Sans calculatrice, je réponds plus lentement, mais je ne veux jamais tricher.

After sans, French often leaves out the article when the noun is being used in a general sense.

• sans calculatrice = without a calculator
• sans eau = without water
• sans problème = without a problem / without difficulty

Here, it means the person is not using any calculator, so the bare noun is natural.

If you meant a specific calculator, you could use an article or possessive:

• sans la calculatrice
• sans ma calculatrice

It is a prepositional phrase headed by sans. It gives the circumstance for the rest of the sentence: under what condition does the person answer more slowly?

So grammatically, it works a bit like an adverbial phrase in English:

• Without a calculator, ...
• In the morning, ...
• After class, ...

It sets the scene before the main clause.

Because Sans calculatrice is an introductory phrase placed before the main clause.

The comma helps separate:

• the setting/circumstance: Sans calculatrice
• the main statement: je réponds plus lentement

In short sentences, French punctuation can sometimes be flexible, but this comma is very natural and makes the sentence easier to read.

Because répondre is the infinitive, meaning the basic dictionary form, and after je you need a conjugated verb.

Present tense of répondre:

• je réponds
• tu réponds
• il/elle répond
• nous répondons
• vous répondez
• ils/elles répondent

So je réponds is the correct present-tense form for I answer / I am answering.

Usually, the final -ds in réponds is not pronounced.

So je réponds sounds roughly like:

• ray-pon

More exactly, the last vowel is nasal in French, so it is not a full English on sound.

Important point for learners:

• spelling: réponds
• pronunciation: final d and s are silent

Because lentement is an adverb, and it modifies the verb réponds.

You are describing how the person answers, so French uses an adverb:

• répondre lentement = to answer slowly
• répondre plus lentement = to answer more slowly

By contrast:

• lent / lente are adjectives
• adjectives describe nouns or pronouns, not the action itself

Examples:

• Je suis lent / lente. = I am slow.
• Je réponds lentement. = I answer slowly.

Because lentement is an adverb, and French adverbs do not agree in gender or number.

So it stays the same no matter who is doing the action:

• je réponds lentement
• elle répond lentement
• ils répondent lentement

That is different from adjectives like lent / lente / lents / lentes, which do change.

In French, adverbs that describe how an action happens often come after the verb.

So:

• je réponds lentement
• je réponds plus lentement

This is the normal position here.

French word order is not always identical to English, but with a verb + manner adverb, this placement is very common.

Because the comparison is implicit.

Plus means more, and sometimes French does not need to say exactly what the comparison is against if the context makes it clear.

Here, the idea is something like:

• more slowly than usual
• more slowly than when I use a calculator

If you wanted to make it explicit, you could add:

• je réponds plus lentement que d’habitude
• je réponds plus lentement qu’avec une calculatrice

So plus lentement can stand on its own when the comparison is understood.

Because jamais is already the negative word here.

In standard French, ne ... jamais means never:

• je ne veux jamais tricher = I never want to cheat

You do not normally add pas as well.

Common negative patterns:

• ne ... pas = not
• ne ... jamais = never
• ne ... plus = no longer / no more
• ne ... rien = nothing

So jamais replaces pas in this sentence.

Because veux is the conjugated verb, and tricher is an infinitive that depends on it.

In structures like vouloir + infinitive, French usually places the negative adverb after the conjugated verb:

• je ne veux jamais tricher
• il ne peut pas venir
• nous ne devons plus attendre

So the pattern is:

• ne + conjugated verb + negative word + infinitive

That is why jamais comes after veux, not after tricher.

Because after vouloir (to want), French normally uses another verb in the infinitive.

Pattern:

• vouloir + infinitive

Examples:

• je veux partir = I want to leave
• elle veut apprendre = she wants to learn
• nous voulons tricher = we want to cheat

So:

• je ne veux jamais tricher

is grammatically the same structure.

It would be similar, but not exactly the same.

• je ne veux jamais tricher = I never want to cheat
• je ne triche jamais = I never cheat

The first talks about desire or intention. The second talks about actual behavior.

So the original sentence is slightly more about principles or willingness: the speaker says they do not ever want to cheat.

It can mean either, depending on context, because the French present tense covers both ideas.

• I answer
• I am answering

In this sentence, it most likely has a general/habitual sense:

• when I do not have a calculator, I answer more slowly

So even though English often chooses a simple present here, French just uses the regular present tense.