EXAMINATION PAPERS, 1932.
61
4. [a) Solve the equations—•
x—2y , 5y — 2%
(i) + -
(ii)
3
3y — x
3x-4
x — 2
y — x
X — % _ os
3^4 _d4-
(b) Prove that x—a and x-j-c are factors of
x3-l-2(c—a)x2-j-(c2—3ca-{-iz2)x—ca(c—a)
and find the other factor. (18)
Section II.
Only three questions should be attempted from this Section.
5. (a) Simplify—
x 1 x — 2 x l
x2 — 2x — 15 2x2 — 9x — 5 2x2 + 7% + 3
(b) A farmer buys n sheep at s shillings each. Three
of them die. He sells one-third of the remainder at
p shillings each, and the rest at q shillings each. What
is his total profit in shillings ? (15)
6. The heights of the barometer, in inches, at different
heights above the sea level, in thousands of feet, are given
in the following table :—
Height above
i6
sea
Height of
barometer. .
0
30-0
24-9
10
20-5
15
17-0
20
14-2
25
10-9
Draw a graph to show the fall of the barometer due
to rise above sea level, and estimate the height of the
barometer at 7,500 feet and at 19,000 feet. (15)
7. The base of a triangle exceeds its altitude by 5 feet.
If each is increased by 3 feet, the area of the triangle is
increased by 15 square feet. Find the area of the original
triangle.
If the original triangle is isosceles, use your tables to
find the size of its base angles. (15)