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1 Oct 2018

Leaving Certificate Examination 1944 Honours Applied Mathematics

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Question 1

quicklatex.com-0583d6d2788896443d34c799ae91c2df_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds is a steel rod, the portion quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds being straight and of length quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds feet and the portion quicklatex.com-3675ba693016b80ac93fbf734e15678b_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds being curved. The whole rod lies in one plane. The end quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds is hinged to the floor and a load of quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds cwt. is suspended from quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds by a rope which is quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds feet from quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds which is kept vertical by applying a horizontal force quicklatex.com-6024d8b1a86917dc3144686a41ea70aa_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds feet from quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds. The eight of the whole rod may be taken to be quicklatex.com-294859fdbb1fdda439ec2363e11fdfa1_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds cwt. acting at a distance of one foot from quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds when the latter is in the vertical position. Find the horizontal force and the reaction at the hinge in magnitude and direction.

Question 2

quicklatex.com-0bc2407dfe67fc49000363238a97afd0_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds is a trapezium, quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds being parallel to quicklatex.com-fd7eb40724ff36c7d87599742f06177e_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds. quicklatex.com-b9b4cb71d330ca6a34a92d00fcf45343_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds, quicklatex.com-64505a0eeb059140f3dd8c88bb580266_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds. Show that the centroid of the area is one the line joining the mid-points quicklatex.com-7b14fa9f950652c6b6f4cfa6074d7021_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds, quicklatex.com-8c28ca9825a5e0ff6a01cc15dd4efff1_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds of quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds, quicklatex.com-fd7eb40724ff36c7d87599742f06177e_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds and that it divides quicklatex.com-ee1d7461b0409606fa62f717e3dd2db1_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds in the ratio quicklatex.com-cf469ff3a95d468561a052b56cf45fc7_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds.

Question 3

It is found that when a plane is inclined at quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds to the horizontal a block of iron weighing quicklatex.com-2b18fa15a2f284d990fd81b9cae524ce_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds lb. slides uniformly down the plane. Show that the angle of friction is quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds.

When the plane is inclined at quicklatex.com-9c3fb28be0c20ddb0b2c4bd59c303de8_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds to the horizontal the block is dragged slowly up the plane by a cord inclined at an angle quicklatex.com-d6ffefedf9d4e7e4f42ba65b9f3b9416_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds to the plane. By means of the triangle of forces, or otherwise, find the tension in the cord and show that the tension is least when quicklatex.com-c7293b3bf74f0badae7c38ab2ab770b7_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds.

Question 4

A wheel of radius quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds feet is rolling, without slipping, on a horizontal plane ; the centre moving a uniform velocity of quicklatex.com-ced9adf500abe3e625f021cf18429a9e_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds feet per second. What is the angular velocity of the wheel?

What is the velocity of the extremity of the radius which is inclined at quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds to the upward vertical through the centre of the wheel, the angle being measured in the direction of rotation of the wheel?

Question 5

A quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds lb. weight is drawn up a rough plane, coefficient of friction quicklatex.com-a5990b654956436786b5311c7aada3b3_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds, inclined at quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds to the horizontal by a string, passing over a light smooth pulley at the top of the plane, to which is attached an quicklatex.com-2b18fa15a2f284d990fd81b9cae524ce_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds lb. weight. Find the acceleration.

Calculate the kinetic energy when the system has moved a distance of quicklatex.com-2b18fa15a2f284d990fd81b9cae524ce_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds ft. and show that it is equal to the loss in potential energy minus the work done against friction.

Question 6

A car weighing quicklatex.com-a1932753a828b715f77ce7ebbb061c1c_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds pounds starts under the action of a force which decreases uniformly from quicklatex.com-fef5d9bb0bd664dfe03d2ae1a00c063d_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds lb. wt. at time quicklatex.com-f4e68921830214bfa2b71e404ea8a1c1_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds to quicklatex.com-5291abebe16995c90201b72e133d15d8_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds lb. wt. at quicklatex.com-a35613fc87fbe6573d7f6e3dc0003228_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds seconds when it remains constant. The resistances to motion remain constant throughout and are equal to quicklatex.com-5291abebe16995c90201b72e133d15d8_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds lb. wt. Show that the accelerating force at time quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds quicklatex.com-150a3cd90fe6ad7dfe62730e2ec46e7e_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds is quicklatex.com-4f5f419d5632d98124641583bc48f3cf_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds lb. wt.

Find (a) the velocity at time quicklatex.com-a35613fc87fbe6573d7f6e3dc0003228_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds sec.; (b) the distance travelled at time quicklatex.com-a35613fc87fbe6573d7f6e3dc0003228_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds sec.; (c) the horsepower required when quicklatex.com-5ccadef2a2a607fdbd8a60f9ac6ed407_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds sec. and also when quicklatex.com-4d6ff52b621ee5f223b8695b99569e87_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds secs.

Question 7

A gun fires a projectile with initial velocity quicklatex.com-ba05715987b9d18252648b0ecfc8eb72_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds and elevation quicklatex.com-0dce58ae1ea930bb9c39e85ab5e4c977_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds. Show that (a) the range quicklatex.com-0199d210e397b198f37906f103312534_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds; (b) the greatest height quicklatex.com-443979ed229514f3493de82e55a04f3c_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds, neglecting air resistance.

Show that the maximum range which can be obtained with the same initial velocity is quicklatex.com-aab1372e0c68b172cf7140ab71327929_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds.

Question 8

A cyclist is travelling round a curve quicklatex.com-4fbb80c3d7c3c9bdfaf780287e19f597_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds feet radius at quicklatex.com-8a0f60b8ca3ec09a3984d53508863c9a_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds miles per hour. At what angle must the track be inclined radially so that there may be no tendency to slip?

If quicklatex.com-b6238d26012711898571864b7567f890_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds what is the maximum speed on a level track of the same radius so that skidding may not occur? (quicklatex.com-74ddc0a71cf47b34f1f6eb6eda14a2ea_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds is the coefficient of friction).

Question 9

If the period of a simple harmonic vibration is quicklatex.com-6460d10729af641188d49a36153c8def_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds seconds and the amplitude quicklatex.com-84fdf06eaf2b99889abd1c8acdc13d5f_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds feet, show that the maximum acceleration is quicklatex.com-b516b3583df7f6b22e583816a559d956_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds.

A boy weighing quicklatex.com-2b18fa15a2f284d990fd81b9cae524ce_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds stone standing on a plank oscillates vertically in simple harmonic motion of amplitude of quicklatex.com-9a61841f2abe3e6f5e5b707bbfade7f4_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds foot and period quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1944 Honours Applied Mathematics | Maths Grinds second. Find the greatest and least reactions of the plank.

 


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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