The prefix ā- exhibits quite a range of semantic functions, both basic and idiomatic. However, since de Silva’s book is a primer, not a comprehensive reference grammar, it’s no surprise that she doesn’t wish to overburden new students by describing all of them.
In the Section on Prefixative Words (Opasaggikapada) in the Padarūpasiddhi, the grammarian Buddhapiya summarised the uses of the prefix -ā as follows:
Ā iti abhimukhabhāvu’ddhakamma mariyādā’bhividhi
patti’cchāparissajana ādikammaggahaṇa nivāsa-
samīpa’vhānādīsu; abhimukhabhāve āgacchati, uddhakamme
ārohati, mariyādāyaṃ āpabbatā khettaṃ, abhividhimhi ākumāraṃ
yaso kaccāyanassa, pattiyaṃ āpattimāpanno, icchāyaṃ ākaṅkhā,
parissajane āliṅganaṃ, ādikamme ārambho, gahaṇe ādīyati
ālambati, nivāse āvasatho, samīpe āsannaṃ, avhāne
“The prefix ‘ā’ has such meanings as a state of approaching towards, an upwardly directed or overhead action, bordering, complimenting, reaching, wishing, embracing, commencing, taking, residence, propinquity and addressing.”
1. Abhimukhabhāve: āgacchati.
In the sense of ‘a state of approaching towards’, as in the verb ‘to come’.
2. Uddhakamme: ārohati.
In the sense of ‘an upwardly directed or overhead action’, as in the verb ‘to ascend or rise into the air’.
3. Mariyādāyaṃ: āpabbatā khettaṃ.
In the sense of ‘bordering’, as in ‘a mountain-bordered territory / territory-bordering mountains’.
4. Abhividhimhi: ākumāraṃ yaso kaccāyanassa.
For the sake of complimenting by highlighting something surprising or unexpected, as in, ‘Kaccāyana’s fame, even though he was yet a child’.
5. Pattiyaṃ: āpattimāpanno
In the sense of ‘reaching or arriving at’, as in ‘arriving at [= falling into] a Vinaya offence’.
6. Icchāyaṃ: ākaṅkhā,
In the sense of ‘wishing’, as in ‘desire’.
7. Parissajane: āliṅganaṃ
In the sense of ‘[literally or figuratively] embracing’, as in ‘enclasping’.
8. Ādikamme ārambho.
In the sense of ‘commencing action’, as in ‘initiating’.
9. Gahaṇe: ādīyati ālambati.
In the sense of ‘taking’, as in the verbs ‘to take’ and ‘to hold’.
10. Nivāse: āvasatho.
In the sense of ‘residence’, as in ‘refuge place’.
11. Samīpe: āsannaṃ.
In the sense of ‘propinquity’, as in ‘near’.
12. Avhāne: āmantesi.
In the sense of ‘addressing’, as in ‘he addressed’.
As for a-, Pali grammarians don’t regard this as a prefix in the strict sense (i.e. as an upasagga). Rather, it is simply one of the forms that the indeclinable particle ‘na’ can take when it occurs as the first item in a compound. Its semantic range is rather broad, coinciding fully with those of the prefixes ‘ni’ and ‘paṭi’ and partially with that of ‘vi-’.