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24Nov2018

Leaving Certificate Examination 1964 Honours Applied Mathematics

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Question 1

A uniform ladder quicklatex.com-e979ae05a61debd12da167a83e2720d6_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds has a length of quicklatex.com-dd065d3520106e3ce62efb2d1efb1157_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds feet and weighs quicklatex.com-cbbca562b8a27132c102a81b44b1362d_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds lbs. The end quicklatex.com-6ce7c226153d55058c10348c6739a4c5_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds leans against a vertical rough wall (coefficient of friction quicklatex.com-a5990b654956436786b5311c7aada3b3_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds) and the other end quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds is on rough horizontal ground (coefficient of friction quicklatex.com-294859fdbb1fdda439ec2363e11fdfa1_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds) at a distance of quicklatex.com-4c8846d90c9db2c7945bc56cc2df5c3f_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds feet from the wall. A block weighing quicklatex.com-66bafba23129fa8ab0a7d7fd2fc25d52_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds lbs. is placed on the ground against the bottom of the ladder so as to just prevent the ladder from slipping. Find the coefficient of friction between the block and the ground.

Question 2

If the co-ordinates of the vertices of a triangle are quicklatex.com-ff55ad85c45cc7bf9a4b239e894ccd04_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds, quicklatex.com-1c06e666924e7ee5b9eb8534db343877_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds, quicklatex.com-7ec3d0be6b72960b1ec4424a68f94810_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds and if quicklatex.com-35432dfe2e6ae9b47e0bf79e65a5549d_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds are the co-ordinates of the centroid of the triangle, show that

quicklatex.com-878d3b85c63249a322619e42415b8598_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds and quicklatex.com-d381453512cb512cd6c6b93cd3516b87_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds.

Hence, of otherwise, 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 1964 Honours Applied Mathematics | Maths Grinds in which quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds and quicklatex.com-090252563a7d95933f4046a6c256de5b_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds are parallel. quicklatex.com-86ff6908c4c692471cb0919a2b64d205_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds inches, quicklatex.com-4377db2ba995473193b46ea251f11442_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds inches and quicklatex.com-e2e63ce976169656100be991818eee04_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds. Find the position of the centre of gravity of the lamina.

Question 3

The direction of the wind relative to that of a bus travelling in the direction quicklatex.com-43254279a766115b4c8c77b4f9e086ff_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds South of East is from the East, while the direction of the wind relative to that of a car travelling in the direction quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds South of West is from the West. (The velocity of the wind is assume constant). If the speed of the wind relative to that of the bus is added to the speed of the wind relative to that of the car, the total is quicklatex.com-5710ac6ade182d0ad850e6efd2e4a189_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds m.p.h. Find the speed of the bus and the speed of the car.

Question 4

A train is pulled by its engine up an incline of quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds in quicklatex.com-5291abebe16995c90201b72e133d15d8_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds at a uniform speed of quicklatex.com-66bafba23129fa8ab0a7d7fd2fc25d52_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds m.p.h. against a resistance to motion of quicklatex.com-fef30ec83d548cacaa4710d12bb69dc3_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds lb. wt. per ton. If the weight of the train and its engine is quicklatex.com-c56abbec0d3913124ffb3d82e4b46ab3_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds tons, find the horse-power at which the engine is working.

If the train travels on a level track at a speed of quicklatex.com-ced9adf500abe3e625f021cf18429a9e_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds m.p.h. against a resistance to motion of quicklatex.com-fef30ec83d548cacaa4710d12bb69dc3_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds lb. wt. per ton, find its acceleration if the engine is developing the same horse-power as before.

Question 5

A system consists of two masses quicklatex.com-cbfc2b823986c7623815c2cf6f04b686_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds, quicklatex.com-b999b237e25bf5d241351c6ff0601b69_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds suspended by a light inextensible string over a light frictionless pulley. The pulley is at  the intersection of two smooth planes equally inclined to the horizontal at an angle of quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds (see diagram) and the masses weigh quicklatex.com-3883c8dfa7e1fd380cd2fa2674d982e2_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds oz. and quicklatex.com-edeca52e97715225ceecec173423f15e_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds oz., respectively. The system, initially held at rest, is released and after quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds sec. of motion a mass of weight quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds oz. is detached from the quicklatex.com-3883c8dfa7e1fd380cd2fa2674d982e2_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds oz. mass. Find the distance traversed by the quicklatex.com-edeca52e97715225ceecec173423f15e_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds oz. mass before it again reaches its initial position.

HAM-1964-Q5-300x105 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds
Question 6

Define Simple Harmonic Motion.

A particle is moving in a straight line with simple harmonic motion. When it is quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds feet from its mean position its velocity is quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds feet per second and its acceleration is quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds feet per secondquicklatex.com-025303222356a63c2332a429c33d35a9_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds. Find the amplitude and the period of the motion.

How long does the particle take to travel a distance quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds feet from its mean position and how far from its mean position is the particle in quicklatex.com-530bddd72ec65d751f3371c4d91ffdb5_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds of the period?

Question 7

A roof may be taken to be a smooth plane sloping at an angle of quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds to the horizontal with its lower edge along the top of a vertical wall. A body slides down the roof and hits the ground (assimed horizontal) at an angle whose tangent is quicklatex.com-ccb2d4c8c5b4f192dac548645cd4d791_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds. When the speed of the body is quicklatex.com-2b18fa15a2f284d990fd81b9cae524ce_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds ft. per  sec. it has a distance of quicklatex.com-3c4de7b9ce82b47f9788dc2416e4c750_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds feet to traverse before it leaves the roof. Find the height of the wall.

Question 8

A circular piece of tin rotates at the rate of quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds revolutions per minute about an axis through its centre quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds, the axis being perpendicular to the plane of the tin. quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds and quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds are two points on the tin such that quicklatex.com-7ca3cadee3c9509bb2efe841b204d9b2_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds foot, quicklatex.com-b95cac93acea7f09b9ce378cdd660475_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds feet and quicklatex.com-c39359fbf0d00be7b934323701bd1c4b_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds. Weights of quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds lb. and quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds lb. are placed respectively at quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds and quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds. Find the magnitude and direction of the resultant centrifugal force on the axis.

Question 9

A vessel in the shape of a cube has internal edges each quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds ft. long. A liquid, of specific gravity quicklatex.com-c6b8c788f59d9a8f4874b51d23036122_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds, fills the vessel to a certain height and water which does not mix with the liquid occupies the remainder of the vessel. On each vertical side the total thrust on that part in contact with the water is equal to the total thrust on that part in contact with the liquid. Calculate the depth of the liquid pf a specific gravity quicklatex.com-c6b8c788f59d9a8f4874b51d23036122_l3 | Leaving Certificate Examination 1964 Honours Applied Mathematics | Maths Grinds in the vessel.


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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