Im Test brauchen Sie nur die richtige Antwort anzukreuzen.

Im is a contraction of in dem.

• der Test = the test
• in dem Test = in the test
• contracted: im Test

This contraction is extremely common in German:

• im Haus = in dem Haus
• im Kurs = in dem Kurs

So Im Test means something like in the test or on the test, depending on how you would naturally say it in English.

Capitalized Sie is the formal word for you in German.

So:

• du = informal singular you
• ihr = informal plural you
• Sie = formal you (singular or plural)

In this sentence, Sie brauchen means you need in a polite/formal way.

The capital letter is important, because lowercase sie can also mean:

• she
• they

Because Sie here means formal you, and formal Sie always takes the same verb form as they.

So:

• ich brauche
• du brauchst
• er/sie/es braucht
• wir brauchen
• sie brauchen = they need
• Sie brauchen = formal you need

That is why the verb is brauchen, not braucht.

This is the pattern brauchen + zu + infinitive, which means to need to do something.

So:

• Sie brauchen anzukreuzen would not be correct by itself
• German needs zu with the infinitive here:
  • Sie brauchen ... anzukreuzen

In this sentence:

• brauchen = need
• anzukreuzen = to tick/check off

Together:

• Sie brauchen nur die richtige Antwort anzukreuzen = You only need to tick the correct answer

Nur means only.

Its position shows what idea it is focusing on. Here it means that the task is limited: all you have to do is tick the correct answer.

So:

• Sie brauchen nur ... anzukreuzen = you only need to ...

This is a very common position for nur in German:

• Du musst nur warten. = You only have to wait.
• Wir brauchen nur zu fragen. = We only need to ask.

Anzukreuzen is the zu-infinitive of ankreuzen.

The verb ankreuzen means:

• to tick
• to check off
• to mark with an X

It is often used in tests, forms, and questionnaires.

Examples:

• Bitte kreuzen Sie die richtige Antwort an. = Please tick the correct answer.
• Ich habe das falsche Kästchen angekreuzt. = I ticked the wrong box.

Because ankreuzen is a separable verb.

Its parts are:

• an-
  • kreuzen

When a separable verb is used with zu, the zu goes between the prefix and the verb stem:

• ankreuzen → anzukreuzen
• aufmachen → aufzumachen
• mitkommen → mitzukommen

So zu ankreuzen is not correct.

It is the direct object of ankreuzen, so it is in the accusative case.

The noun is:

• die Antwort = the answer

Antwort is feminine, and the feminine accusative article is also die, so it looks the same as the nominative:

• nominative: die richtige Antwort
• accusative: die richtige Antwort

That is why the form does not visibly change here.

Because richtig is being used as an adjective before a noun, and in German adjectives get endings.

Here we have:

• die
  • richtige
    • Antwort

After the definite article die, the adjective takes the ending -e in this form.

Compare:

• die richtige Antwort
• der richtige Test
• das richtige Wort

This is normal adjective declension after der-word articles.

In German, infinitives with zu usually go to the end of the clause.

So the sentence structure is:

• Im Test = adverbial phrase
• brauchen Sie = main verb + subject
• nur die richtige Antwort = object/material in the middle
• anzukreuzen = infinitive at the end

This final position is very common:

• Ich hoffe, dich bald zu sehen.
• Wir versuchen, pünktlich anzukommen.
• Sie brauchen nur zu warten.

Because German does not automatically put a comma before every zu-infinitive.

In this sentence, the infinitive group is closely connected to brauchen, so normally no comma is used:

• Sie brauchen nur die richtige Antwort anzukreuzen.

A comma may appear in some infinitive constructions, especially if:

• the infinitive group is long,
• it is separated for clarity,
• or it depends on a noun or pointing word such as darauf.

But here, no comma is the standard choice.

Yes, but not exactly the same.

• Sie müssen die richtige Antwort ankreuzen. = You must tick the correct answer.
• Sie brauchen nur die richtige Antwort anzukreuzen. = You only need to tick the correct answer.

Müssen sounds stronger: obligation or necessity.

Brauchen + zu + infinitive often emphasizes that this is the only thing required, especially with nur.

So in this sentence, brauchen is softer and more reassuring than müssen.

Yes, that is grammatically correct, but it is slightly different in tone.

• müssen ... ankreuzen = stronger, more direct
• brauchen ... anzukreuzen = focuses on what is required, often sounding a bit more neutral or helpful

Also note the verb form:

• with müssen, you use the plain infinitive: ankreuzen
• with brauchen, you use zu + infinitive: anzukreuzen

So both are possible, but the original sentence is a little more like All you need to do is tick the correct answer.

German often uses the singular here because it refers to the correct answer for each item/question.

So even if the whole test has many questions, the instruction can still say:

• die richtige Antwort anzukreuzen

It means something like:

• for each question, choose the correct answer

You could also see plural forms in other contexts, but the singular is perfectly natural here.