5. Add a perfect fifth to (i.e. above) each of the following notes. 5. Write the Lal mode in every form with which you are acquainted. 6. What are the contents of a bar marked i ? Of a bar marked ? 6. Give an example of a change of pulse measure. a ARITHMETIC. For Male Candidates only. THREE Hours allowed for this Paper. Candidates are not permitted to answer more than one question in each Section. The solution must in every instance be given at full length. A correct answer, if unaccompanied by the solution, or if not obtained by an intelligible method, will be considered of no value. SECTION I. Write in figures(a) Seven hundred and fifty-six thousand and thirty. And (6) Six hundred and fifty-five thousand two hundred and twenty-six. Find the sum of these two numbers, and also their difference; and divide the sum by the difference. SECTION II. 1. A hospital is to be built for £10,000. The promoters have received the following sums, viz. : £4318 78. 10}d., £295 9s. 9d., £2867 58. 2 d., and £47 18s. 81d. How much more have they to raise ? 2. If I have to pay £7 88. 91d. to each of 37 people, how much money do I require ? SECTION III. 1. If I have £2832 14s. 7d. to divide among 235 people, how much will each receive ? 2. How many contained in £2049 178. 6d., and how many guineas in 16,254 pence? SECTION IV. 1. How many square yards are there in a field of 17 acres 3 rods 16 poles ? are 2. How many tons, hundredweights, etc., are there in 76,409 ounces avoirdupois ? 3. How many grams are there in 7 quintals 65 kilograms and 9 decagrams? SECTION V. 1. Find the value of 2089 articles at £1 17s. 8d. each. 2. Find the cost of 15 cwt. 3 qrs. 173 lbs. at £6 178. 8d. per ton. a 3. What is the tax on an income of £655 138. 4d. at 3d. in the £? SECTION VI. 1. State clearly the steps by which you would teach children to multiply any sum of money by a prime number, such as 29, supposing them able to do compound multiplication up to 12 times. 2. Write full notes of a lesson on (a) the addition of vulgar fractions, or (b) the division of one decimal by another. 3. Explain, as you would to a first class in a school, the facilities for teaching arithmetic which would arise from having a decimal coinage and a decimal system of weights and measures. SECTION VII. 1. Find the sum of 63, 74, 8725, 19, 1071, 126 2. Simplify (3 + 43) • (715 23), and find the equivalent decimal. 3. What is the difference between 22:4735 of £1, and 17.2845 of a guinea ? 4. Express 27 miles 5 furlongs 184 yards in metric denominations, assuming that 1 metre = 39-3708 inches. SECTION VIII. A garrison of 1000 men, provisioned for 60 days, was reinforced at the end of 18 days, and the provisions were exhausted at the end of 30 days from that time. Of how many men did the reinforcement consist ? 2. Two engines, 40 miles apart, are approaching each other at the rate of 25 and 35 miles an hour. Determine the time and place of their meeting: 3. If a sixpenny loaf weigh 4:35 lbs. when wheat is at 5.758. per bushel, wbat ought to be paid for 46 lbs. of bread when wheat is at 8.78. per bushel ? SECTION IX. 1. What is the difference between the simple interest of £50 198. for 7 years at 3 per cent., and that of the same sum for 8 years at 2} per cent. ? 2. What principal, put out at simple interest for 5 years, at 3} per cent., will amount to £1000 ? 3. Find the side of a square field measuring 810 acres. ARITHMETIC. THREE HOURS allowed for this paper. each Section. The solution must in every instance be given at full length. A correct answer, if unaccompanied by the solution, or if not obtained by an intelligible method, will be considered of no value. SECTION 1. 1. Add together forty-one thousand six bundred and sixty-two; eight million five thousand two hundred and thirty-four; nine hundred and nineteen thousand and nineteen; thirty thousand and six hundred; eight hundred and eight thousand and eighty eight; and from the sum take away seven hundred and thirteen thousand six hundred and ninety-four; and write the answer in words. SECTION II. 1. Divide 30,000 by 9375 by long division and by factors. 2. Multiply 227,351 by 429. SECTION III. 1. Divide £9661 168.0 d. by 29. 2. How many ounces are there in 2 tons 3 cwt. 1 qr. 17 lbs. 1 oz. ? SECTION IV. 1. Find the value of 4928 articles at 78. 9 d. each. 2. Find the value of 9 decametres 1 metre 2 deci. metres of silk at 6 francs 25 centimes per metre. Section V. Make out the following bill :-1} lbs. of Valentia almonds at 10d. per lb.; 3 lbs. of ginger nuts at 7d. per lb.; 44 lbs. of citron at 1s. ld. per lb. ; 12 lbs. of currants at 4 d. per lb.; 5 bottles of cherries at 8 d. per bottle; } lb. of gelatine at 38. per lb.; 5 lbs. of Sul. tana raisins at 6 d. per Ib. Euclid and Algebra. 55 SECTION VI. 1. If a pane of glass 18 inches long and 12] inches wide cost 10d., what will be the cost at the same rate of a pane 224 inches long and 15 inches wide ? 2. If 5 oxen are worth 24 sheep, and 4 sheep are worth £13, what are 55 oxen worth? SECTION VII. 1. Reduce to a simpler form (1 + } + %) +(9 X X ). 2. Multiply £2 198. 07d. by 7). SECTION VIII. 1. How often will a wheel, 2 metres 9 decimetres 7 centimetres in circumference, revolve in passing over a distance of 2 kilometres 7 hectometres 2 decametres 9 metres 4 decimetres 3 centimetres ? 2. Add together 3-754, 4:63, 2.4, and 5:21. 3. Multiply 31.5 by 27.9, and divide the product by 9.765, giving the reason for the position of the decimal point in each result. SECTION IX. 1. Reduce £104 38. 3 d. to farthings; and explain, as you would to a class, each step of the process. 2. Define 6 Ratio and “Proportion," and work an example in Proportion in illustration of your definitions. 3. Explain the terms “Principal," “Interest," ' Amount,” and work an example, such as you would give to a class, in illustration. 9 EUCLID AND ALGEBRA. THREE Hours allowed for this paper. EUCLID. Capital letters, not numbers, must be used in the diagrams. Not more than ten questions to be answered. 1. Give Euclid's definitions of a plane rectilineal angle, and of a triangle. Prove that if two triangles have two sides of the one equal to two sides of the other, each to each, and have also the angles contained by those sides equal to one another, they shall also have their bases or third sides equal; and the two triangles shall be equal, and their other angles shall be equal, each to each, namely, those to which the equal sides are opposite. 2. When is one straight line said to be perpendicular to another P Draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it. Why must the given straight line be of unlimited length ? 3. Make a triangle of which the sides shall be equal to three given straight lines; but any two whatever of these must be greater than the third. Why is it made a condition, in working this problem, that any two of the given lines must be greater than the third ? 4. What are parallel straight lines ? The straight lines which join the extremities of two equal and parallel straight lines towards the same parts, are also themselves equal and parallel. 5. What is a parallelogram ? Describe a parallelogram which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal triangle. 6. In any right-angled triangle, the square which is described on the side subtending the right angle is equal to the squares described on the sides which contain the right angle. ALGEBRA. The solution ' must in every instance be given at full length A correct answer, if unaccompanied by the solution, or if not obtained by an intelligible method, will be considered of no value. 1. Add together 2-3 + 3x2y + 3xy? + y*, 5043 – 15.xoy + 1Eæya — 573, 10x3 + 10 y3, 17x“y — 17xy?; and from their sum take away 1323 39x2y + 39xya 13y. 2. What is a vinculum, and what effect has it when preceded by a minus sign! Collect the following, 12 (ab cd) 6 ac – bd) - 5 (ab – cd) — 7 (ac - bd) + 3ab 2 (ac + bd - cd). 3. Multiply a* + 49a2 + 2401 by a — 49, and divide 203 2x2 + 3x — 6 by a — 2. 4. Multiply a3 2a2b + 3ab2 + 463 by a? 2ab - 36?, and divide x* + (262 — a^)ava + 64 by a2 + ax + 6%. |