ALGEBRA. July, 1880. [State what text-book you have studied, and to what extent.] I. 1. Resolve the following expressions into factors, 16 a1 b2 — 24 a2 bmx + 9 m2x2; 2. Given find x and y. 9a2b2-16 a2c2; a3 — 8b3. 3. Given Va- x + √ b − x = 4. (a) From 2√72a take V162 a2. 3 (b) Find the value of √2 × 3 × √5. 1 = a+b 7. Given 2+ xy = ay2 + xy =b, to find x and y. 8. Expand 1+2x 1- x - x2 into a series by the method of inde terminate coefficients. 134 9. The number of permutations of n things, 3 together, is 6 times the number of combinations, 4 together; find n. NOTE. The first division of the paper extends as far as Quadratic Equations, and will be all that is required of candidates who propose to pass the partial examination only. a+b a b 4. Simplify √24+√54-√6; - b√ a + b W a a V x x b V y x c Vz; (√−1)*; (√−1)2. 5. Extract the square root of 4a+16a-12 ax3-24 a3x + 25 a2x2. 6. Solve the equation 3x2+2x-9=76. 8. Having the first term (a), the ratio (r), and the last term (1), of a geometric progression, find the sum (s), and the number (n) of the terms. 9. Expand b √x2 + a2 into a series by the binomial formula. 10. Solve the equations a" = y and x2 = y2. NOTE 1. June, 1881. Candidates for examination in this subject, as a whole, should take the whole of this paper; those for the first year's partial examination, the first part of it; those for the second year's partial examination, the second part. NOTE 2. State at the head of your paper what text-book you have studied on the subject, and to what extent. I. 1. Find the greatest common divisor of 5a3 +10 a1b+5a3b2 and a3 b + 2 a2 b2 + 2 ab3 + b*. 3. Two masons, A and B, propose to build a wall. If both work together, they can finish it in 12 dys.; but if A work 2 dys. and B 3 dys., they will complete only one-fifth of the job. How long will it take each of them separately to do the work? 4. (a) Reduce Va, Võ, Ve, to the same index. (b) Simplify the following expressions: 7. Determine by inspection the roots of the equation, x2 − (a+b)x+(a + c) (b − c) = 0, and state the principle upon which you do so. 8. Given x2y+xy2 = a and x2y — xy2 = b, to find x and y. 9. Expand (a+b3) to four terms by the binomial for mula. 10. Show that the modulus of any system of logarithms is equal to the reciprocal of the Naperian logarithm of the base of the system; and also that it is equal to the logarithm of the Naperian base taken in the system. September, 1881. [State what text-book you have studied on the subject, and to what extent.] 1. Resolve a b6 into four factors. 7 2. Given 4 1 2 + = 4 and + =1, to find x and y. Tx √y √x Vy 4. Resolve the trinomial x2 + 2x−120 into its binomial 7. A ball rolls down an inclined plane, describing 1 ft. the first second, 3 ft. the second, and so on. How far will it go in 10 sec., and how far in the tenth second? 8. If the population of a certain city is now 10,000, and it increases at the annual rate of 10 per cent for the next 10 yrs., what will it be at the end of that time? [Given (1.1) 10 = 2.5937+.] 9. Expand 2+3x minate coefficients. into a series by the method of indeter 10. Find the number of combinations of 10 things taken 4 together, and also taken 6 together. June, 1882. NOTE 1. Candidates for examination in this subject, as a whole, should take the whole of this paper; those for the first year's partial examination, the first part of it; those for the second year's partial examination, the second part. NOTE 2. - State at the head of your paper what text-book you have studied on the subject, and to what extent. 3. There are three workmen, A, B, C. A and B together can perform a certain piece of work in a days; A and C together, in b days; and B and C together, in c days. In what time could each singly perform it, and in what time could they finish it if all worked together? 5. (a) Write equivalent expressions for the following: |