The correct answers are couldn't have and must have.
Couldn't have is used for a strong negative deduction in the past—it is historically impossible for ancient Egyptians to have invented digital watches.
Must have expresses a strong positive deduction—since Professor Jones was the only person there, it is the only logical conclusion that he dropped it.
Modal verb
Must vs should vs might: the most confused modal trio. Must = strong obligation/near-certainty. Should = advice/expectation. Might = possibility. Getting these wrong changes the force of your statement: You must see a doctor (urgent) vs You should see a doctor (advice) vs You might need a doctor (maybe).
Modal verbs are auxiliaries that encode modality: ability (can), permission (may), necessity (must), advice (should), possibility (might), future (will).
Diagnostic: what meaning are you adding? Obligation → must/have to. Advice → should. Possibility → might/could. Ability → can. Future → will.
Past tense
Simple past vs past perfect: simple past puts events on the main timeline (I arrived. She left.). Past perfect marks an event as earlier than another past event (She had left before I arrived). If all events are in sequence, simple past is enough. Only use past perfect when you need to show "earlier than the main story."
The past tense has four forms encoding different temporal relationships: simple past, past progressive, past perfect, past perfect progressive.
Diagnostic: are events in sequence? → simple past is fine. Need to show one event happened before another past event? → past perfect for the earlier one.
Perfect tense
Present perfect vs simple past: I lost my keys (past: specific time, done). I have lost my keys (perfect: result matters NOW — I still don't have them). The perfect always connects past action to present relevance. If the time is specified (yesterday, in 2010) → simple past. If the result matters now → present perfect.
The perfect aspect = have + past participle. Marks completion relative to a time point. Three forms: present/past/future perfect.
Diagnostic: does the sentence mention a specific finished time (yesterday, last year, in 1999)? → simple past. Is it about the result/relevance NOW? → present perfect.
Negation
Single vs double negatives: standard English uses ONE negative per clause (I don't see anything or I see nothing). Double negatives (I don't see nothing) are grammatical in many languages and some English dialects, but are non-standard in written/formal English. This is the #1 negation trap for speakers of Spanish, Russian, and French.
Negation = not after auxiliary/modal, or do-support. Negative words (never, nobody, nothing) negate alone without adding not.
Diagnostic: count the negatives in the clause. More than one? → double negative. Fix by replacing one with a positive (anything, anyone, ever).
Verb
Verb vs noun vs adjective: nouns name things. Adjectives describe. Verbs express what happens or what IS. The test: can it take tense (walked, will walk)? Can it take -ing? Can it follow to as an infinitive (to walk)? Yes to any → verb. English often converts freely between classes (run = noun or verb), so context decides.
A verb = action/state/occurrence word. 5 forms (base, -s, past, past participle, -ing). Carries tense, aspect, mood, voice. The one required element in every sentence.
Diagnostic: does it change for tense (walk → walked)? Can you put to before it (to walk)? Does it take -ing (walking)? → verb.
B1 | Intermediate
B1 vs B2: B1 handles standard everyday communication and simple opinions. B2 handles abstract topics, sustained arguments, and nuanced register. If you can chat about your life but struggle to debate an issue or write a formal essay, you're B1.
B1 is the intermediate CEFR level: independent handling of familiar topics, second conditional, basic passive, reported speech, and linking words for cause and contrast.
Diagnostic: can you read a newspaper article on a familiar topic and summarise the argument? Comfortably → B2. Struggle with abstractions → still B1.
Medium
Medium vs Easy: Easy has one obviously correct answer and clearly wrong distractors. Medium has one correct answer but plausible distractors — you need to actually know the rule, not just guess from sound.
The Medium tag filters for A2–B1 challenges with realistic difficulty: one rule per question, plausible alternatives, everyday contexts.
Diagnostic: if you're scoring 90%+ on Easy, move here. If you're below 60% on Medium, go back to Easy for that topic. Target 70–80% accuracy for maximum learning.