differentiate between be used to+ gerund and be used to +infinitive

bobak_ro

I know that we can be used to +gerund and a noun means be accustomed to it, but I can't understand these below sentence when I found in dictionary and grammar book. (actually is grammar rules)
1. Quizzes are used to determine how much material students have learned.
2. The simple present is used to express
habitual or everyday activities.
the determine and express are a verb.

DavidCrosbie

@bobak_ro

The four letters used look like a WORD, but in a way the spelling is several different WORDS or parts of TWO-WORD FORMS.

1. one-word PAST SIMPLE form — e.g. We used a new method.
2. one-word ADJECTIVE — e.g. a used car
3. part of two-word PRESENT PERFECT or PAST PERFECT form — e.g .We have/had used a new method.
4. part of two-word PASSIVE form —e.g. A new method is/was etc used.
5. part of two-word AUXILIARY VERB — e.g. I used to do it = 'I was my habit in the past to do it'.
6. part of two-word ADJECTIVE — e.g. I'm used to doing it ='I'm accustomed to doing it'.

Quizzes are used to determine how much material students have learned.
The simple present is used to express habitual or everyday activities.

Neither or these sentences are examples of [6].
Both are examples of [4] with an added PHRASE beginning with to- and expressing PURPOSE.

— Quizzes are used.
— Why?
— To determine how much material students have learned.

— The simple present is used.
— What for?
— To express habitual or everyday activities.