USED AT THE EXAMINATIONS FOR Direct Commissions, AND FOR ADMISSION TO THE ROYAL MILITARY COLLEGE, IN JUNE, 1858. BIBT . LONDON : HARRISON, 59, PALL MALL, Bookseller to the Queen. 1858. a DIRECT COMMISSIONS. June 1858. MATHEMATICS. REV. J. W. HEAVISIDE, A.M. DISTRIBUTION OF MARKS. Max. Marks. Obligatory Portion 1200 (Of these, 500 Marks are required to be obtained for Qualification.) Voluntary Portion.. 2400 Total 3600 OBLIGATORY PORTION. Arithmetic. 1. How many tons, hundredweights, quarters &c., are there in 1895485 ounces avoirdupois ? A 3 3. Multiply 3 of 7jby (+-5 5 9 13 3 2. What is meant by the greatest common measure of two numbers ? Find the greatest common measure of 1808 and 3955. 2 7 å. Divide 8 21 By what fraction must û be divided, so 24 11 as to give a quotient : 5 4. Express 12s. 4d. as a fraction in its lowest terms, (1) of 1l.; (2) of 1001. Express 31. 178. 6d. as the decimal of 501. 5. Divide :175 by 2-5 and 4 by .00025. In the last example verify the result by means of vulgar fractions. 6. Extract the square root of 127598.9841. 1:44 3 2:56 4 7. 4000 men in a garrison have provisions for 95 days, after 15 days 800 men are removed; how long will the provisions last the remainder at the same rate ? si 8. Find the simple interest on 34561. 10s. at 4 per cent. for four years. If Consols are at 96, how much stock will 11581. purchase ? Algebra. 1. Explain the following terms as used in Algebra, and give examples : “Coefficient,” Exponent,” « Like and unlike quantities." Find the value of (x2 + y2) x (x - y) when x=4 y=2 2. Perform the operations indicated in the following examples (1) (7x2 — 9y2) + (3x2 - 11y?) – (5x2 + 20y?) (z? — 7)*(x2 - 9) * (x2 +11) 1-2a-361+2a+36 a a 4. In numbering the men of two regiments, it was found that there were 3 men in one regiment for every 2 men in the other; after 400 recruits were added to each regiment, it was found that there were 7 men in the one for every 5 men in the other. How many men were there in each regiment at first ? 5. Explain why log 157 = 7 log 15. Is this true of logarithms calculated to any base. How many digits are there in 315 ? Find by logarithms (1) (3•1416)* (2) 3.1416X.045 A 2 |