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15Nov2018

Leaving Certificate Examination 1958 Honours Applied Mathematics

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Question 1

quicklatex.com-0583d6d2788896443d34c799ae91c2df_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds is a triangle in which quicklatex.com-16f9ef863bbcec4727a938792b131cad_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds cm., quicklatex.com-5e995573be973fe4c69fe52c7c7dd061_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds, and quicklatex.com-9746a2c0793b39f377561a3706018a5e_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds. Forces of quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds, quicklatex.com-2b18fa15a2f284d990fd81b9cae524ce_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds, quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds lb. wt. act along quicklatex.com-ef15da5ad110b3b57097bbc0518f5eef_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds, quicklatex.com-3675ba693016b80ac93fbf734e15678b_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds, quicklatex.com-c703974f82fa531d93879bbfbfb6c9cb_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds, respectively. If their resultant acts along the straight line quicklatex.com-8505284533a1a3ccf8ec77ac45d1f92e_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds, cutting quicklatex.com-3675ba693016b80ac93fbf734e15678b_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds in quicklatex.com-e24826b0fac28861acd034428af346f0_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds, calculate the length of quicklatex.com-ad679c8257689140280c7ab78dc1bccf_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds and the size of the angle quicklatex.com-9533aa4571697c6da11c10d1721e2a58_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds.

Question 2

Show that the centre of gravity of a triangular lamina is the same as that of three equal masses situated at the vertices of the triangle.

A lamina is in the shape of a trapezium quicklatex.com-0bc2407dfe67fc49000363238a97afd0_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds in which quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds and quicklatex.com-090252563a7d95933f4046a6c256de5b_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds are parallel. quicklatex.com-4ebc618ecccf9a916124e937e6c8500b_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds, quicklatex.com-c7f2f86d02e80513dc0fda25be61611c_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds, quicklatex.com-3960c36edd8b2218b0c14c3389994f68_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds and quicklatex.com-f1ab07b3afbe34a0c4ac655895f3eaa3_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds. Find the perpendicular distance of the centre of gravity of the lamina (i) from quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds, and (ii) from quicklatex.com-7eb8f30e99944d2a38f0872981ee6aa3_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds.

Question 3

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

A horizontal force of quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds lb. wt. would just keep a block of mass quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds lb. from sliding down a rough plane which is inclined to the horizontal at an angle of quicklatex.com-43254279a766115b4c8c77b4f9e086ff_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds. Calculate the coefficient of friction between the block and the plane.

Find the direction and magnitude of the least force that would keep the block from sliding down the plane.

Question 4

quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds, quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds, quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds are three ships at sea. To an observer on quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds, quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds appears to be travelling South-East at quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds knots. To an observer on quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds, quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds appears to be travelling due North at quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds knots. Find the velocity of quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds relative to quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds in magnitude and direction.

Question 5

A car travelling on a level road was uniformly accelerated for quicklatex.com-ed5decd492fdc6648538222379ceaf27_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds seconds and was then uniformly retarded for quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds seconds. In that quicklatex.com-e2ceb65b3a6ab9dc7212d896621f4092_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds seconds it travelled from quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds to quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds, a distance of quicklatex.com-14c24f9ee262324d414a8d93e055ca61_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds yards. Its velocity at quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds was quicklatex.com-8a0f60b8ca3ec09a3984d53508863c9a_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds m.p.h. and its velocity at quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds was quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds m.p.h. Find the uniform acceleration and the uniform retardation, in feet per sec.quicklatex.com-025303222356a63c2332a429c33d35a9_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds.

Calculate the horse-power at which the car was working when its velocity was quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds m.p.h., given that the car weighed one ton and that the frictional resistances to motion were equivalent to quicklatex.com-7260fe4f20eb47e11e44b79da133e21c_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds lb. wt.

Question 6

A quicklatex.com-d2a5ac082f8383090a608c4c7c1c9961_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds gm. mass is projected vertically upwards with an initial velocity of quicklatex.com-4b0d4dcf22295c195c00f05d04a405f7_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds ft. per sec. and half a second later a quicklatex.com-cbbca562b8a27132c102a81b44b1362d_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds gm. mass is projected vertically upwards from the same point with an initial velocity of quicklatex.com-5291abebe16995c90201b72e133d15d8_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds ft. per sec. Calculate the height at which the masses will collide.

If the masses coalesce on colliding, find the greatest height which the combined mass will reach and the velocity it will have on returning to the point of projection.

Question 7

If a body is describing a circle of radius quicklatex.com-95d7c225dd31ad7d6dd5fb9f0980b531_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds with constant angular velocity quicklatex.com-d66dbaeb0eebc210a255b3fd356eacd0_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds, show that its acceleration is quicklatex.com-6bb1c9c0af463a17b06a2234aa9af88e_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds directed towards the centre of the circle.

A particle of mass quicklatex.com-7a02bd7300eeadcf269af0186938941e_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds, suspended from a fixed point by a string of length quicklatex.com-7e66f8d3fbb50779ceb68e5184deb32d_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds, is describing a horizontal circle with uniform angular velocity quicklatex.com-d66dbaeb0eebc210a255b3fd356eacd0_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds. Express in terms of quicklatex.com-7a02bd7300eeadcf269af0186938941e_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds, quicklatex.com-7e66f8d3fbb50779ceb68e5184deb32d_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grindsm quicklatex.com-d66dbaeb0eebc210a255b3fd356eacd0_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds (i) the tension in the string, (ii) the cosine of the angle which the string makes with the vertical.

Show that the time taken by the particle in making one revolution is less than the time of oscillation of a simple pendulum of length quicklatex.com-7e66f8d3fbb50779ceb68e5184deb32d_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds.

Question 8

Define simple harmonic motion.

A particle is moving along a straight line. At time quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds (secs.) its distance quicklatex.com-ada3765a264ac03a253ee0ccbe61f602_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds (cms.) from its mean position is given by the formula

    quicklatex.com-b84ee9350b70aeea1942fa3f7978857a_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds

Show that the motion is simple harmonic and find the periodic time.

Calculate the velocity of the particle (i) when it is in its mean position, (ii) half a second later.

Question 9

There are quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds feet of water on one side of a lock-gate and quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds feet of water on the other. The gate is rectangular and is quicklatex.com-ed5decd492fdc6648538222379ceaf27_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds feet wide. Calculate the resultant thrust of the water on the date, in tons.

By how much should the level of the water on the deeper side be lowered so that the resultant thrust would be quicklatex.com-c8bca1c094a21862cc5bcbd5e030e58e_l3 | Leaving Certificate Examination 1958 Honours Applied Mathematics | Maths Grinds lb. less?

[A cubic foot of water weighs quicklatex.com-287a55b2d8cfd44f5f1f05ad3a5a70db_l3 | Leaving Certificate Examination 1958 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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