My Journal

All things Mathematical
18Oct2018

Leaving Certificate Examination 1951 Honours Applied Mathematics

/
Posted By
/
Comments0
Question 1

Two pegs quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds and quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds are at the same height above the ground, and are quicklatex.com-edeca52e97715225ceecec173423f15e_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds feet apart. One end of an inextensible string quicklatex.com-2b18fa15a2f284d990fd81b9cae524ce_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds feet in length is attached to quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds, and the other end is attached to quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds. A quicklatex.com-24746e8a1a6c5c694c7889aa45349e68_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds lb. weight is suspended from the string at a point quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds feet from quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds and quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds feet from quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds. Find the tension in each part of the string.

Question 2

Two roads cross at right angles at quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds. Two men, quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds and quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds, are walking towards quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds. quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds is walking at quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds m.p.h. on one road, quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds at quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds m.p.h. on the other road. When quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds is quicklatex.com-4fbb80c3d7c3c9bdfaf780287e19f597_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds yards from quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds, quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds is quicklatex.com-0a7d1908dc17ba7c399644cfaecdaeba_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds yards from quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds. Find the velocity of quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds relative to quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds.

Find the distance of quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds from quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds and from quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds, when quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds and quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds are nearest to each other.

Question 3

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

quicklatex.com-0bc2407dfe67fc49000363238a97afd0_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds is a quadrilateral lamina. A mass equal to one-third the mass of the lamina is placed at the intersection of the diagonals quicklatex.com-371fe833e9a89e2790fc66adb618b944_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds and quicklatex.com-ad679c8257689140280c7ab78dc1bccf_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds. Show that the centre of gravity of the lamina and the mass together is the same as that of four equal masses situated at the vertices of the quadrilateral.

Question 4

Two masses of quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds lb. and quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds lb. connected by a light inextensible string quicklatex.com-3883c8dfa7e1fd380cd2fa2674d982e2_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds feet long, are lying on a smooth horizontal table quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds feet high. The quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds lb. mass is at the edge of the table and the other mass is quicklatex.com-2b18fa15a2f284d990fd81b9cae524ce_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds feet away in a direction perpendicular to the edge. If the quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds lb. mass is pushed gently over the edge of the table, find how long it takes to reach the ground, and how much longer the quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds lb. mass takes to reach the edge of the table.

Find also the change in kinetic energy when the quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds lb. mass is jerked into motion.

Question 5

A train ascending an incline of quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds in quicklatex.com-4fbb80c3d7c3c9bdfaf780287e19f597_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds accelerates uniformly from quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds m.p.h. to quicklatex.com-cbbca562b8a27132c102a81b44b1362d_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds m.p.h. in a distance of quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds miles. Find this acceleration. If the train and the engine together weigh quicklatex.com-0a7d1908dc17ba7c399644cfaecdaeba_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds tons, and if the frictional resistances to motion are equivalent to quicklatex.com-edeca52e97715225ceecec173423f15e_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds lb. wt. per ton, find the horse-power at which the engine was working when the speed of the train was quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds m.p.h.

Question 6

A point quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds is describing a circle, centre quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds, with uniform speed. If quicklatex.com-6ce7c226153d55058c10348c6739a4c5_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds is the foot of the perpendicular from quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds to a fixed diameter, show that quicklatex.com-6ce7c226153d55058c10348c6739a4c5_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds moves with simple harmonic motion.

When quicklatex.com-6ce7c226153d55058c10348c6739a4c5_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds is quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds feet from quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds its velocity is quicklatex.com-b88f0cf2457f55aa21df550745cabb36_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds feet per second, and when it is quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds feet from quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds its velocity is quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds feet per second towards quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds. Find how long quicklatex.com-6ce7c226153d55058c10348c6739a4c5_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds takes to reach quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds from the latter position.

Question 7

A gun is fixed at a point quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds at the top a vertical cliff quicklatex.com-c5e1fff724fe36afee16a8302b93e856_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds feet high. quicklatex.com-6ce7c226153d55058c10348c6739a4c5_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds is the foot of the perpendicular from quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds to the sea. A ship is travelling away from the cliff at quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds feet per second along a straight line that passes through quicklatex.com-6ce7c226153d55058c10348c6739a4c5_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds. When the ship is quicklatex.com-832988d7b85b3784b072284b63fdfa60_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds feet from quicklatex.com-6ce7c226153d55058c10348c6739a4c5_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds a shell is fired from the gun at an angle of quicklatex.com-9c3fb28be0c20ddb0b2c4bd59c303de8_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds and strikes the ship. Find the initial velocity of the shell.

Question 8

A mass of one ounce attached to a fixed point by an inextensible string quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds feet long, describes a horizontal circle at a uniform rate of quicklatex.com-cbbca562b8a27132c102a81b44b1362d_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds revolutions per minute. Find the tension in the string and the vertical distance from the fixed point to the plane of the circle.

What vertical distance will the mass rise if its speed is increased to quicklatex.com-5710ac6ade182d0ad850e6efd2e4a189_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds revolutions per minute?

Question 9

Prove that if a plane surface is immersed in a liquid the total thrust on it due to the liquid is equal to the area of the surface multiplied by the pressure at its center of gravity.

A triangular lamina quicklatex.com-0583d6d2788896443d34c799ae91c2df_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds is totally immersed in water so that the plane of the lamina makes an angle of quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds with the horizontal plane. The base quicklatex.com-3675ba693016b80ac93fbf734e15678b_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds is quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds inches in length and the height of the triangle is quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds inches. Find the total thrust of the water of quicklatex.com-0583d6d2788896443d34c799ae91c2df_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds

(i) when its vertex quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds is at the surface of the water and its base quicklatex.com-3675ba693016b80ac93fbf734e15678b_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds is horizontal;

(ii) when its base quicklatex.com-3675ba693016b80ac93fbf734e15678b_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds is at the surface of the water.

[quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds cubic foot of water weighs quicklatex.com-96052cd1530c9b803b2359dea67ec819_l3 | Leaving Certificate Examination 1951 Honours Applied Mathematics | Maths Grinds lbs.]

 


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

print

Leave a Reply

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