XV. TRINITY TERM, 1905. 1. Find the value, when a = 3 and b = 5, of: (1) (9—b) (a + 1 ) + (a + 5) (b + 7)—110; (2) 3a-[5b-{2a-(3c-3b)+2c-(a-2b-c)}]. (2) (a2 — b2)2+2c2 (a2 — b2) + c1 − 2 d2 (a2 — b2 + c2) + da. - 5. Find H. C. F. and L. C. M. of x2-7x-6 and x2+x3-11x2-9x+18. 6. Show that if the first and last of any three consecutive integers be added together, the sum is twice the middle number. Make a similar theorem in regard to any three consecutive even or odd integers. 7. Solve: 4x (1) † (3 − x) + † ( 5 – 1 ~ ) = § ( 4 – 7TM) ; 2 8. A man has 10 hours' holiday; how far may he walk out at 4 miles an hour in order that after 3 hours' rest he may just reach home again by walking at 3 miles an hour? 9. A bag contains £5. 28. in crowns, florins, and shillings; the number of florins is twice the number of crowns; the number of florins and crowns together is eleven times the number of shillings. Find how many coins of each kind there are. 10. When A was as old as B is now, he was twice as old as B was then. Their united ages are at present 60. How old are A and B? XVI. SEPTEMBER, 1905. 1. Find the value when a = 1, b-1, c = 0, d = 2, of: 2. Multiply 3x2-4xy + y2 by 2x2+3xy+4y2, and test your result by substituting x = 2 and y = 1 in question and answer. 3. Divide a2 (b+c)− b2 (c + a) + c2 (a + b) + abc by a−b+c. (2) bc (d—a)2 a-b a2+b2 ; ab (d—c)2 + (a a—b) (a — c) + (b −c) (b − a) * (c — a) (c — b) ' a2c (2) (a + x) (b + x) − a (b + c) = b2 + x2 ; 8. A gentleman distributing alms to some mendicants finds he lacks 108. to be able to give them 58. apiece; he gives 48. to each and finds he has 58. left. Required the number of shillings and of mendicants. 9. Find two consecutive numbers such that the difference between their squares is 51. 10. The forewheel of a carriage makes 6 revolutions more than the hindwheel in 120 yards; but only 4 revolutions more when its own circumference is increased by one-fourth, and that of the hind wheel by one-fifth. Find the circumference of each wheel. XVII. MICHAELMAS TERM, 1905. 1. (1) If a, b = −2, c = 1, find the values of ac a-b{a-2e()+c (1+ab) + }; 865 (2) If a 3, b-1, c = 5, show that = 2 (a+b−c) (a + c—b) (b+c− a) = 3(a2+b2+c2) (a2-2b2-c2) 2a-4b+5c 2. Divide 4-17x+4x by 2x2-3x-2, and multiply the result by 2x2+3x+2. 3. Find the H. C. F. and the L. C. M. of x2+4x2+3x3-3x2-4x-1 and x2+x3—4x2+x+1. 6. Resolve into factors: (1) x2-19x+78; (2) a2+b2-c2-d2-2ab-2cd; (3) (a+2b)3 + (2 a + b) 3 − 36 (a + b) ab. 7. Solve : (1) (7—6x) (3—2x) = (4x+3) (3 x − 2) — 17 ; ab+x b2-x x-b ab-x (2) ; 8. I bought a certain number of oranges at two a penny and the same number at three a penny. I sold them at five for twopence and lost a penny. How many oranges did I buy? 9. If two pipes open separately fill a vessel in a and b minutes, and a third pipe open separately empties it in c minutes, in what time will the vessel be filled when all three are open together? 10. A room is twice as long as it is broad. The floor is covered with a carpet which has a border half a yard wide. The total area covered by the border is 11 square yards. What is the size of the room? XVIII. HILARY TERM, 1906. 1. If a = 1, b = 0, c = 3, d = 16, find the value of a+3b+c 5 acd +10a3b + 3 (d−4c) + (a+c) (d—b) * 2. Find the G. C. M. of 2x3-9x2+13x-6 and 6x3-7x2-5x+3,. and the L. C. M. of x2+3xу, x2+9xy2, x3-9xy3, xy-3y2. (3) X (x−y + 1)(x + y + 6x2-7x-20 x +5–14 2x2+x-15 3x2-2x-8 4. Find the square root of: (1)x+2x3+7x2+6x+9; (2) 15376a2+31000 xy + 156252. |