23 Oct 2018

### Leaving Certificate Examination 1954 Honours Applied Mathematics

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Question 1 $A$ and $B$ are the ends of a uniform bar which is $8$ inches in length and which weighs $5$ lb. The bar is supported by two strings $AC$ and $BC$ attached to a fixed peg $C$. If $AC=5$ inches and $BC=4$ inches, find the tensions in the strings. What weight attached at... Read More

22 Oct 2018

### Leaving Certificate Examination 1953 Honours Applied Mathematics

Question 1 The ends of a light inextensible string $5$ feet long are attached to two pegs which are $4$ feet apart and in the same horizontal line. A mass of $20$ lb. is suspended from the string at a point which is $2$ feet from one peg and $3$ feet from the other. Find... Read More

19 Oct 2018

### Leaving Certificate Examination 1952 Honours Applied Mathematics

Question 1 A light string $ABCD$ hangs from two fixed points $A$, $D$ which are in the same horizontal line. The string carries a weight of $10$ lb. at $B$ and weight of $W$ lb. at $C$. The angles $DAB$, $ABC$, $BCD$ are $45^\circ$, $150^\circ$, $120^\circ$, respectively. Find, graphically or otherwise, the value of $W$.... Read More

18 Oct 2018

### Leaving Certificate Examination 1951 Honours Applied Mathematics

Question 1 Two pegs $A$ and $B$ are at the same height above the ground, and are $7$ feet apart. One end of an inextensible string $8$ feet in length is attached to $A$, and the other end is attached to $B$. A $28$ lb. weight is suspended from the string at a point $3$... Read More

17 Oct 2018

### Leaving Certificate Examination 1950 Honours Applied Mathematics

Question 1 If the velocities of two bodies $A$ and $B$ are known, indicate by means of a diagram, or otherwise, how the velocity of $A$ relative to $B$ may be found. When a man is travelling due east at $4$ miles per hour, the wind appears to blow from the north, but when he... Read More

16 Oct 2018

### Leaving Certificate Examination 1949 Honours Applied Mathematics

Question 1 $ABC$ is a triangle in which $AB=8$ cm., $BC=10$ cm., and $CA=11$ cm. Forces of $4$, $5$, $5$ lb. wt. act along the sides $AB$, $CA$, $CB$, respectively. Find the magnitude of their resultant and find how far from $C$ it cuts $CA$ and the angle it makes with $CA$. Question 2 (a)... Read More

5 Oct 2018

### Leaving Certificate Examination 1948 Honours Applied Mathematics

Question 1 A liner proceeding on a course $25^\circ$ North of East appears to be moving N.E. as seen from a tug moving at $10$ knots in an easterly direction. Find the speed of the liner. How much must the tug increase its speed so that the liner will now appear to be moving due... Read More

4 Oct 2018

### Leaving Certificate Examination 1947 Honours Applied Mathematics

Question 1 A body moving in a straight line travels distances $AB$, $BC$, $CD$ of $104$ ft., $264$ ft., $240$ ft. respectively in three successive intervals of $2$ secs., $6$ secs., and $8$ secs. Show that these facts are not inconsistent with the hypothesis that the body is moving with uniform retardation. On this hypothesis... Read More

3 Oct 2018

### Leaving Certificate Examination 1946 Honours Applied Mathematics

Question 1 A train travelling at $44$ feet per second is brought to rest, its speed after $t$ secs. being given by the table : $t$ secs. $0$ $5$ $15$ $25$ $35$ $40$ $50$ $v$ ft./sec. $44$ $36$ $24$ $14.5$ $8$ $5$ $0$ Draw the velocity-time graph. Find, approximately, (i) how far the train travelled... Read More

2 Oct 2018

### Leaving Certificate Examination 1945 Honours Applied Mathematics

Question 1 The velocities of two points $A$ and $B$ being known in magnitude and direction, explain with the aid of a diagram how to find the velocity of $B$ relative to $A$. A ship $A$ sailing north at $20$ miles per hour observes a ship $B$ $10$ miles to the north-east which is sailing... Read More