P7 children are due to sit the test on Saturday for most catholic grammars.
The Association of Quality Education (AQE) organises the entrance exams for other non-denominational grammars.
"There are dialect grammars and there are also grammars for texting, " he said.
The National Grammar School Association says many other grammars would like to expand.
BBC: Grammar school: Kent County Council backs expansion plan
The Post Primary Transfer Consortium (PPTC) provides the GL assessment tests mainly for Catholic grammars, along with some integrated colleges and a few non-denominational schools.
However, in the 1960s, as the abolition of most grammars was beginning, a study by the British Psychological Society failed to prove this widely touted claim.
Beginning in the 1960s, continuing under both Labour and Tory governments, most state-run grammars were forced to become comprehensive (ie, to admit pupils of all abilities).
And last year the watchdog told three Warwickshire grammars to stop admitting high-fliers from outside the county, on the grounds that they were undermining other areas' comprehensives.
Most of Northern Ireland's 69 grammar schools have said they will administer other, unregulated entrance tests including at least eight Catholic grammars, despite the opposition of their church's hierarchy to academic selection.
That is basically communication and information technology and as it is already part of the GNVQ courses offered mostly in secondary schools , those schools feel they are better prepared than the grammars.
He defended his party's new education policy, saying there would be no reintroduction of grammar schools or the 11-plus, but a handful of new grammars might be built in areas where selection already takes place.
BBC: NEWS | UK | UK Politics | Cameron 'won't flinch' on change
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