ed5decd492fdc6648538222379ceaf27_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds feet above the ground. Find the two possible angles of projection. Using the same initial velocity, what angle of projection will give the greatest height up the wall?

Question 5

A body of mass quicklatex.com-054ef36c6e54f65ccdd586c0869b4fb0_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds lb. is resting on a rough plane inclined to the horizontal at an angle quicklatex.com-0dce58ae1ea930bb9c39e85ab5e4c977_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds, the coefficient of friction being quicklatex.com-74ddc0a71cf47b34f1f6eb6eda14a2ea_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds. Find an expression for the force acting along the line of greatest slope which will just drag the body up the plane.

Find also an expression for the least force required (when applied in the most suitable direction) to drag the body up the plane, and find the value of this force when quicklatex.com-7e1fa4a884cc764c95f326cef85da859_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds, quicklatex.com-dc405d8d1378883800a518630d8a8172_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds, quicklatex.com-899264a347f34058b57eef0989590975_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds.

Question 6

Two masses of quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds and quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds lb. are connected by a light inextensible string of length quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds ft. Both masses rest on a smooth horizontal table, the quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds lb. mass being one foot from the edge of the table and from the quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds lb. mass which is resting at the edge. If the quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds lb. mass is pushed gently over the edge, find the speed of quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds lb. mass (i) when it is jerked into motion, and (ii) when it reaches the edge of the table.

Question 7

A triangular lamina quicklatex.com-0583d6d2788896443d34c799ae91c2df_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds is immersed in a vertical position in water with its vertex quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds at the surface and its base quicklatex.com-3675ba693016b80ac93fbf734e15678b_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds parallel to the surface. If quicklatex.com-93d30279aba4b0d1a831bc131b20e5e1_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds inches and the height of the triangle is equal to quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds inches, find the thrust on quicklatex.com-0583d6d2788896443d34c799ae91c2df_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds due to the water. If quicklatex.com-e24826b0fac28861acd034428af346f0_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds, quicklatex.com-7b14fa9f950652c6b6f4cfa6074d7021_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds are the middle points of quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds, quicklatex.com-371fe833e9a89e2790fc66adb618b944_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds, respectively, compare the total thrusts on quicklatex.com-f8947b514e1fe5c6c2bbd5f35c4b7eba_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds and quicklatex.com-ad587526a5e3fde5a155d79b20857aa6_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds.

In what ratio must a parallel to quicklatex.com-3675ba693016b80ac93fbf734e15678b_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds cut the other sides of the triangle quicklatex.com-0583d6d2788896443d34c799ae91c2df_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds so that the thrusts on the two portions of triangles may be equal?

[quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds cubic ft. of water quicklatex.com-fdb20f69ad5dc47f8f01a3b0d6f71e61_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds quicklatex.com-96052cd1530c9b803b2359dea67ec819_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds lbs.]

Question 8

A mass of quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds lb. fastened to a string quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds ft. long revolves as a conical pendulum, the mass moving in a horizontal circle with a speed of quicklatex.com-ed5decd492fdc6648538222379ceaf27_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds feet per second. Find the tension of the string and its inclination to the vertical.

Question 9

What is Simple Harmonic Motion? What is meant by the period, amplitude, and frequency of a S.H.M.?

A particle is moving in S.H.M. of period quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds seconds and amplitude quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds cm. Find the displacement, speed an acceleration of the particle quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1948 Honours Applied Mathematics | Maths Grinds second after it reaches its maximum positive displacement.

 


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/

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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.

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https://circulars.gov.ie/pdf/circular/per/2016/12.pdf

https://creativecommons.org/licenses/by/4.0/legalcod

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