CONTENTS. XXI. Spherical and Nautical Astronomy I. Practical, Plane, and Solid Geometry II. Machine Construction and Drawing XXIII. Physiography (Section I. only of Stage I.) - XIX. Metallurgy"- Results 1st Class, 632; 2nd Class, 1,138; Failed, 1,423; Total, 3,193. A. The questions in ARITHMETIC were, perhaps, a little harder than usual. Those most frequently attempted were Questions 1 and 3. The latter contains two questions on the metrical system of measures, which were often correctly answered. Q. 2. Find by contracted multiplication the product of 32:5467 and 2:4918 so as to obtain the product true to four decimal places. Express as a decimal and find the square root of the expression true to four decima places. From this question it would appear that more attention is paid to contracted work than was formerly the case, so that several good answers were sent up to the first part of the question. Very few treated the second part properly. Q. 4. A rectangular box measures externally (when the lid is down) 4 ft. long, 2 ft. wide, 1 ft. high; it is made of wood an inch thick. Taking account of the wood only, find the ratio of the weight of the lid to the weight of the whole box. By how much does the ratio exceed !? Is an easy question in the mensuration of rectangles; it requires care and a correct appreciation of the data; these were often wanting, and so there were many failures, but the right result (81/308) was obtained fairly often. Q. 6. An alloy of silver is mixed with an alloy of gold in the ratio of 57 to 13; the percentage of lead in the silver alloy is 13.75 and that in the gold alloy 16:25; what is the percentage of lead in the mixture? Was answered correctly in a good many cases; but only by those who otherwise did well. On the whole the work in Arithmetic was well done. 9201. 4,000-Wt. 7762. 12/03. Wy. & S. 4971r. A B. The book work in GEOMETRY was, on the whole, fairly well done. The deductions and problems came in for a good deal of attention and were done well by one and another. Q. 7. BC is the base of an isosceles triangle ABC, and D is the middle point of BC; show that the straight line AD is perpendicular to BC. Define a triangle, an isosceles triangle, and a right angle. Was, of course, very often taken. The work, however, was marked by some very prevalent faults, viz.: (a) It was very often said that in the triangles ABD and ACD, the sides AB, AC are equal, AD common, and the angle ABD equal to ACD, therefore the triangles are equal in all respects. (b) The definitions were often faulty, e.g. a triangle was defined as a figure having three sides; an isosceles triangle as a triangle having two equal sides and two equal angles; a right angle as an angle of 90°. It hardly admits of a doubt that the prevalence of such faults as (a) and (b) proves that the teaching in many schools was not good. Q. 8. If two straight lines cut one another, show that the vertically opposite angles are equal. A and B being two points on the same side of a straight line PQ, from A a perpendicular AC is drawn to PQ, and is produced to D so that CD is equal to AC; show that, if DB cuts PQ in E, the straight lines AE, BE make equal angles with PQ. The second part of the question is given in most text books; both the first and second parts were very often answered. Q. 9. Two triangles have equal bases, and the angles at the base of one triangle are equal to the angles at the base of the other triangle, each to each; show that the triangles are equal in all respects. ABCD is a parallelogram, and in DC or DC produced a point E is taken such that BE is equal to BC; also CA, EA, and BD are joined; show that the angle CAE equals the difference between the angles DCA and DBA. In reference to the first part of this question, it is worth noticing that the proof by superposition (in itself, of course, a good proof) did not seem to be as well understood as the proof by a reductio ad absurdum. The second part is, perhaps, harder than it looks; it was very occasionally well answered, e.g., there were four good answers in about 400 consecutive papers. Q. 10. Define parallelograms about a diagonal of a parallelogram, and the complements of those parallelograms. Show that the complements of the parallelograms about a diagonal of any parallelogram are equal to one another. In a given parallelogram construct complements each threesixteenths of the area of the parallelogram. Q. 11. Define a square. E, F, G, II are the middle points of the sides of a square ABCD; show that EFGH is a square. Hence, in the particular case when a right-angled triangle has two equal sides, show that the square on the hypotenuse equals the sum of the squares on the other two sides. Q. 12. ADEF is a rhombus, having the angle at A a little greater than a right angle, and B and C are points in DE and EF respectively such that ABC is an equilateral triangle; if ADEF be such that a side of it equals a side of the triangle ABC, show that the angle DEF is ten-ninths of a right angle. These three questions elicited a few good answers, particularly the first parts of Q's. 10 and 11. The force of the word "Hence" in Q. 11 was not felt by more than a very few, but most of those few found the required answer easily. |