28Nov2018

### General Derivative Test Flow Chart

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I was teaching my students today how one could use higher derivates to determine the shape of a curve at a particular point. The problem that really can be confusing is the case when I felt that a flow chart with pictures would be the best way to represent the process for deciding... Read More

28Nov2018

### Leaving Certificate Examination 1968 Honours Applied Mathematics

Question 1 Show how to find the centre of gravity of a non-rectangular parallelogram. A thin uniform square sheet of metal of area square inches weighs ounces. At the corners , , , weights of oz., oz., oz., and oz., respectively are placed. Locate the centre of gravity of the system. Question 2 Establish... Read More

27Nov2018

### Leaving Certificate Examination 1967 Honours Applied Mathematics

Question 1 A body is projected under gravity with initial velocity at an angle to the horizontal. Find in terms of , , (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... Read More

26Nov2018

### Leaving Certificate Examination 1966 Honours Applied Mathematics

Question 1 (a) Represent any two velocities and by a vector diagram, and illustrate the vectors and . (b) When the sun, S, is above the horizon, an aeroplane glides in for landing with the sun behind, moving with a speed of m.p.h. along a path sloping down from the horizontal, as in the diagram.... Read More

25Nov2018

### Leaving Certificate Examination 1965 Honours Applied Mathematics

Question 1 Two pegs are fixed at points and in the same horizontal line. One end of a light string is attached to and the other end to . When masses of and lb. are attached to points and , respectively, on the string, the and . Find the tension, in lb. wt., in each... Read More

24Nov2018

### Leaving Certificate Examination 1964 Honours Applied Mathematics

Question 1 A uniform ladder has a length of feet and weighs lbs. The end leans against a vertical rough wall (coefficient of friction ) and the other end is on rough horizontal ground (coefficient of friction ) at a distance of feet from the wall. A block weighing lbs. is placed on the ground... Read More

23Nov2018

### Leaving Certificate Examination 1963 Honours Applied Mathematics

Question 1 and are two fixed pegs in the same horizontal line. One end of a light string is attached to and the other end to . When two masses are attached to the string, one at a point and the other at a point , the angles , , are , , , respectively.... Read More

22Nov2018

### Leaving Certificate Examination 1962 Honours Applied Mathematics

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

21Nov2018

### Leaving Certificate Examination 1961 Honours Applied Mathematics

Question 1 is a triangle in which , , . Forces of , , lb. wt. act along , , , respectively. How far from does the line of action of their resultant cut ?. Find the magnitude of the resultant in lb. wt., correct to one place of decimals, and find the angle which... Read More

20Nov2018

### Leaving Certificate Examination 1960 Honours Applied Mathematics

Question 1 A mass of gm. is supported at by two light strings , which are attached to fixed pegs at , , respectively, the straight line being horizontal. If ins., ins., ins., find the tensions in the strings. Question 2 Explain the terms “limiting friction”, “coefficient of friction.” A uniform ladder of weight rests... Read More