Calendar for the year 1896-97 / University of Durham College of Medicine.

  • University of Durham. College of Medicine.
Date:
1896
Catalogue details

Licence: Public Domain Mark

Credit: Calendar for the year 1896-97 / University of Durham College of Medicine. Source: Wellcome Collection.

    159/178 (page 139)
    Algebra. 1 —On dividing a certain expression by - a; + 1, the quotient is a;'' + a; + 1 and the remainder - 1: determine what the expression must be. 2 —Find the G.C.M. of Sx' + 6x* + 5x^ - llx'' - 28x - 7, and 6a:* - 15a:^ - 6x^ + 35a; - 21. 3. —Prove the rule for finding the G.C.M. of two algebraical expressions. 4. —Add the Fractions— x{y + z) y{z + x) z{a) + y) , [x -y){x-z)^ (y- z) {y - x) (z - x) {z - y) 5. —Find the value of— X- {2a;'-l - [2(a;-l) + S{x^-x)]] X- j2a:'^ - 1 - a;[3 (a: - 1) + 4] j 6. —Write down the factors of + + — 3abc ; also all factors of x^ — y^ which are of lower degree than the fourth. 7. —Simplify— X -^2 - a-b • T^ + T^^ b~ a 8. —If 2s = a + b + c, show that— 2 (s - a) (s - b) (.s - c) + a{s -b){s-c) + b{s - c) {s - a) + c{s — a) (s — 6) = abc. 9. —Solve the equations— ■ (1) v^a:^ - 7a; + 4 + (a: - 1) (a; - 5) = (a; - 2) (a; - 3). .2 (2) ax + by = ay — ox = ^ • 10.—The length of a room is four feet more than its breadth. If it were one-fourth as long again, but of the same area, the cost of papering would be as many guineas as it now is pounds. Find its dimensions.