Со вторника я готовлюсь к экзамену.

Both с and со mean from here, but со is used for easier pronunciation before certain consonant clusters.

• вторника begins with the cluster вт-
• Saying с вторника is awkward
• So Russian normally uses со вторника

This is a pronunciation-driven choice, not a change in meaning.

Вторника is genitive singular of вторник.

You use the genitive after с / со when it means from or since in time expressions.

So:

• вторник = Tuesday
• со вторника = since Tuesday / from Tuesday onward

Compare:

• во вторник = on Tuesday
• со вторника = since Tuesday

In this sentence, it usually means since Tuesday.

Because the verb is in the present tense and describes an ongoing action, the idea is:

• the action started on Tuesday
• it is still continuing now

So the most natural English translation is often:

• I have been preparing for the exam since Tuesday

A more literal translation, from Tuesday, is possible, but since Tuesday usually sounds better in English here.

Because the verb here is готовиться, not готовить.

These are different verbs:

• готовить = to prepare something, to cook, to get something ready
• готовиться = to prepare oneself, to get ready, to study/prepare for something

So:

• Я готовлю ужин = I am preparing dinner
• Я готовлюсь к экзамену = I am preparing for the exam

The -сь ending is the reflexive marker.

-сь is a shortened form of -ся, the reflexive ending.

It often shows that the action relates back to the subject. In this case, готовиться means something like to get oneself ready or to prepare oneself.

English usually does not translate this reflexive part directly, so you just say:

• I am preparing for the exam not
• I am preparing myself for the exam in most normal contexts

Экзамену is dative singular of экзамен.

The verb готовиться normally takes the preposition к, and к requires the dative case.

So:

• готовиться к чему? = to prepare for what?
• к экзамену = for the exam

This is just a verb-preposition pattern you need to learn together:

• готовиться к + dative

Because готовиться is normally used with к.

So the standard pattern is:

• готовиться к экзамену
• готовиться к уроку
• готовиться к поездке

Using на экзамен would not fit this verb in standard Russian.

A helpful way to remember it is:

• к often has the sense of toward or in preparation for
• so готовиться к экзамену is literally something like to prepare toward the exam

Russian often uses the present tense for an action that:

• began in the past
• is still continuing now

So я готовлюсь literally looks like I am preparing, but with со вторника the full meaning becomes:

• I have been preparing since Tuesday

This is a very normal difference between Russian and English grammar.

Готовлюсь is imperfective, which is the right choice because the sentence describes an ongoing process.

The focus is on:

• the activity itself
• its duration
• the fact that it has been happening since Tuesday

A perfective verb would suggest completion or a single finished result, which does not match this sentence well.

So:

• Я готовлюсь к экзамену = I am preparing / I have been preparing
• a perfective form would change the meaning significantly

Yes. Russian often omits subject pronouns when the verb ending already makes the subject clear.

So both are possible:

• Со вторника я готовлюсь к экзамену
• Со вторника готовлюсь к экзамену

The first is slightly more explicit. The second is very natural in context.

Russian word order is flexible, and putting со вторника first emphasizes the starting point in time.

So this version highlights:

• Since Tuesday, I’ve been preparing for the exam

You could also say:

• Я готовлюсь к экзамену со вторника

That is also correct, but it sounds a bit less focused on the time expression.

It can absolutely include studying for an exam.

The phrase is broader than just memorizing material. It can mean:

• studying
• reviewing
• practicing
• generally getting ready for the exam

So in many contexts, a natural English translation is:

• I’ve been studying for the exam since Tuesday

even though the Russian literally means preparing for the exam.