this is a true convert
If your faith is genuine, it will produce works.
"But he that received the seed into the good ground is he that heareth the word, and understandeth it; which also beareth fruit, and bringeth forth, some and hundredfold, some sixty, some thirty"
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this is a false convert
There are a number of people that have believed the good news of eternal salvation by grace through faith and not gone on to do good works, because of a lack of discipleship.
"When any one heareth the word of the kingdom, and understandeth it not, then cometh the wicked one, and catcheth away that which was sown in his heart. This is he which received seed by the way side.
But he that received the seed into stony places, the same is he that heareth the word, and anon with joy receiveth it; Yet hath he not root in himself, but dureth for a while: for when tribulation or persecution ariseth because of the word, by and by he is offended.
He also that received seed among the thorns is he that heareth the word; and the care of this world, and the deceitfulness of riches, choke the word, and he becometh unfruitful."