On this solution page we will tell you where you can find the different warp zones in Super Mario Bros. 2 and thus shorten the game considerably. There are four warp zones in total.
World 1-3
In World 1-3 you have to use the magic potion to the right of the castle door. In the other dimension you have to crawl into the big jar to reach World 4.
World 3-1
In World 3-1 there is a door at the start of the level. Go through and jump down the waterfall. You end up in a cave where you can find a magic potion. Take this and carry it to the jug. Go into the jar in the other dimension to end up in World 5.
World 4-2
In World 4-2 you have to get the magic potion from the whales. Use this to jump to the jug on the small island. In the other dimension you can get to World 6 through the jar.
World 5-3
You have to start World 5-3 with Luigi. After you leave the cave from the beginning of the level via a ladder, you have to charge your jump (hold down arrow key) in order to reach the jug at the top. With the magic potion you can reach the other dimension and get to World 7 via the jug.