Baada ya somo, tulirudia mifano yenye maneno mapya ili msisitizo wa mwalimu ubaki vichwani mwetu.

Baada is originally a noun meaning after / the time after, and it normally takes the associative ya, giving the fixed pattern baada ya + noun = after (the) X.

• baada ya somo = after the lesson
• baada ya kazi = after work
• baada ya chakula = after the meal

The ya here agrees with baada, not with somo.
Even though somo is class 5 (which on its own might take la: somo la Kiswahili), in this construction we are really saying something like the after of the lesson, so the link is baada ya.

So:

• baada ya somo = correct, idiomatic
• baada la somo / baada wa somo = not used

You can, but the meaning shifts slightly:

• Baada ya somo – After the lesson (class period)
  Focuses on the event called a lesson, a class session.
• Baada ya kusoma – After studying / after reading
  Focuses on the activity of studying or reading, not the formal lesson.

In your sentence, Baada ya somo fits better because you are referring to what happened after a classroom lesson set by a teacher, not just any act of studying.

Tulirudia is the simple past tense of kurudia (to repeat, to do again).

Breakdown:

• tu- = we (subject prefix, 1st person plural)
• -li- = past tense marker
• -rudia = verb root rudi (return / do again) + -a final vowel used for the infinitive/finite verb

So:

• tulirudia = we repeated / we went over again

Other relevant forms:

• ninarudia – I am repeating
• tutarudia – we will repeat
• rudia tena – repeat again (emphasizes “again” with tena)

Kurudia by itself already means to repeat or to do again:

• tulirudia mifano – we repeated the examples / we went over the examples again

Adding tena simply emphasizes the idea of “again”:

• tulirudia tena mifano – we repeated the examples again (once more)

In many contexts kurudia alone is enough to convey repeat, so tena is optional and used mainly for extra emphasis.

Mifano is the plural of mfano (example).

• mfano – class 3, singular
• mifano – class 4, plural

This matters because adjectives and certain relative words (like yenye) must agree with the noun’s class.

That’s why we see:

• mifano yenye maneno mapya
  yenye agrees with class 4 (mifano) and means which have / with.

If it were singular:

• mfano wenye neno jipya – an example with a new word
  Here wenye agrees with mfano (class 3).

Yenye is a class‑agreeing form of an adjective/relative that means having or with.

Structure:

• mifano – examples
• yenye – which have / that have / with (agreeing with mifano)
• maneno mapya – new words

So mifano yenye maneno mapya = examples that have new words or more naturally examples with new words.

You could think of yenye as functioning like:

• English: examples *with new words / examples that have new words*

Yes, you can say both, and both are correct.

• mifano yenye maneno mapya
  Very natural, compact, everyday way to say examples with new words.

• mifano iliyo na maneno mapya
  Literally examples that are with new words or examples which have new words.
  A bit more explicit and slightly more formal or bookish, but still common.

Meaning-wise they are effectively the same, with yenye as the shorter, common choice in speech.

Ili introduces a purpose clause: it corresponds to so that, in order that, or simply so in English.

• … tulirudia mifano … ili msisitizo wa mwalimu ubaki vichwani mwetu.
  = … we repeated the examples … so that the teacher’s emphasis would remain in our heads.

After ili, Swahili normally uses the subjunctive form of the verb to express intention or desired outcome.

Here:

• verb root: baki (stay, remain)
• subject: msisitizo → class 3 subject prefix u-
• subjunctive ending: -i instead of normal -a

So we get u-bak-i → ubaki.

Pattern:
ili + [subject prefix] + verb root + -i

Because after ili (when it means so that / in order that), Swahili normally switches to the subjunctive, which:

• drops the tense marker (no -na-, -ta-, -li-, etc.)
• changes the final -a to -i

So:

• Indicative present: msisitizo unabaki vichwani mwetu – the emphasis remains in our heads
• Purpose/subjunctive: ili msisitizo ubaki vichwani mwetu – so that the emphasis may remain in our heads

That’s why it is ubaki, not unabaki or utabaki, in this sentence.

The u- is the subject prefix for the noun msisitizo.

• msisitizo (emphasis) is in noun class 3.
• Class 3 subject prefix is u- for most verbs in the present/subjunctive.

So:

• msisitizo ubaki – let the emphasis remain
• msisitizo unabaki – the emphasis remains

If the subject were plural or a different noun class, the subject prefix would change accordingly.

Msisitizo wa mwalimu means the teacher’s emphasis (the emphasis given by the teacher).

The element wa/ya/la/cha, etc., is the associative/possessive marker, and it normally agrees with the first noun (the one possessed or described).

Here:

• msisitizo – class 3 → associative wa
• mwalimu – teacher (the one who “owns” or gives the emphasis)

So:

• msisitizo wa mwalimu – the teacher’s emphasis

If the head noun changed class, the marker would change:

• mfano wa mwalimu – the teacher’s example (class 3)
• somo la mwalimu – the teacher’s lesson (class 5)
• mifano ya mwalimu – the teacher’s examples (class 4 plural)

Base forms:

• kichwa – head (class 7)
• vichwa – heads (class 8)

Then:

• vichwani = vichwa
  • -ni → in/on the heads (locative form)
• mwetu = our

So vichwani mwetu literally means in our heads.

Contrast:

• vichwa vyetu – our heads (as simple possession, body part)
• vichwani mwetu – in our heads (emphasizes location, often metaphorical: in our minds / in our memory)

In this sentence, vichwani mwetu is appropriate because you’re talking about the emphasis remaining in your minds, not just referring to your heads as objects.

Yes, katika vichwa vyetu is also grammatically correct and understandable:

• ubaki katika vichwa vyetu – remain in our heads

Differences:

• vichwani mwetu – more compact and idiomatic; the locative -ni is very common and sounds very natural here.
• katika vichwa vyetu – slightly more explicit/neutral; using the preposition katika.

Both are acceptable, but vichwani mwetu is particularly natural in the sense of stay in our minds.