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23Nov2018

Leaving Certificate Examination 1963 Honours Applied Mathematics

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Question 1

quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds and quicklatex.com-e0f17e01fb67b2164e7656895346ce8b_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds are two fixed pegs in the same horizontal line. One end of a light string is attached to quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds and the other end to quicklatex.com-e0f17e01fb67b2164e7656895346ce8b_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds. When two masses are attached to the string, one at a point quicklatex.com-6ce7c226153d55058c10348c6739a4c5_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds and the other at a point quicklatex.com-b90475b22ab5c52e8edfa41828a34159_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds, the angles quicklatex.com-ed1c5d6b28947b29e005c07000910135_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds, quicklatex.com-97f40c4129ab1714819f97c43965ac2f_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds, quicklatex.com-1005ab6e1d7727b096a9a416433d441a_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds are quicklatex.com-08bd7dd7d66bdf57cea2741a7e8d1788_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds, quicklatex.com-1a142f85ecebc62538b415aa5ef6033b_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds, quicklatex.com-9c3fb28be0c20ddb0b2c4bd59c303de8_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds, respectively. Find the weight of each mass if the two together weigh quicklatex.com-3883c8dfa7e1fd380cd2fa2674d982e2_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds lbs.

Question 2

quicklatex.com-0bc2407dfe67fc49000363238a97afd0_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds is a quadrilateral lamina in which quicklatex.com-3d8175e646bb8c3124c753557bc26f11_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds cms., quicklatex.com-e2d93dd8025452c1a2ab43d14087fa15_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds cms., quicklatex.com-7f7f00b29011f892c213f1e00d30fcb3_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds cms., quicklatex.com-6ccad7be9f7cfc4361219aee89d0af42_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds cms. and quicklatex.com-5cd56ee5c77ffad70fb8ac637c34b27d_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds. Find the perpendicular distance of the centre of gravity of quicklatex.com-0bc2407dfe67fc49000363238a97afd0_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds from quicklatex.com-ad679c8257689140280c7ab78dc1bccf_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds.

Find, also, the perpendicular distance of the centre of gravity of quicklatex.com-0583d6d2788896443d34c799ae91c2df_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds from quicklatex.com-7eb8f30e99944d2a38f0872981ee6aa3_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds.

Question 3

To a person on a ship travelling due East at quicklatex.com-66bafba23129fa8ab0a7d7fd2fc25d52_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds m.p.h. another ship quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds miles due North appears to be travelling at quicklatex.com-8a0f60b8ca3ec09a3984d53508863c9a_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds m.p.h. in a direction quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds West of South. Find the velocity of the second ship in magnitude and direction as accurately as you can by using your tables.

Find the distance between the ships when they are nearest to one another.

Question 4

An engine develops a horse-power of quicklatex.com-c1cd1b16f46ca94409053bf043493944_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds as it accelerates at the rate of quicklatex.com-294859fdbb1fdda439ec2363e11fdfa1_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds ft. per secquicklatex.com-025303222356a63c2332a429c33d35a9_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds. when travelling at a speed of quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds m.p.h. down an incline of quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds in quicklatex.com-5291abebe16995c90201b72e133d15d8_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds. If the eight of the engine is quicklatex.com-0a7d1908dc17ba7c399644cfaecdaeba_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds tons, calculate the frictional resistance to motion in lb. wt. per ton.

Question 5

A pile of mass one ton is driven vertically quicklatex.com-b88f0cf2457f55aa21df550745cabb36_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds feet into the ground by quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds blows of a hammer of mass quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds tons which falls vertically through a height of quicklatex.com-3883c8dfa7e1fd380cd2fa2674d982e2_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds feet.

Hence find the least mass which, when placed on top of the pile, would begin to drive the pile down. (Assume that the resistance of the ground is uniform and neglect the resistance-effects of side-friction on the pile.)

Question 6

A mass of quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds ounces attached to a fixed point by a light inextensible string of length quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds feet describes a horizontal circle at a uniform rate of quicklatex.com-40fe3cbfc0edaafd26b8d131f34e902b_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds radians per minute. Find the radius of the circle in feet and the tension in the string in lb. wt., correct to two significant figures in each case.

What angle would the string make with the vertical if the angular velocity were increased to quicklatex.com-41279769c1077af8f1b14e58e929229e_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds radians per minute?

Question 7

A dense fog is assumed to cover a horizontal plane to a uniform height of quicklatex.com-9877cd275001809be3290e131f82c653_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds feet. A mass projected from the plane rises above the fog after quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds sec. and then travels a horizontal distance of quicklatex.com-a76a229a4a01d6aee369fc37e0359f22_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds feet before re-entering the fog. Find the initial velocity of the mass and its angle of projection.

Question 8

A particle moves in a straight line so that its displacement quicklatex.com-ada3765a264ac03a253ee0ccbe61f602_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds(cm.) from a fixed point at time quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds(sec.) is given by the formula

    quicklatex.com-e379c82426370337d9ac84b5b2ae4d82_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds

Show that the motion is simple harmonic and find (i) the amplitude, (ii) the maximum velocity of the particle.

Find, also, the least time, correct to three significant figures, taken by the particle to travel a distance quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds cm. from its mean position.

Question 9

quicklatex.com-ed1c5d6b28947b29e005c07000910135_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds is a triangular lamina in which quicklatex.com-884c85ce5b52d87ac395c0d82978e2ac_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds, quicklatex.com-6e51dab1d89d882274cf04724369b96d_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds, and quicklatex.com-76f112d192433c97739304c4b43bc8d2_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds, where quicklatex.com-6460d10729af641188d49a36153c8def_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds is the mid-point of quicklatex.com-a81944f37f837f351ee503de581d7393_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds. The lamina is immersed in a vertical position in a liquid of specific gravity quicklatex.com-0e3a084eb240597822671ffac1df4c2d_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds so that the base quicklatex.com-a81944f37f837f351ee503de581d7393_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds is at the surface. Find the total thrust of the liquid on quicklatex.com-ed1c5d6b28947b29e005c07000910135_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds.

How far must the lamina be withdrawn vertically upwards out of the liquid, the base quicklatex.com-a81944f37f837f351ee503de581d7393_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds remaining parallel to the surface, if the thrust on the portion in the liquid is quicklatex.com-294859fdbb1fdda439ec2363e11fdfa1_l3 | Leaving Certificate Examination 1963 Honours Applied Mathematics | Maths Grinds lb. wt. ?

(One cubic foot of water weighs quicklatex.com-2a62b4fd8e04c54613a6683d3f1636ef_l3 | Leaving Certificate Examination 1963 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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