Question

1(a) A binary operation * is defined on the set T={-2,-1,1,2} by p*q=p²+2pq−q², where p,q∈T. Copy and complete the table for p*q.
(b) Using the table in (a), find the value of p such that (−2*p)*2=−7.

Accepted Answer

(a) Completed table (rows=p, columns=q):
p*q | q=−2 | q=−1 | q=1 | q=2
p=−2 |  8  |  7  | −1 | −8
p=−1 |  1  |  2  | −2 | −7
p=1  | −7  | −2  |  2 |  1
p=2  | −8  | −1  |  7 |  8
(each entry computed from p²+2pq−q²)

(b) −2*p = (−2)²+2(−2)p−p² = 4−4p−p². Substituting this into (4−4p−p²)*2 = (4−4p−p²)²+2(4−4p−p²)(2)−(2)² and setting the result equal to −7, solving gives p = 1.

WAEC Further Mathematics 2022 Theory — Question 1

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