Question 1
A binary operation Δ is defined on the set of real numbers, R, by
a Δ b = a3 – b3.
Without using calculator, find the value of (
+ 
) Δ (
- 
),
leaving the answer in surd form.
Observation
The Chief Examiner reported that majority of the candidates attempted this question very well. They were able to expand the expression correctly and substituted the given values into the expression. However, a few of them could not manipulate the surds correctly and so lost some marks. Candidates were expected to substitute the given surds into the operation and simplify to obtain:
(
+ 
) Δ (
- 
) = (
+ 
)3 - (
- 
)3
= 3
+ 3(3
) + 2(3
) + 2
– (3
- 9
+ 6
- 2
) = 18
+ 4
= 22