How do I level out my patio?

There are two different levels of concrete out my back door. One used to be for a room that has since been torn down the other was a patio area. There is anywhere from a 1/2 inch to 1 inch difference. I would like it all one level but have been told if I pour concrete it will need to be deeper than the 1inch to make it strong. I also want to make sure there is a slope so the water does not pool up at the back door. There is about a 2 1/2 to 3 inch drop from the back door to the concrete slab.

Thank you

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