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19Nov2018

Leaving Certificate Examination 1959 Honours Applied Mathematics

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Question 1

A uniform rod quicklatex.com-cacf86ec54fe47688ea7a15a4ca0d7d0_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds, which weighs quicklatex.com-ed5decd492fdc6648538222379ceaf27_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds lbs., is supported by two strings quicklatex.com-da13502ddc36729d8ccadfa7fd90bec4_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds, quicklatex.com-f8c6b4193243000bcbfe888197b871ca_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds, attached to a fixed peg quicklatex.com-a6a7269cfeb6bd1b31d6d6ca7a75489b_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds. If quicklatex.com-2b836eaffbdbb1648292152612678d65_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds, quicklatex.com-478f19a0347630755e091c7a77df63f1_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds, quicklatex.com-e4f74a745542b6948d9d363e753bb47e_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds, calculate the tensions in the strings.

Question 2

quicklatex.com-0bc2407dfe67fc49000363238a97afd0_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds is a quadrilateral lamina. quicklatex.com-d77013fc126dc886ba9a53dc1763f909_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds cm., quicklatex.com-43bd4a6a4c4ebe851c06d05266862edc_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds cm., quicklatex.com-7a5c784bbeb66bf3ed10493c0c4fb277_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds and quicklatex.com-1936bfda168083fc1094f216b88135a0_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds. Find the perpendicular distance of the centre of gravity of the lamina (i) from quicklatex.com-371fe833e9a89e2790fc66adb618b944_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds, (ii) from quicklatex.com-7eb8f30e99944d2a38f0872981ee6aa3_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds.

Question 3

A light string passes over a smooth pulley at the top of a smooth plane inclined to the horizontal at an angle whose sine is quicklatex.com-a5990b654956436786b5311c7aada3b3_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds. The string connects a quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds lb. mass which is on the plane to a quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds lb. mass which is hanging freely: find the acceleration of the masses when the system is released.

When it has fallen quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds feet the quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grindslb. mass is brought to rest on hitting the ground. It remains at rest for quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds seconds and is then jerked into motion with velocity quicklatex.com-8bafe7d16e660869fc203e8bffd77abc_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds : find the values of quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds and quicklatex.com-8bafe7d16e660869fc203e8bffd77abc_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds.

Question 4

A man is walking due east while a steady wind is blowing. When he walks at quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds m.p.h. the wind appears to him to blow from the north, but when he walks at quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds m.p.h. it appears to blow from a direction quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds east of north. Find the velocity of the wind in magnitude and direction.

At what speed must the man walk so that the wind will appear to him to blow from the north-east?

Question 5

Show that the range of a projectile on a horizontal plane is quicklatex.com-cbc6b45fe86553c97074f3ca9638db5d_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds, where quicklatex.com-ba05715987b9d18252648b0ecfc8eb72_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds is the initial velocity and quicklatex.com-0dce58ae1ea930bb9c39e85ab5e4c977_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds the angle of projection. A shell is fired from ground level and after quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds seconds it is quicklatex.com-f9e692a6460ddd19961c6d80050cd59c_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds feet above the ground. If the point at which it returns to ground level is quicklatex.com-7eb98dd8d4c1ed57a8315279d49eb79e_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds feet from the point of projection, find the initial velocity of the shell.

Question 6

An engine weighing quicklatex.com-4fbb80c3d7c3c9bdfaf780287e19f597_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds tons is pulling a train weighing quicklatex.com-f1f207cf5d3c4f0c0d76a93586bcd29b_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds tons up an incline of quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds in quicklatex.com-e2421346fe4da17e1d74a7cb53af7968_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds. The frictional resistances to motion are equivalent to quicklatex.com-2b18fa15a2f284d990fd81b9cae524ce_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds lb. wt. per ton. Find the horse-power at which the engine is working

(i) when the train is travelling at steady speed of quicklatex.com-ced9adf500abe3e625f021cf18429a9e_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds m.p.h.;

(ii) when the speed of the train is quicklatex.com-ced9adf500abe3e625f021cf18429a9e_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds m.p.h. and it is accelerating at the rate of quicklatex.com-0ec045393ff984641d86b4ee444e6208_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds feet per second per second.

Question 7

A cyclist is travelling at a steady speed of quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds m.p.h. round a track which is banked at an angle of quicklatex.com-0c559742eb6542699185a371f9051330_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds to the horizontal. If he is describing a horizontal circle of radius quicklatex.com-4fbb80c3d7c3c9bdfaf780287e19f597_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds feet, find the angle which he makes with the normal to the track.

Find the greatest speed at which he could travel round that circle without slipping sideways, if the coefficient of friction between the track and the tyres is quicklatex.com-d87274adcc3e9b397c1d81918125c810_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds.

Question 8

Describe how you would investigate experimentally the possible effect of various factors on the time of oscillation of a simple pendulum.

Establish the formula for the time of oscillation of a simple pendulum.

Question 9

A lamina immersed in water is in the shape of a trapezium quicklatex.com-0bc2407dfe67fc49000363238a97afd0_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds in which quicklatex.com-7eb8f30e99944d2a38f0872981ee6aa3_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds, quicklatex.com-3675ba693016b80ac93fbf734e15678b_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds are parallel, quicklatex.com-c4838db10f4efdca48f7b94aad861313_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds, quicklatex.com-f42e7e8421912d76e972c21ecff79593_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds, quicklatex.com-71bd46c15fd4fee87a43418c66480bb9_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds, quicklatex.com-31b866d272d0664b282b5676c350ba17_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds. Find the thrust of the water on the lamina, to the nearest lb. wt.,

(i) if it is immersed horizontally quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds inches below the surface;

(ii) if it is immersed vertically with quicklatex.com-7eb8f30e99944d2a38f0872981ee6aa3_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds at the surface.

By how much would the thrust in (ii) be increased if the lamina were pushed down vertically until quicklatex.com-7eb8f30e99944d2a38f0872981ee6aa3_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds was quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds inches below the surface and parallel to it?

[A cubic foot of water weighs quicklatex.com-287a55b2d8cfd44f5f1f05ad3a5a70db_l3 | Leaving Certificate Examination 1959 Honours Applied Mathematics | Maths Grinds lb.].


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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