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7 Nov 2018

Leaving Certificate Examination 1955 Honours Applied Mathematics

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Question 1

quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds and quicklatex.com-e24826b0fac28861acd034428af346f0_l3 | Leaving Certificate Examination 1955 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-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds and the other end to quicklatex.com-e24826b0fac28861acd034428af346f0_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds. The string carries a weight of quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds lb. at quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds and a weight of quicklatex.com-05d30bc5e19b413cea824383c6bce148_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds lb. at quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds. The angles quicklatex.com-0583d6d2788896443d34c799ae91c2df_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds, quicklatex.com-e41fe322b1cb631fac9700833f9d502d_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds, quicklatex.com-d5f468736f81ceac52e18da87254303c_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds are quicklatex.com-08bd7dd7d66bdf57cea2741a7e8d1788_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds, quicklatex.com-2deb000f7d47a4c73b5ce3d6bfacf1fa_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds, quicklatex.com-9c3fb28be0c20ddb0b2c4bd59c303de8_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds respectively. Find the value of quicklatex.com-05d30bc5e19b413cea824383c6bce148_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds.

Question 2

Explain the terms “coefficient of friction,” “angle of friction.”

A block weighing quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds lb. is resting on a rough plane which is inclined to the horizontal at an angle of quicklatex.com-209c1958604e9f7d31e020b608033e83_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds, the coefficient of friction between the block and the plane being quicklatex.com-d87274adcc3e9b397c1d81918125c810_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds. Find the direction and the magnitude of the least force that will just cause the block to move up the plane.

Question 3

A car descending an incline of quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds in quicklatex.com-c5e1fff724fe36afee16a8302b93e856_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds accelerates uniformly from quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds m.p.h. to quicklatex.com-9e7ec55fdcc4467668102a4d17def052_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds m.p.h in a distance of quicklatex.com-0a7d1908dc17ba7c399644cfaecdaeba_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds yards. Find the uniform acceleration in ft. per sec.quicklatex.com-025303222356a63c2332a429c33d35a9_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds

If the car weights quicklatex.com-66bafba23129fa8ab0a7d7fd2fc25d52_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds cwt. and if the frictional resistances to motion are equivalent to quicklatex.com-cbbca562b8a27132c102a81b44b1362d_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds lb. wt. per tone, find the horse-power at which the car was working when its speed was quicklatex.com-6fa002e1799dcb54bc79a06dc47ef0af_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds m.p.h.

Question 4

quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds and quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds are two points quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds feet apart in the same horizontal plane. A particle is projected from quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds with an initial velocity of quicklatex.com-ba05715987b9d18252648b0ecfc8eb72_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds feet per second at an angle of quicklatex.com-90fb8553012b54579673c50331fab678_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds to the horizontal. At the same instant a balloon is released at quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds and rises vertically with a uniform velocity of quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grindsft. per sec. If the particle strikes the balloon, find the value of quicklatex.com-ba05715987b9d18252648b0ecfc8eb72_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds.

Question 5

Two bodies, weighing quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds lb. and quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds lb. respectively, are lying on a smooth horizontal table which is quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds feet high. The quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds lb. body is at the edge of the table and the quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds lb. body is quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds feet away in a direction perpendicular to the edge, the bodies being connected by a light inextensible string which is quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds feet long. If the quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds lb. body is pushed gently over the edge, how long will it take to reach the ground?

Question 6

A bullet weighing quicklatex.com-294859fdbb1fdda439ec2363e11fdfa1_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds ounce, moving horizontally with a velocity of quicklatex.com-e29d23c3214666afe77f6e6f800670fa_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds feet per second, strikes a wooden block weighing quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds lb. which is resting on a smooth horizontal plane. If the bullet becomes embedded in the block, find the velocity of the block after the impact.

What fraction of the kinetic energy is lost by the impact?

What constant resisting force would bring the block to rest in quicklatex.com-3883c8dfa7e1fd380cd2fa2674d982e2_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds inches?

Question 7

quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds and quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds are two fixed pegs, one quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds feet vertically above the other. A mass quicklatex.com-7a02bd7300eeadcf269af0186938941e_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds, connected to quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds and quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds by two light inextensible strings of equal length, is describing a horizontal circle with uniform angular velocity quicklatex.com-d66dbaeb0eebc210a255b3fd356eacd0_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds.

(i) Show that quicklatex.com-d66dbaeb0eebc210a255b3fd356eacd0_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds must exceed quicklatex.com-41a05eecc5fdad5ab82d2db3149083d3_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds in order that the lower string will be taut.

(ii) For what value of quicklatex.com-d66dbaeb0eebc210a255b3fd356eacd0_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds will the tension in the upper string be double the tension in the lower?

Question 8

What is Simple Harmonic Motion?

A particle is moving in a straight line with Simple Harmonic Motion. Its greatest velocity is quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds feet per second and its greatest acceleration is quicklatex.com-e47ae213394600a1ce75c8892d75480e_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds feet per secondquicklatex.com-025303222356a63c2332a429c33d35a9_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds. Find the amplitude and the periodic time.

How long does the particle take to travel from its mean position to a point half-way towards its extreme position?

Question 9

A triangular lamina is immersed in a vertical position in water. The base, which is at the surface, is quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds inches in length, and the vertex of the triangle is quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds inches below the surface. Find the total thrust quicklatex.com-796d210fbc9f8b29316f8432989d3566_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds of the water on the lamina.

The lamina is then drawn vertically upwards so that it is partly out of the water, the base being parallel to the surface. If the thrust on the portion immersed is now quicklatex.com-20947622409a4c9c6b035b099a502533_l3 | Leaving Certificate Examination 1955 Honours Applied Mathematics | Maths Grinds, how far is the vertex below the surface in the new position?

[One cubic foot of water weighs quicklatex.com-2a62b4fd8e04c54613a6683d3f1636ef_l3 | Leaving Certificate Examination 1955 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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