1. He is a good swimmer.

= He swims well.

2. He is a fast learner.

= He learns fast.

3. He is a careful examiner.

= He examines carefully.

4. He is a slow worker.

= He works slowly.

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Are the expressions the same and correct?

Yes, they all are -- the same and correct!

Nice work.

Yes, the expressions you provided are both the same and correct. In each sentence, the adjective is describing a noun (he), and the phrase following "is a" indicates the quality or characteristic of that noun. However, to make the sentences more concise and natural, you can use the alternative forms, where the adverb is used to modify the verb directly.