p is a machine, not a letter
Grade 11 taught you to read a pH. Grade 12 asks what the symbol MEANS, because the same move is about to be played on four other quantities. Lowercase p is an operator: it takes the base-ten logarithm of whatever follows and flips the sign. So — read aloud: pH equals negative log of H-plus. Naming the parts: is the hydrogen-ion concentration in mol/L (the square brackets are read the concentration of), and pH is a pure number — the logarithm ate the units on the way through. The hydroxide side gets the identical treatment: , where is the hydroxide-ion concentration, also in mol/L.
Why two scales chained together? Because water quietly ionizes itself, and the product of the two ion concentrations is fixed: at 25 °C, where is the ion product of water, a pure number. Run p over both sides — the log of a product is a sum — and the whole of grade 11's see-saw drops out as a theorem: . It was never a rule to memorise. It is wearing a p.