23 Nov 2018

### Leaving Certificate Examination 1963 Honours Applied Mathematics

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Question 1 $P$ and $S$ are two fixed pegs in the same horizontal line. One end of a light string is attached to $P$ and the other end to $S$. When two masses are attached to the string, one at a point $Q$ and the other at a point $R$, the angles $PQR$, $QRS$, $RSP$... Read More

22 Nov 2018

### Leaving Certificate Examination 1962 Honours Applied Mathematics

Question 1 A uniform ladder is put leaning against a rough vertical wall (coefficient of friction $0.5$), the bottom of the ladder being on a rough horizontal plane (coefficient of friction $0.4$). What is the least angle the ladder can make with the plane without slipping? Question 2 $ABCD$ is quadrilateral lamina in which $AB=3″$,... Read More

21 Nov 2018

### Leaving Certificate Examination 1961 Honours Applied Mathematics

Question 1 $ABC$ is a triangle in which $BC=8″$, $\cos B = \frac{1}{2}$, $\cos C = \frac{11}{14}$. Forces of $3$, $12$, $7$ lb. wt. act along $BA$, $BC$, $CA$, respectively. How far from $B$ does the line of action of their resultant cut $BC$?. Find the magnitude of the resultant in lb. wt., correct to... Read More

20 Nov 2018

### Leaving Certificate Examination 1960 Honours Applied Mathematics

Question 1 A mass of $21$ gm. is supported at $O$ by two light strings $OA$, $OB$ which are attached to fixed pegs at $A$, $B$, respectively, the straight line $AB$ being horizontal. If $AB=7$ ins., $AO=3$ ins., $BO=5$ ins., find the tensions in the strings. Question 2 Explain the terms “limiting friction”, “coefficient of... Read More

19 Nov 2018

### Leaving Certificate Examination 1959 Honours Applied Mathematics

Question 1 A uniform rod $XY$, which weighs $12$ lbs., is supported by two strings $XZ$, $YZ$, attached to a fixed peg $Z$. If $XY=14″$, $XZ=9″$, $YZ=7″$, calculate the tensions in the strings. Question 2 $ABCD$ is a quadrilateral lamina. $AB=AD=12$ cm., $AC=15$ cm., $\angle BAC=30^\circ$ and $\angle ADC=90^\circ$. Find the perpendicular distance of the... Read More

15 Nov 2018

### Leaving Certificate Examination 1958 Honours Applied Mathematics

Question 1 $ABC$ is a triangle in which $BC=5$ cm., $\angle BCA=30^\circ$, and $\cos ABC = \frac{3}{5}$. Forces of $10$, $8$, $6$ lb. wt. act along $BA$, $BC$, $CA$, respectively. If their resultant acts along the straight line $DE$, cutting $BC$ in $D$, calculate the length of $BD$ and the size of the angle $CDE$.... Read More

14 Nov 2018

### GNIB Bot

As a teacher of international students I am aware of the need among my students to visit GNIB (Garda National Immigration Bureau) office to get their visa and GNIB card. When I lived in Dublin I would pass Burgh Quay every morning and would be stunned by the queues. Here is a picture of a... Read More

14 Nov 2018

### Leaving Certificate Examination 1957 Honours Applied Mathematics

Question 1 If three co-planar non-parallel forces acting on a rigid body are in equilibrium, prove that their lines of action are concurrent and that the forces may be represented in magnitude and direction by the sides of a triangle taken in order. A uniform bar $AB$ which weighs $8$ lb. is supported by two... Read More

13 Nov 2018

### Leaving Certificate Examination 1956 Honours Applied Mathematics

Question 1 A warship is travelling on a course $30^\circ$ East of North. To an observer on a liner travelling due East at $15$ knots the warship appears to be moving due North. Find the speed of the warship. In what direction should the warship travel at that speed so that it would appear to... Read More

7 Nov 2018

### Leaving Certificate Examination 1955 Honours Applied Mathematics

Question 1 $A$ and $D$ are two fixed pegs in the same horizontal line. One end of a light string is attached to $A$ and the other end to $D$. The string carries a weight of $5$ lb. at $B$ and a weight of $X$ lb. at $C$. The angles $ABC$, $BCD$, $CDA$ are $135^\circ$,... Read More