My Journal

All things Mathematical
21 Nov 2018

Leaving Certificate Examination 1961 Honours Applied Mathematics

/
Posted By
/
Comments0
Question 1

quicklatex.com-0583d6d2788896443d34c799ae91c2df_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds is a triangle in which quicklatex.com-0b015e3dc77f8516e1e985f366a6b858_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds, quicklatex.com-c1c4a0293a00ccf2ff4fced248c46d90_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds, quicklatex.com-2d848dad24fa9c03667668a7365c3fcf_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds. Forces of quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds, quicklatex.com-ed5decd492fdc6648538222379ceaf27_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds, quicklatex.com-edeca52e97715225ceecec173423f15e_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds lb. wt. act along quicklatex.com-ef15da5ad110b3b57097bbc0518f5eef_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds, quicklatex.com-3675ba693016b80ac93fbf734e15678b_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds, quicklatex.com-c703974f82fa531d93879bbfbfb6c9cb_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds, respectively. How far from quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds does the line of action of their resultant cut quicklatex.com-3675ba693016b80ac93fbf734e15678b_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds?.

Find the magnitude of the resultant in lb. wt., correct to one place of decimals, and find the angle which its line of action make with quicklatex.com-3675ba693016b80ac93fbf734e15678b_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds, correct to the nearest degree.

Question 2

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

When a truck is ascending an incline of quicklatex.com-24746e8a1a6c5c694c7889aa45349e68_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds in quicklatex.com-4fbb80c3d7c3c9bdfaf780287e19f597_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds with a uniform acceleration of quicklatex.com-e37a7ce3683aa7c32967f8f4105807da_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds ft. per sec. per sec., a box on the floor of the truck is just about to slide backwards. Show by diagram the forces acting on the box, and find the coefficient of friction between the box and the floor of the truck.

Question 3

A man is cycling at quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds m.p.h. in a steady wind. When he cycles in a direction quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds north of east the wind appears to him to blow directly from the east. When he cycles due east the wind appears to him to blow from the south-east. Find the velocity of the wind in magnitude and direction.

Question 4

Two bodies, of mass quicklatex.com-7260fe4f20eb47e11e44b79da133e21c_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds gm. and quicklatex.com-18d78dbab2726faa0bd1e841a16b345e_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds gm. respectively, are lying on a smooth horizontal bench which is quicklatex.com-8625bdab4dcb84d7031c39eca5bcfa81_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds feet high. The quicklatex.com-7260fe4f20eb47e11e44b79da133e21c_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds gm. body is at the edge of the bench and the quicklatex.com-18d78dbab2726faa0bd1e841a16b345e_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds gm. body is quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds feet away in a direction perpendicular to the edge, the bodies being connected by a light inextensible string quicklatex.com-2b18fa15a2f284d990fd81b9cae524ce_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds feet long. If the quicklatex.com-7260fe4f20eb47e11e44b79da133e21c_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds gm. body is pushed gently over the edge, find how many seconds later it will reach the ground.

Question 5

Derive an expression for the total time of flight of a projectile in terms of its initial velocity and angle of projection.

quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds, quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds, quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds, are three collinear points on a horizontal plane. A projectile fired from quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds passes over quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds at a height of quicklatex.com-20b2359777f6479b766141ee1eb47708_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds feet and reaches its greatest height as it passes over quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds. If quicklatex.com-bac0a9a73f302ebcf8d462953df3ea77_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds feet and the total time of flight of the projectile is quicklatex.com-c20f4cdda6f8d62e84bdeecce0a65eb8_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds seconds, find its initial velocity.

Question 6

A mass of quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds lb. suspended from a fixed point by a light inextensible string quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds feet long acts as a conical pendulum, the mass describing a horizontal circle at a uniform rate of quicklatex.com-5710ac6ade182d0ad850e6efd2e4a189_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds revolutions per minute. Find the tension in the string, in lb., wt., and the inclination of the string to the vertical.

Question 7

A particle is moving along a straight line so that is distance quicklatex.com-ada3765a264ac03a253ee0ccbe61f602_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds (cms.) from a fixed point quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds at the time quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds (secs.) is given by the formula

    quicklatex.com-c8392da16e440f0044f09166b3eb10d4_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds

.

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

If the velocity of the particle at quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds is quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds cm. per sec., find its acceleration at quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds, and find the least time the particle takes to travel to quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds from quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds.

[See Tables, p. 30].

Question 8

A triangular lamina quicklatex.com-0583d6d2788896443d34c799ae91c2df_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds is immersed in a liquid of specific gravity quicklatex.com-6ebce5037cfda094c0dcc90ccac6d10f_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds so that the vertex quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds is at the surface and the sides quicklatex.com-371fe833e9a89e2790fc66adb618b944_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds is vertical. If quicklatex.com-f2938742cd3196f56d9629c85c7ff1ef_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds, quicklatex.com-a8856cf92524d2ce25911ac60741ad48_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds, quicklatex.com-3fd99f6cb20eb91600a75f941123e37a_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds, find the thrust of the liquid on quicklatex.com-0583d6d2788896443d34c799ae91c2df_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds in ounces.

quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds is a point on quicklatex.com-371fe833e9a89e2790fc66adb618b944_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds such that the thrust of the liquid on quicklatex.com-3de2b0b865490a151ecc2b242fac4599_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds is give-ninths of the thrust on quicklatex.com-0583d6d2788896443d34c799ae91c2df_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds. Find the length of quicklatex.com-44ea9eed55b10c9ce67bf6ee5623a82c_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds.

[A cubic foot of water weights quicklatex.com-287a55b2d8cfd44f5f1f05ad3a5a70db_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds lb.]

Question 9

quicklatex.com-0bc2407dfe67fc49000363238a97afd0_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds is a quadrilateral lamina in which quicklatex.com-f42e7e8421912d76e972c21ecff79593_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds, quicklatex.com-4fa44a123454e810fa19bc55368d80bb_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds, quicklatex.com-0b015e3dc77f8516e1e985f366a6b858_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds, quicklatex.com-2ee3b4d6ac3ce12e0e83231a76dff410_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds. Find the perpendicular distance of the centre of gravity of quicklatex.com-0bc2407dfe67fc49000363238a97afd0_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds from quicklatex.com-371fe833e9a89e2790fc66adb618b944_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds.

Find, also, the perpendicular distance of the centre of gravity of quicklatex.com-e41fe322b1cb631fac9700833f9d502d_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds from quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1961 Honours Applied Mathematics | Maths Grinds.


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

 

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.