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27Nov2018

Leaving Certificate Examination 1967 Honours Applied Mathematics

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Question 1

A body is projected under gravity with initial velocity quicklatex.com-7037dec17f4a6620ec536567c455a084_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds at an angle quicklatex.com-d6ffefedf9d4e7e4f42ba65b9f3b9416_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds to the horizontal. Find in terms of quicklatex.com-ba05715987b9d18252648b0ecfc8eb72_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds, quicklatex.com-d6ffefedf9d4e7e4f42ba65b9f3b9416_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds, (a) the maximum height attained, (b) the time required to reach that height, and (c) the distance it has travelled in a horizontal direction on reaching the maximum height.

A man strikes a gold ball which, at the instant it reaches maximum height of quicklatex.com-55947b5971ee17c162024320bb0d3a09_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds feet above the ground, strikes a tree  quicklatex.com-f1f207cf5d3c4f0c0d76a93586bcd29b_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds feet away. Assuming the ground to be level, find the magnitude and direction of the initial velocity of the gold ball, to the nearest ft. per sec. (neglecting effects of air resistance).

Question 2

Show that quicklatex.com-b83ab98d86175fbd9915e14d6de4b379_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds is the work done on a stationary mass quicklatex.com-7a02bd7300eeadcf269af0186938941e_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds in order to give it a velocity quicklatex.com-ecffa0daef95d0e24bb22fc5711a6bc3_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds.

A mass of quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds kg. moving East with a velocity of quicklatex.com-c5e1fff724fe36afee16a8302b93e856_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds cm. per sec. makes direct impact on a mass of quicklatex.com-7260fe4f20eb47e11e44b79da133e21c_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds kg. which is at rest. After the impact the quicklatex.com-7260fe4f20eb47e11e44b79da133e21c_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds kg. mass moves East with a velocity of quicklatex.com-0a7d1908dc17ba7c399644cfaecdaeba_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds cm. per sec. Assuming conservation of momentum find

(a) the velocity of the quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds kg. mass after impact,

(b) the kinetic energy lost on impact.

Question 3

Define Simple Harmonic Motion.

(i) If the bob of a pendulum is given a very small displacement quicklatex.com-ada3765a264ac03a253ee0ccbe61f602_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds to one side, the string being kept taut, and then released, show that the resulting motion is approximately simple harmonic.

(ii) A bob of mass quicklatex.com-55947b5971ee17c162024320bb0d3a09_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds grams hangs motionless at one end of an elastic string the other end of which is fixed in the ceiling. If the bob is pulled vertically down a distance quicklatex.com-7e66f8d3fbb50779ceb68e5184deb32d_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds until the tension in the string is quicklatex.com-cbbca562b8a27132c102a81b44b1362d_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds grams weight and then released, with what velocity will it pass the position of equilibrium assuming its motion about that position is simple harmonic?

Question 4

quicklatex.com-71f35a08f77df73ec68b187623047a26_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds is a velocity fixed in magnitude and direction. quicklatex.com-aff1ec3f51bd2191b7623b0a578f1a64_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds is a velocity fixed in magnitude only. If quicklatex.com-046105abf539cab104127043452037b8_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds, use vector diagrams to illustrate the situations where

(a) the magnitude of quicklatex.com-95e7c5fdc423fed67530009208aedd5a_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds is greatest.

(b) the magnitude of quicklatex.com-95e7c5fdc423fed67530009208aedd5a_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds is least.

(c) the magnitude of quicklatex.com-95e7c5fdc423fed67530009208aedd5a_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds is neither greatest nor least.

A boat crosses a straight river quicklatex.com-0a7d1908dc17ba7c399644cfaecdaeba_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds ft. wide which flows with a uniform velocity of quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds miles per hour. The boat’s velocity relative to the water is quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds miles per hour. Calculate to the nearest foot how far down-stream the boat lands if it crosses the stream in such a direction that it reaches the other side in exactly one minute.

Question 5

(i) A rectangular lamina quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds inches long and quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds inches wide is marked off in six equal squares. One corner square is removed. Calculate the position of the centre of gravity of the remainder.

(ii) quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds is a point outside a triangle quicklatex.com-6fcb9a5bbe28efc6b830fe33ef42b9a2_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds whose centre of gravity is quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds. Three forces quicklatex.com-f846a832a212d6153f2ee544ae825b7a_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds, quicklatex.com-6d37165fcac7d8f22ebaa1fd9b786cd9_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds, quicklatex.com-2094aafaab212d087ebbe8e8333b8a01_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds act at quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds. Show that their resultant is quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds quicklatex.com-8e71fd3fe787d15d63aaba4391659d06_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds.

Question 6

A uniform circular hoop of radius quicklatex.com-84fdf06eaf2b99889abd1c8acdc13d5f_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds rolls on the outer rim of a fixed wheel of radius quicklatex.com-91dc9a245a0f25a550d41a6feb58273f_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds, hoop and wheel being coplanar. (See diagram.) If the angular velocity quicklatex.com-c1d4e7cd934349c6c2f0b0fcd41f31cd_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds of the hoop about its centre is constant find

(i) what distance the hoop travels along the circumference of the wheel in time quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds;

(ii) the velocity and acceleration of the centre of the hoop;

(iii) the velocity of that point of the hoop which is farthest from the wheel.

HAM-1967-Q6 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds

Question 7

Say what you know about the pressure in a liquid, and the transmission of pressure in liquid.

The diameter of the small piston of a hydraulic press (see diagram) is quicklatex.com-a740037f818c3f0104a245035116aaa8_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds inches and the diameter of the large piston is quicklatex.com-8a0f60b8ca3ec09a3984d53508863c9a_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds inches. What weight on the small piston will support two tons weight on the large piston at the same horizontal level?

HAM-1967-Q7-300x118 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds

Question 8

Give three properties of friction.

Two light rings can slide on a rough horizontal rod. The rings are connected by a light inextensible string of length quicklatex.com-7e66f8d3fbb50779ceb68e5184deb32d_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds to the mid point of which is attached a weight quicklatex.com-054ef36c6e54f65ccdd586c0869b4fb0_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds. If quicklatex.com-74ddc0a71cf47b34f1f6eb6eda14a2ea_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds is the coefficient of friction between either ring and the rod, and quicklatex.com-fc85ef309591bf8b549446f3ebd0b450_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds is the distance between the rings, show that for equilibrium

    quicklatex.com-f9102d3647a4c31e3d3a88aa8e04db80_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds

Question 9

A straight light rigid rod of length quicklatex.com-113ccf3e1bb48ca142bc0de8db3b6e92_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds terminated by heavy particles of masses quicklatex.com-7a02bd7300eeadcf269af0186938941e_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds and quicklatex.com-941d689ad0e65c5d5733efadca408734_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds respectively is placed inside a smooth hemispherical bow of radius quicklatex.com-95d7c225dd31ad7d6dd5fb9f0980b531_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds, which is fixed with its rim horizontal. If the particle of mass quicklatex.com-7a02bd7300eeadcf269af0186938941e_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds rests just below the rim show that

    quicklatex.com-a7a61b1f7fdd1ae6e1007a4d048df0cc_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds

OR

Question 9

A train weighing quicklatex.com-e2421346fe4da17e1d74a7cb53af7968_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds tons is being pulled down a slope of quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds in quicklatex.com-5291abebe16995c90201b72e133d15d8_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds by an engine weighing quicklatex.com-5710ac6ade182d0ad850e6efd2e4a189_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds tons. The train has velocity quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds m.p.h. and is accelerating at the rate of quicklatex.com-294859fdbb1fdda439ec2363e11fdfa1_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds ft. per secquicklatex.com-025303222356a63c2332a429c33d35a9_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds. If the frictional resistance to its motion is quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1967 Honours Applied Mathematics | Maths Grinds lbs. weight per ton find the horse-power at which the engine is working.


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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