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18 Sep 2018

Leaving Certificate Examination 1935 Honours Applied Mathematics

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Question 1

A particle moves along a straight line and its distance in feet quicklatex.com-273ac051ff0a53582365352ee5b6950d_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds from a fixed point in the line is given by the formula quicklatex.com-dab85cd4aa1f361f9b4103a76a907d04_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds where quicklatex.com-84fdf06eaf2b99889abd1c8acdc13d5f_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds, quicklatex.com-91dc9a245a0f25a550d41a6feb58273f_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds, quicklatex.com-5403eeae09f3e9689d2ad28aa6fe1599_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds are constants and quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds denotes the time in seconds. The distance is quicklatex.com-3c4de7b9ce82b47f9788dc2416e4c750_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds when quicklatex.com-af11a671ea147428c4b168db973a1c52_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds and the velocity is zero when quicklatex.com-54c45c8cbc7c23209477adcfe2a9c031_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds and quicklatex.com-d98be122de21e52cbadec4e38c59432b_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds. Find the values of quicklatex.com-84fdf06eaf2b99889abd1c8acdc13d5f_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds, quicklatex.com-91dc9a245a0f25a550d41a6feb58273f_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds, quicklatex.com-5403eeae09f3e9689d2ad28aa6fe1599_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds and verify that the acceleration is zero when quicklatex.com-97070a407d7f4e49aa7dcd8bfb746b35_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds. Draw rough diagrams showing how (a) the acceleration, (b) the velocity varies between quicklatex.com-f4e68921830214bfa2b71e404ea8a1c1_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds and quicklatex.com-b9d8163ab8760c0c349545c617380207_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds.

Question 2

A body weighing quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds lb. is moving in a straight line with Simple Harmonic Motion. If the greatest velocity is quicklatex.com-a9b2215f667b62f01d2e85cb98256ba5_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds ft. per second. and the amplitude of the oscillation is quicklatex.com-294859fdbb1fdda439ec2363e11fdfa1_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds ft., find the period of oscillation and the force of attraction towards the centre when the body is at its greatest distance from the centre.

Question 3

A body is projected with velocity quicklatex.com-ba05715987b9d18252648b0ecfc8eb72_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds, at an inclination quicklatex.com-0dce58ae1ea930bb9c39e85ab5e4c977_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds to the horizon, from the foot of a plane inclined at angle quicklatex.com-402735c0bdab0b3477755624fc9b4d06_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds to the horizon. Determine its range up the plane. Show that for a given value of quicklatex.com-ba05715987b9d18252648b0ecfc8eb72_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds, the range is a maximum when the direction of projection bisects the angle between the inclined plane and the vertical. Determine the least velocity with a ball can be thrown to reach the top of a cliff quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds ft. high and quicklatex.com-aaebfe489f9320ecf3c4a13c6672d86b_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds ft. away from the thrower, neglecting air resistance.

Question 4

If the velocities and accelerations of a number of particles be know, how many the velocity and acceleration of their centre of gravity be found?

A quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds lb. weight is placed on a smooth table and is attached to a quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds lb. weight, which vertically by a light inextensible string passing over a smooth pulley at the edge of the table. Show that the acceleration of the centre of gravity of the two weights is constant in magnitude and direction, and that the centre of gravity moves in a straight line.

Question 5

A car weighing one tone is rounding a curve of quicklatex.com-e2421346fe4da17e1d74a7cb53af7968_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds yards radius on a level road. What is the greatest speed at which this is possible, without causing the car to overturn, if the wheel gauge is quicklatex.com-1da1cb1ca453a77092946dc106385b32_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds ft. and the C.G. is mid-way between the wheels transversely and at a height of quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds ft. from the ground? What is the frictional force between the road and tyres at this speed?

Question 6

An engine pumps one ton of water per minute to a height of quicklatex.com-bd7202b6cf8beeda1b46bb2799ac945c_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds ft. and delivers it through a pipe whose cross-sectional area is quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds square inches. Find (i) the work done against gravity per minute in ft. lbs.; (ii) the kinetic energy of the water delivered in one minute in ft. lbs.; (iii) the Horse Power of the engine, neglecting all losses due to friction. (A cubic foot of water weights quicklatex.com-287a55b2d8cfd44f5f1f05ad3a5a70db_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds lbs.)

Question 7

A pin-jointed framework of the form shown in diagram, is pin-jointed to a vertical wall at quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds and quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds and carries a vertical load of quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds ton at quicklatex.com-e24826b0fac28861acd034428af346f0_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds. Find the forces exerted by the frame on the wall, and determine the stresses in the bards, indicating whether the bar is in thrust or in tension in each case.

HAM-1935-Q7-300x250 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds

 

Question 8

A weight of half-a-tone is allowed to fall freely through a height of quicklatex.com-ed5decd492fdc6648538222379ceaf27_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds ft. to drive a pile weighing quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds cwt. into the ground. Find the average resistance to the motion of the pile if it is driven quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds inches by the blow, assuming that the weight moves on with the pile.

Question 9

A body, weighing quicklatex.com-ed5decd492fdc6648538222379ceaf27_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds lbs., is kept in equilibrium on a rough plane inclined at quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds to the horizontal by a cord inclined at quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds to the plane. Find the frictional force between the body and the plane and indicate its direction when the tension in the cord is 6lbs. Find the work done in dragging the body slowly through a distance of one foot up the plane, assuming the coefficient of friction to be quicklatex.com-294859fdbb1fdda439ec2363e11fdfa1_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds and the cord to remain constantly at an angle of quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds to the plane.

Question 10

The two balls, quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds and quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds, of a governor, weigh quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds lbs. each; the arms quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds and quicklatex.com-371fe833e9a89e2790fc66adb618b944_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds are each inclined at quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds to the vertical and are quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds ft. long. Find the number of revolutions per minute they are making and the tension in each rod; the weights of the rods, quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds, quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1935 Honours Applied Mathematics | Maths Grinds [sic], may be neglected.

 


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/legalcode

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