To remove stubbornly stuck-on soap residue and calcium stains from the bathtub, sink and surrounding tiles, use a paste made from cream of tartar and 3-percent hydrogen peroxide. In a small container, mix just enough hydrogen peroxide into the cream of tartar to form a thick paste. Apply the paste directly to the scummy surface and use a firm-bristled brush to scrub the surface with the paste. Then rinse clean and wipe dry.
If you don't have a firm-bristled brush, improvise with an old pair of nylon stockings. Rolled into a ball or slipped over an old (but clean) cotton sock that's been rolled into a ball, those nylons become excellent non-scratch scrubbers for cleaning the sink and tub.