raisyuu no siken no tame ni, konsyuu ha mainiti ganbarimasu.

They are doing two different jobs:

• 来週の試験 = next week’s exam
  Here, の connects 来週 and 試験.

• 試験のために = for the exam / for the sake of the exam
  Here, の connects the noun 試験 to the grammar pattern ために.

So the whole chunk means something like:

• 来週の試験 = the exam next week
• 来週の試験のために = for next week’s exam

In this sentence, ために means for, for the sake of, or for the purpose of.

So:

• 来週の試験のために = for next week’s exam

It shows the reason or goal behind the action in the second part of the sentence:

• 今週は毎日頑張ります = I’ll work hard every day this week

Together, the idea is:

• For next week’s exam, I’ll work hard every day this week.

Because when ために follows a noun, the usual pattern is:

• noun + のために

So:

• 試験のために = for the exam
• 家族のために = for my family
• 将来のために = for the future

You do not say 試験にために.

は marks 今週 as the topic:

• 今週は = as for this week / this week

It helps frame the sentence: the speaker is talking about what they will do this week.

It can also create a slight contrast:

• 来週 = next week: the exam happens then
• 今週は = this week: this is the period when I’ll work hard

So the sentence naturally separates the goal and the time of effort.

Many time expressions in Japanese do not need に, especially relative times like:

• 今日 = today
• 明日 = tomorrow
• 今週 = this week
• 来週 = next week
• 去年 = last year

So 今週は is completely natural.

Also, in this sentence は is more important than に, because the speaker is making this week the topic.

毎日 means every day, and it works adverbially here, modifying 頑張ります.

So:

• 今週は毎日頑張ります = This week, I’ll work hard every day.

A useful point: 毎日 usually does not need a particle.

Compare:

• 毎日勉強します = I study every day
• 毎日頑張ります = I’ll work hard every day

Because many expressions of frequency and some time expressions can be used directly without a particle.

So 毎日 often appears by itself:

• 毎日日本語を勉強します
• 毎日運動します
• 毎日頑張ります

This is very normal Japanese.

頑張ります is the polite non-past form of 頑張る.

In this kind of sentence, it usually means:

• I’ll do my best
• I’ll work hard
• I’ll keep at it

It does not literally mean one specific action like study. It is broader and more general. In context, it often implies studying hard, making effort, or pushing oneself.

So here, the speaker is not only saying I will study, but more like:

• I’m going to put in effort every day this week.

Japanese non-past covers both present and future, depending on context.

So 頑張ります can mean:

• I will work hard
• I work hard
• I’m going to do my best

In this sentence, because the speaker is talking about a plan for this week, it is understood as future/intention:

• This week, I’ll work hard every day.

Yes, but the meaning would shift.

• 頑張ります = I will work hard / I intend to work hard
• 頑張っています = I am working hard / I have been working hard

So:

• 今週は毎日頑張ります sounds like a plan, promise, or decision.
• 今週は毎日頑張っています sounds like a report about what is already happening.

In your original sentence, 頑張ります fits well because it sounds like the speaker is expressing determination.

Japanese often puts background information first and the main action later.

So the sentence is organized like this:

• 来週の試験のために = for next week’s exam
• 今週は = this week
• 毎日 = every day
• 頑張ります = I’ll work hard

This order is very natural in Japanese: set up the reason/purpose and time, then give the main action.

Yes, Japanese word order is somewhat flexible, as long as the particles make the relationships clear.

For example, these are possible:

• 今週は来週の試験のために毎日頑張ります。
• 来週の試験のために今週は毎日頑張ります。

Your original sentence sounds very natural. Putting 来週の試験のために first gives the reason strong emphasis.

Yes, that is the most natural interpretation.

• 来週 = next week
• 試験 = exam
• 来週の試験 = the exam next week / next week’s exam

Japanese often uses noun + の + noun where English might use either:

• next week’s exam
• the exam next week

Both capture the idea well.

Japanese often leaves out the subject when it is clear from context.

Here, since the sentence ends with 頑張ります, it naturally sounds like the speaker is talking about themselves:

• (私は) 来週の試験のために、今週は毎日頑張ります。

Including 私は is possible, but it is not necessary unless you want contrast or emphasis.

Yes. Besides marking the topic, は can give a slight contrastive feeling.

In this sentence, it subtly highlights:

• next week = the exam time
• this week = the effort time

So 今週は can feel a little like:

• as for this week, I’ll work hard every day

That contrast is very natural and fits the meaning well.

A helpful way to see it is:

• [purpose/reason] + [time/topic] + [frequency] + [action]

So here:

• 来週の試験のために = purpose/reason
• 今週は = time/topic
• 毎日 = frequency
• 頑張ります = action

This is a very common Japanese sentence structure.