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scene of domestic happiness, I with many a glowing image 1 of conjugal and maternal love, / with delightful hours of social pleasure, / with nothing that is ungenerous, ungraceful, uncharitable, or falso.
SCHOLARSHIP QUESTIONS, ,
ARITHMETIC. Three hours allowed for this paper. Candidates may not answer more than THREE of the sections under Question 1, and may answer ELEVEN other questions.
The solution must be given at such length as to be intelligible to the Examiner, otherwise the answer will be considered of no value.
1. (a) Give illustrations of the statement : If a number measure two other numbers, it also measures their difference. (b) Make a diagram, showing that,
1+1-1=1.. (c) Show that not more than four aliquot parts are required for finding by Practice the value of 3178 articles at £1 13s. 9 d. each.
(d) Write out the rule for finding the L.C.M. of two given numbers.
(e) How would you prove the correctness of the ordinary method of converting the vulgar fraction into a decimal ?
2. Find the least number which if multiplied by 43 and divided by 41 leaves a remainder of 18.
3. Find the number of yards of paper, 2 feet wide, required for a room 35 feet long, 25 feet wide, and 10 feet high, allowing for a door 7 feet high and 6 feet wide, two windows each 6 feet high and 4 feet wide, and a fireplace covering 18 square feet.
4. The value of a Spaniard's work to that of a Frenchman's being as 3:4, and their rate of daily wages being 58. and 78. respectively, find the gain obtained by employing 100 Spaniards for 21 days instead of Frenchmen.
5. If 4 acres 2 roods 39 poles of land cost £768 93. Id., what would 9 acres 2 roods 13 poles cost ?
6. What fraction of 4s. 7d. will exceed of 5 of 2s. 1d. by 1s. 5d. ?
7. Add together 1:3 of 2s. 6d., 1.025 of 1s. 8d., 3.4 of 28. Od., 3.15 of 2s. 9 d., and reduce their sum to the decimal of £1.
8. Find (by Practice) the value of 73,360 articles at £5 14s. 3 d. each.
9. In what time will £4000 amount to £8574 73. 1.2576d. at 10 per cent. per annum compound interest?
10. Find the breadth of a tank 70 feet long and 3 feet deep, which contains 36,288 gallons (a gallon contains 277:274 cubić inches).
11. Find, in inches, to three places of decimals, the side of a square which contains 41:9 square feet.
12. Find the annual rent of a house, on which, after deducting 20 per cent., a rate of 3s. ld. in the pound produces a sum of £38 17s.
13. Find the length of a floor, 18 feet wide ; the difference of cost if covered with asphalte, 2 inches deep, at 18s. per cubic yard, or with gravel six inches deep, at 78. per cubic yard, amounting to £6.
14. A wine merchant buys 500 gallons of brandy at 40s. per gallon, and 600 at 50s. per gallon : at what price should he sell them, mixed together, to make a gain of 10 per cent. ?
15. A person invests in the 3 per Cents. so as to obtain interest at the rate of £2 19s. 330d. per cent. per annum : find the price of the stock,
EUCLID, ALGEBRA, AND MENSURATION.
(Three hours allowed for this paper.) Candidates who attempt either of the questions in Mensuration must omit questions 5 and 6. (Marks are given for portions of questions.)
In the Euclid questions all generally understood abbreviations for words may be used, but no symbols of operations (such as +, x) are admissible.
N.B.- Capital letters, not numbers, must be used in the diagrams.
1. Any two sides of a triangle are together greater than the third side.
If a straight line be drawn from the vertex of a triangle bisecting the base, the line together with half the base is greater than half the sum of the two sides.
2. Every parallelogram is bisected by its diameter.
Under what conditions will the lines bisecting the opposite angles of parallelograms be coincident?
3. If the square described on one of the sides of a triangle be equal to the squares described on the other two sides of it, the angle contained by these two sides is a right angle.
Write out the corresponding formula for the square on the side subtending the obtuse angle of an obtuse-angled triangle.
4. To describe a square that shall be equal to a given rectilineal figure.
To divide a given straight line into two parts so that the rectangle contained by the two parts shall be equal to the square on one-fourth of the line given.
5. To draw a straight line from without the circumference of a given circle which shall touch the circle.
Find the locus of a point without a circle such that the tangents drawn from it to the circle shall form an equilateral triangle with the chord joining the points of contact.
6. If from any point without a circle two straight lines be drawn, one of which cuts the circle and passes through the centre, and the other touches it, the rectangle contained by the whole line which cuts the circle and the part of it without the circle shall be equal to the square on the line which touches it.
7. Write down the factors of mo? + 3x – 10, 20% – 1, 9x? + 15x – 14.
1 1 1 Add together
? 8. Divide 7%? x+
9. Solve the equations
5x - 9 7x -1 11x +-7
=254 10. In the quadratic equation x + ax + b= 0, show that - a= the sum of the roots.
Solve the equation 2x + Vx+ 7x + 23 – 25 = 0.
11. An avenue is planted with trees 20 feet apart ; if the trees had been planted 15 feet apart, the cost would have been increased by £5 at 2s. for each tree : find the length of the avenue.
MENSURATION. 12. Show that the area of a triangle whose sides are in the ratio of 3:3:4 is greater than ; of the area of a square described on one of the shorter sides.
13. Find the length of the side of a parallelogram, one angle being half a right angle, the altitude being equal to half the base, and the area containing 1250 square feet.