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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) Write out the rule for division of decimals when the number of decimal places in the divisor exceeds the number of decimal places in the dividend.
(6) In dividing a number by 315, if I divide the number consecutively by 5, 7, 9, and obtain remainders 3, 2, 1, what is the complete remainder ?
(c) Show that the ratio of two numbers may be expressed by a fraction.
(d) Make a diagram showing how a line or a cube may be divided in such a way as to prove the truth of the proposition } - = 24
(e) Work a sum in simple interest by the method of proportion, so as to show the truth of the shortened process which is commonly employed.
(f) Explain clearly in what sense 1.3 is represented by 11.
2. °A chest containing 350 oranges is bought at Naples for 42 pence, and the cost of carriage is 10 per cent. additional; the oranges are retailed in London at the rate of ten for threepence; find the profit upon 100 oranges.
3. If 4 of a ship is worth £101 Os. 1d. ; what share can be bought for £3,131 2s. 7d.:P
(73–5*+1,1.-) 37 of £1 38. 4d.
7 5. What decimal of one pound multiplied by 3is equal to. £1 78.8
6. The inhabited house duty at ninepence in the pound on the rent of a house is £3 10s. more than the income tax at sixpence in the pound. Find the annual rent of the house.
7. What principal will amount to £42998·1696 in eight years at 20 per cent. compound interest per annum ?
8. If the ratio of threepenny to fourpenny picces in a given sum which consists entirely of those coins were altered from 3: 7 to 7:3 the sum would be diminished by £20. Find the sum.
9. Find the square root of 89820:09; find also the cube root of 16503.
10. The rainfall for the first four weeks of the year was 1:08, 95, 3.15, 1:72 respectively; and the average was 1.25 higher than the average of the first four weeks of the previous year. Find the arerage of the two years together.
11. A Hoor is half as long again as it is broad, and contains 13,824 square feet. Find the length of the shorter side and the cost of flooring at 4 d. per square yard.
12. A man makes 15 per cent. profit by selling 700 tons of coal for £1,006 5s. What would have been his profit per cent. and per ton if he had sold them for £936 5s.?
13. The Three per Cents. are at 1014; the Four per Cents. at 121}. Find the gain in income obtained by transferring £10,000 stock from the Three per Cents. to the Four per Cents.
14. A sum of £3,070 3s. 3d. has to be divided between A, B, and C, so that A may have į of of B's share, B of A's and C's together. Find their respective shares.
15. A tax of 5d. in the pound is paid on a certain sum, and a further tax of 12 per cent. on the remainder. The sum now remaining is £31 2s. Od. Find the original
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.)
EUCLID. 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. If a straight line fall on two parallel straight lines, it makes the alternate angles equal to one another.
Show that the lines bisecting the external angles of an equilateral triangle are parallel to the sides.
2. Triangles on equal bases and between the same parallels are equal to one another.
If the perpendiculars drawn from the vertices to the bases of two triangles be equal, the bases being equal and in the same straight line, the triangles are equal.
3. Draw the figure required for Euclid, Book I., Prop. 47.
If perpendiculars be drawn from the middle point of the hypotenuse of a right-angled triangle to the two sides, the square on the hypotenuse will be equal to four times the sum of the squares on the two perpendiculars.
4. If a straight line be divided into any two parts, the rectangles contained by the whole and each of the parts are together equal to the square on the whole line.
State this algebraically.
5. The diameter is the greatest straight line in a circle.
Draw a chord equal to the radius of a given circle, and parallel to a given diameter.
6. The opposite angles of a quadrilateral figure inscribed in a circle are together equal to two right angles.
If two sides of a quadrilateral figure inscribed in a circle be parallel, the other sides will be equally inclined to them.
7. Write down in their simplest forms the factors of 204 — 1, — 20 — 12.
Show that (a -1)- Sal (b − a)= a-13. 8. Find the G. C. M. of
23 — 3ic? — 13x + 15,
and 23 + 9x2 + 11x — 21. 9. Solve the equations
(2) 3 + %
4y - 3x =0 10. Form the equation whose roots are 3 and — 3. If a2 + ax + 576 is a perfect square, what is the value of a?
5 Solve the equations
11. A purse contains only threepenny and fourpenny pieces, equal in value to £2 108. 7d. ; if the number of threepenny and fourpenny pieces were interchanged, the value would be £2 88. 7d., find the number of coins of each sort.
MENSURATION. 12. If 15 trees can be planted on two square chains of ground, how many can be planted on a rectangular area, 1,210 yards in length, 2,244 yards in depth ?
13. One diagonal of a rhombus is 1,014 feet, the length of a side is 815 feet, find the area of the rhombus and the length of the other diagonal.
MALE AND FEMALE CANDIDATES.
GEOGRAPHY AND HISTORY.
Three hours allowed for this Paper. All candidates must draw a map, and answer Question 8. They may answer four other questions in each of the two subjects.
GEOGRAPIY. 1. Draw an outline map, with meridians and parallels, if you can, noting thereon the principal physical features only, of (a) Scotland, or (6) Spain, or (c) Italy, or (d) Hindostan.
2. Explain, and illustrate by a diagram, (a) the phases of the moon, or (b) the succession of the four seasons, 01 (c) the variation in the length of day and night.
3. What is meant by the terms, as applied to rivers, of “ watershed,” “tributary,” “affluent," left bank,” “ bed," “ fall," "volume," and " basin ?" Draw or describe the basin of the Thames, or the Po, or the St. Lawrence.
4. Name and give the situation of the principal seaports, and the chief seats of manufacturing industry in the British Isles.
5. Describe the most interesting and important features of a voyage from London by the overland route, or from Dantzic by long sea, to Bombay.
6. Name the chief productions imported into Great Britain from her possessions in Asia, specifying the place from which each of them comes to us.
7. What is meant by “climate ?” What are the chief causes affecting it? Describe the influence upon it of each.
HISTORY. 8. Arrange in chronological order, and give the dates of the following events :- The legislative Union of Great Britain and Ireland ; of England and Scotland; the Act of Habeas Corpus; of Catholic Emancipation; the beginning of Popular Representation in Parliament; the American Declaration of Independence ; the introduction of printing; the destruction of the Spanish Armada; the battles of Blenheim, Newbury, Bosworth, Dettingen, Flodden, Pinkie, and Inkerman.