WAEC 2016 · Paper 2 · Q13

(a)
Find the equation of a straight line which passes through the point $(2, -3)$ and is parallel to the line $2x + y = 6$ .
Show the answer
$2x + y - 1 = 0$
(b)
The operation $\Delta$ is defined on the set $T = \{2, 3, 5, 7\}$ by $x\,\Delta\,y = (x + y + xy) \bmod 8$ . (i) Construct the modulo 8 table for the operation $\Delta$ on the set $T$ . (ii) Use the table to find: I. $2\,\Delta\,(5\,\Delta\,7)$ ; II. $n$ if $2\,\Delta\,n = 5\,\Delta\,7$ .
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

Each entry is $x + y + xy$ reduced modulo 8.
For example $2\,\Delta\,3 = 2 + 3 + 6 = 11 \equiv 3$ and $5\,\Delta\,7 = 5 + 7 + 35 = 47 \equiv 7$ .
$\Delta$ 2 3 5 7

2 0 3 1 7

3 3 7 7 7

5 1 7 3 7

7 7 7 7 7

$\Delta$	2	3	5	7
2	0	3	1	7
3	3	7	7	7
5	1	7	3	7
7	7	7	7	7

I.
$5\,\Delta\,7 = 7$ , so $2\,\Delta\,(5\,\Delta\,7) = 2\,\Delta\,7$
$= 7$ .
II. $2\,\Delta\,n = 5\,\Delta\,7 = 7$ : in the row of 2, the 7 is in the column of 7, so $n = 7$ .