Marks
2. (i) Without using logarithms, solve the equation
23*-5 = 128. (3)
(ii) Solve, correct to three significant figures, the equation
3*-i = 2*+1. (6)
(iii) The adjacent sides of a rectangle are of lengths
4a/3 + 3 units and 3-\/3 — 4 units. Find the exact
length of a diagonal. (4)
3. (i) Differentiate with respect to ^ :
(a) x* (4a; + 1) — 4%- * ; (3)
(b) I . (2)
w V(3 - 4*)
(ii) Find the volume obtained by revolving about the .v-axis
the finite area bounded by the lines 2x y — 5 = 0,
x = 2, and the coordinate axes. (5)
4. (i) Solve the equation
V(x + 4) + V(* + 11) = 7,
positive values of the square roots being taken. (6)
(ii) F is the sum of two quantities one of which is constant
and the other of which varies directly as the square of
v and inversely as r. If F = 9 when v = 2 and r — l,
and F = 10 when v = 4 and r = 2, express F in terms
of v and r. (6)
5. With the usual notation for the sides and angles of a
triangle, and assuming that
2bc
smM= A* ~ W* - c> (5)
V be
Find the size of the angle A in the triangle ABC in which
a = 6-5, b = 7-3, and c = 8-2. (4)
If H is the orthocentre of triangle ABC, find the length
of AH. (6)
Page two