Add a few drops of HCl to the sample in a test tube, connect this test tube to a test tube of limewater, and if carbonate ions are present, carbon dioxide will be produced causing the limewater to turn cloudy
Add HCl to remove any CO3^2- ions, then add a couple of drops of barium chloride, and if sulfate ions are present a white precipitate of barium sulfate will form
Add a couple of drops of nitric acid to react with any carbonate ions, then add a couple of drops of silver nitrate and observe the colour of the precipitate