The correct answers are Not knowing the formula, he made an educated guess on the test and Not having memorized the formula, he made an educated guess on the test.
For negative participle clauses, place "Not" before the -ing form: Not knowing… or Not having + past participle. "Not known" is incorrect (wrong form), and "Knowing not" is ungrammatical word order in English.
Participle
If you've ever written I should have went and been corrected to should have gone — you've hit the past participle's main rule. The participle isn't an exotic form; it's the workhorse that builds perfect tenses, passive voice, and dozens of common adjectives. Get the irregular ones automatic and your tenses fall into place.
A participle is a verb form acting as an adjective or adverb. The present participle is the -ing form (running, sitting); the past participle is -ed (regular: walked) or irregular (broken, gone, written). Participles build perfect tenses, progressive tenses, and the passive.
Clause
If you've ever been told your sentence is a "run-on" or that you've used a comma where there should be a semicolon — you've hit the limits of writing without seeing clauses. Get this concept solid and most punctuation problems quietly disappear: you can finally tell a complete thought from a fragment without guessing.
A clause is a grammatical unit built around a verb, usually with a subject and a predicate. Independent clauses stand alone (I missed the bus); dependent clauses can't (Because I overslept). Combine them and you build complex sentences.
Negation
If your native language uses double negatives (I don't see nothing) — like Russian, Spanish, or French — you've probably been told this is wrong in English and not been entirely sure what the fix is. Standard English uses one negative per clause: either I saw nothing or I didn't see anything, never both. Once you internalise that single rule, your written English clears up a lot.
Negation in English uses not after an auxiliary or modal verb: I am not going. Without an auxiliary, you add do-support (I do not go). Negative words like never and nobody already negate the clause — adding not on top creates non-standard double negatives.
B1 | Intermediate
If you can hold a conversation about your weekend, explain why you're late, and follow a short news story without panicking — but still feel lost in fast or technical English — you're probably operating at B1. Knowing this matters: study material at the wrong level either bores you or burns you out, and B1 is the typical target for travel, casual work, and most everyday social English.
B1 is the intermediate level in the CEFR framework, where you handle everyday English independently and start combining ideas with complex sentences, passive voice, and modal verbs.
Difficulty: Medium
If easy questions feel too obvious but hard questions leave you guessing, you're probably ready for Medium — the level where most real learning happens. It pushes just enough to expose the rules you don't quite have yet, without burying you in edge cases. This is where steady fluency is built, one well-aimed challenge at a time.
The Medium difficulty tag marks middle-range challenges — typically A2 to B1. One rule per question, realistic distractors, and contexts that require active thought rather than instant recognition.