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The source:

Atako said that the computer-based test was to ensure transparency in the selection process.

Can you help to identify this structure. Seems like "be + infinitive" has a special meaning of purpose. Can I say "I am to help you with the homework."?

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This structure is be + infinitive. – Damkerng T. Apr 25 '14 at 11:50
"was to ensure" = it was required (or mandated) so that... . "I am to help you" = I am required to help you (i.e., someone told me to help you). – Phil Perry Apr 25 '14 at 16:42
up vote 5 down vote accepted

There is a reasonably common expression BE to VERB which has the approximate meaning “BE expected/obliged/directed to VERB (at some point in the future)”.

I am to help you with your homework = I have been told that I must help you with your homework

John was to go to London the next day, but had to cancel the trip = It was expected that John would go to London the next day, but ...

But I don’t think that construction is in play in this case. I think what you have here is an ordinary ‘infinitive of purpose’, where the infinitive clause to ensure transparency... describes the purpose of the test, combined with a loose colloquial use of the ‘copula’ BE.

Formal English does not like this use, which casts the infinitive clause as a predicate complement; it prefers that you deploy the infinitive clause as a modifier of a either a noun or an active verb:

A computer-based test to ensure transparency in the selection process was incorporated in the design.
The computer-based test was incorporated to ensure transparency in the selection process.

But colloquially, it is a very easy step from a test to ensure transparency to The test is to ensure transparency—it is basically the same step as that from a red ball to The ball is red.

I note that there are many grammatical errors in the source from which you drew this sentence, many of which are the sort made not only by non-native speakers but by native speakers who have not mastered the formal written dialect.

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I have read this structure be + to verb but not frequently. I think though there's nothing confusing, this is not widely accepted structure.

be + to verb is often = must verb. So, it could be...

"....computer-based test must ensure transparency..."

Considering your second example, for better understanding, I'm to help you... can be paraphrased like...

"I am expected to help you ..."
"I am supposed to help you..."
"I must help you..."

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Be to structure

“The test was to ensure transparency” is equivalent to:

“The test had to ensure transparency”.

“I am to help you with the homework” means, similarly, that I have to help you with the homework.

A product feature is to be specified in the manual means that it has to be specified in the manual.

So, in this particular case the verb “be” can be replaced with the construction “have to”, having the sense mentioned above.

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