Study materials
This sentence holds three plurals in a row and takes a singular verb. And it is correct.
The quality of the materials used in these products has improved.
The verb holds on to the head of the subject, not to whatever stands immediately before it. In long phrases that distance is what creates every mistake.
The head, not the nearest word
In a long subject several other nouns may sit between the head and the verb. None of them affects the agreement.
The list of approved suppliers is attached.
The quality of the materials used in these products has improved.
Parenthetical phrases in commas behave the same way, as do along with, as well as and together with. They add participants but do not change the subject.
The director, along with two managers, was present.
How to find the head
The method is mechanical: strip every prepositional phrase, relative clause and parenthesis out of the subject. What remains is the head.
The reasons for the delay in the delivery of the equipment were explained.
A special case is phrases like a number of and a lot of. Here the head is not the first word but whatever follows of.
A number of problems were reported.
The number of problems was surprising.
The mistakes everyone makes
The first is agreeing with the nearest word.
The quality of the materials have improved. → The quality of the materials has improved.
The second is pluralising the subject through along with.
The director, along with two managers, were present. → was present.
The third is confusing a number of with the number of.
The number of applications have risen. → The number of applications has risen.
All three are caught by one test. Strip the subject down and see what is left.
Try it right now
Write three English sentences with a subject of five words or more.
Then underline the head in each and check that the verb form matches it.