My Journal

All things Mathematical
19 Oct 2018

Leaving Certificate Examination 1952 Honours Applied Mathematics

/
Posted By
/
Comments0
Question 1

A light string quicklatex.com-0bc2407dfe67fc49000363238a97afd0_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds hangs from two fixed points quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds, quicklatex.com-e24826b0fac28861acd034428af346f0_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds which are in the same horizontal line. The string carries a weight of quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds lb. at quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds and weight of quicklatex.com-054ef36c6e54f65ccdd586c0869b4fb0_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds lb. at quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds. The angles quicklatex.com-7e168277ac7c1ca04665b1a6b9efe127_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds, quicklatex.com-0583d6d2788896443d34c799ae91c2df_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds, quicklatex.com-e41fe322b1cb631fac9700833f9d502d_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds are quicklatex.com-9c3fb28be0c20ddb0b2c4bd59c303de8_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds, quicklatex.com-2deb000f7d47a4c73b5ce3d6bfacf1fa_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds, quicklatex.com-8a31becb362adc52e8f92b8a182effad_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds, respectively. Find, graphically or otherwise, the value of quicklatex.com-054ef36c6e54f65ccdd586c0869b4fb0_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds.

Question 2

A uniform ladder, of weight quicklatex.com-054ef36c6e54f65ccdd586c0869b4fb0_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds lb. and length quicklatex.com-7e66f8d3fbb50779ceb68e5184deb32d_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds ft., rests with one end in contact with a smooth vertical wall and the other end in contact with a rough horizontal plane, the inclination of the ladder to the horizontal being quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds. A man of weight quicklatex.com-d993c85fe0de1c28d00ef58f0653f60d_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds lb. can ascend just quicklatex.com-d2ae28a5dc7298b20f481ce24a7ae717_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds ft. up the ladder without causing the ladder to slip. Find quicklatex.com-74ddc0a71cf47b34f1f6eb6eda14a2ea_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds, the coefficient of friction between the ladder and the plane.

Question 3

A uniform wiere, weighing quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds ounces, is bent so as to form an isosceles triangle quicklatex.com-0583d6d2788896443d34c799ae91c2df_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds in which quicklatex.com-641d46702cadfd409878d25dd5bfb455_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds inches, and quicklatex.com-55a227d457a792d5d3ad12ca2b9863f7_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds inches. Find the position of the centre of gravity.

What weight must be attached at quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds so that quicklatex.com-371fe833e9a89e2790fc66adb618b944_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds will be horizontal when the triangle is suspended at quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds?

Question 4

A train which is being uniformly retarded covers two successive stages, each quicklatex.com-a5990b654956436786b5311c7aada3b3_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds mile in length, in quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds seconds and quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds seconds, respectively. Find the uniform retardation and find how much farther the train will travel before it comes to rest.

Question 5

A car weighing one tone is ascending an incline of quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds in quicklatex.com-e2421346fe4da17e1d74a7cb53af7968_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds and is accelerating uniformly at the rate of quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds rate per secquicklatex.com-025303222356a63c2332a429c33d35a9_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds. If the frictional resistance to motion are equivalent to quicklatex.com-4d155ce8d09a30956973f6c2da87cd56_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds lb. weight, find the horse-power at which the car is working when its speed is quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds m.p.h.

Question 6

A railway engine weighing quicklatex.com-cbbca562b8a27132c102a81b44b1362d_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds tons travels at quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds m.p.h. round a curve of quicklatex.com-0a7d1908dc17ba7c399644cfaecdaeba_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds yards radius on a level track. The distance between the rails is quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds feet, and the centre of gravity of the engine is quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds feet above the rails and midway between them. Find the vertical pressure upon each of the rails.

What is the maximum speed at which the engine could travel round the curve without losing contact with one of the rails?

Question 7

A particle is projected from ground level so as just to clear a vertical tower quicklatex.com-cde6f09d3cc0e14c252edf4ac6855889_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds feet high which is standing on a horizontal plane. As the particle passes over the tower its velocity is quicklatex.com-5291abebe16995c90201b72e133d15d8_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds feet per second in a direction making an angle of quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds above the horizontal. Find the horizontal distance from the foot of the tower (a) to the point where the particle hits the ground, (b) to the point of projection.

Question 8

What is Simple Harmonic Motion?

A particle is moving with Simple Harmonic Motion. When it is quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds feet from its mean position its velocity is quicklatex.com-d61119651ddf565da4198bb11ee60847_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds feet per second and its acceleration is quicklatex.com-3883c8dfa7e1fd380cd2fa2674d982e2_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds feet per secondquicklatex.com-025303222356a63c2332a429c33d35a9_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds. Find the amplitude and the period of the motion.

Where would the particle be two-thirds of a second after passing through its mean position?

Question 9

A rectangular dock-gate is quicklatex.com-2b18fa15a2f284d990fd81b9cae524ce_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds feet in width. The water on one side of it is quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds feet deep and on the other side it is quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1952 Honours Applied Mathematics | Maths Grinds feet deep. Find the resultant thrust on the gate, in tons.

To what height must the level of the water on the lower side be raised so that the thrust on that side may be equal to half the thrust on the deeper side?

[One cubic foot of water weighs quicklatex.com-287a55b2d8cfd44f5f1f05ad3a5a70db_l3 | Leaving Certificate Examination 1952 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

 

Leave a Reply

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