Value
994
EXAMINATION PAPERS.
20. 3. Solve the following equations, verifying all your results :—
(1) a (x - a) = b (x - b);
(2) A (*-*)- - f) = i (*-#)- i (« - l)
(3) (x + l)(x-2)-(x - 3) (as + 4) = (* — 2) (* - 3).
20. 4. Draw in the same diagram the graphs
y = x2 + x + 1
y =2$ - x,
between the limits cc = — 3 and a: = 1, taking an inch as the unit.
Find from your diagram the co-ordinates of the points common to
both curves, and verify your result by solving the equation
x2 + x + 1 = 2± - x.
Answer TWO questions out of the following five.
15- 5. There are two numbers whose sum is 125. Also f of the one
number exceeds -f of the other by 13. Find the numbers.
15. 6. If 12 eggs cost x pence, and if at the same rate y eggs are bought
for one shilling, find the relation between x and y.
Express this relation by means of a curve on squared paper,
between the limits a; = 4 and x = 36, taking one-tenth of an inch as
the unit.
7. Find the remainder when
as4 + ix2 + ax + b
is divided by
a? + 2x+ 3.
and hence find the values of a and b, which make
a:4 + 4:X2 + ax + b
a multiple of
x2 + 2x + 3.
8. A has a pounds b shillings and c pence, JB has c pounds b shillings
and a pence. If c be less than a, a be less than 12, and b be less than
20, find how much money A has more than B, expressing it in pounds,
shillings, and pence.
9. Prove that the sum of the three fractions
b — c c — a a — b
1 + 1 + co’ 1 + ab’
is equal to their product.
15.