بعد أن أكتب الواجب، أقرأ صفحة أخرى من القصة.

بعد أن means after when it introduces a whole clause.

So:

• بعد أن أكتب الواجب = after I write the homework / after I do my homework
• أقرأ صفحة أخرى من القصة = I read another page from the story

A useful way to think about it is:

• بعد
  • noun = after
• بعد أن
  • verb clause = after (someone does something)

So بعد أن is very common when you want to say after I..., after he..., after they..., etc.

Here أن introduces the verb clause after بعد.

It also affects the grammar of the following verb: it puts the imperfect verb into the subjunctive.

So:

• basic form: أكتبُ = I write / I am writing
• after أن: أكتبَ

In normal unvoweled Arabic writing, you usually see both written the same way as أكتب, so the difference is often invisible unless full vowel marks are added.

In Arabic, the imperfect verb form (often called the present tense) is used for several ideas, not just present time. It can express:

• present actions
• future actions
• repeated or habitual actions
• actions whose time is understood from context

In this sentence, the sequence is made clear by بعد أن:

• first: أكتب الواجب
• then: أقرأ صفحة أخرى

So Arabic does not need a separate future form here. The context already tells you the order.

No, not necessarily.

أقرأ by itself is fine here because the time relationship is already clear from بعد أن.

This sentence can sound like:

• a routine: After I do my homework, I read another page
• a near-future plan: After I do my homework, I’ll read another page

If you want to make the future more explicit, you can say:

• بعد أن أكتب الواجب، سأقرأ صفحة أخرى من القصة.

That would mean more clearly: After I write the homework, I will read another page from the story.

The prefix أ at the beginning of the imperfect verb usually marks first person singular in MSA.

So:

• أكتب = I write
• أقرأ = I read

Compare:

• يكتب = he writes
• تكتب = she writes or you write
• نكتب = we write

So the أ is the clue that the subject is I.

Both are possible, but they mean slightly different things in emphasis.

• الواجب = the homework / the assignment
• واجبي = my homework

In many Arabic contexts, الواجب is enough when it is already obvious whose homework is meant. Arabic often uses the definite form where English might prefer a possessive.

So:

• أكتب الواجب can naturally mean I do/write the homework
• أكتب واجبي makes my more explicit

Both are understandable, but الواجب is very normal.

In Arabic, adjectives usually come after the noun they describe.

So:

• صفحة أخرى = another page

Also, the adjective must agree with the noun in gender, number, definiteness, and case.

Here:

• صفحة is feminine singular
• so the adjective must also be feminine singular
• that is why we get أخرى

A few points:

• صفحة is feminine
• أخرى is the feminine form of آخر
• both are indefinite here, so neither takes ال

So Arabic says:

• صفحة أخرى = another page / one more page

not the other way around.

Here أخرى means another or one more.

So صفحة أخرى means:

• another page
• one more page

It does not mean the other page. If you wanted the other page, the structure would be different, for example:

• الصفحة الأخرى = the other page

So the lack of ال matters here:

• صفحة أخرى = another page
• الصفحة الأخرى = the other page

من here has a partitive sense: a page from the story.

So:

• صفحة أخرى من القصة = another page from the story

This is a very natural way in Arabic to show that the page is part of a larger text.

It is similar to saying:

• a chapter from the book
• a scene from the film

Using من makes the relationship clear: the page belongs to, or comes from, the story.

A fully vowelled version is:

بَعْدَ أَنْ أَكْتُبَ الوَاجِبَ، أَقْرَأُ صَفْحَةً أُخْرَى مِنَ القِصَّةِ.

A few useful things to notice:

• بَعْدَ ends in -a
• أَكْتُبَ has the subjunctive ending because of أن
• الوَاجِبَ is in the accusative here
• أَقْرَأُ keeps the indicative ending
• صَفْحَةً is indefinite and accusative
• القِصَّةِ ends in -i after من

In everyday Arabic writing, most of these vowel marks are normally omitted.