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
A participle is a verb form that doubles as an adjective or adverb. English has two: the present participle ending in -ing (running, sitting) and the past participle (broken, gone, written). Both build tenses (is running, has gone), but they also stand alone modifying nouns (the broken window) or verbs (Exhausted, we fell asleep).
Participles look like simple parts of speech but pull double duty — most learner errors come from confusing the present participle with the gerund (also -ing but acting as a noun) or the past participle with the past tense.
Clause
A clause is a grammatical unit built around a verb — typically a subject plus a predicate (She laughed; The manager approved the budget). Clauses come in two types: independent clauses stand alone as complete sentences; dependent clauses need an independent clause to make sense (Because I overslept — incomplete on its own).
Spotting clause boundaries is the foundation of correct punctuation. Once you can see where one clause ends and another begins, comma rules, run-on sentences, and complex sentence structure stop being mysteries.
Negation
Negation in English usually places not after the auxiliary or modal verb: I am not going, She does not know, You must not go. When there's no auxiliary, you add do-support: I go → I do not go. Most combinations contract: don't, can't, won't, isn't.
The trickiest rule for many learners: double negatives are not standard English. I didn't see nothing is non-standard; the standard forms are I saw nothing or I didn't see anything. Negative words like never, nobody, nothing already carry the negation — adding not on top doubles up.
B1 | Intermediate
B1 is the intermediate level in the CEFR framework — the point where you stop relying on memorised phrases and start handling everyday English independently. At B1 you can describe experiences, explain opinions, and follow most clear standard speech on familiar topics like work, travel, and hobbies.
Grammatically, B1 means combining tenses with precision, building complex sentences, and starting to use passive voice, modal verbs for necessity and possibility, and verb patterns (gerund vs. infinitive). Knowing your level shapes what you study next: pushing too far ahead frustrates you; staying below your level wastes time.
Difficulty: Medium
The Medium difficulty tag marks questions and challenges in the middle of the difficulty range — typically suitable for A2 to B1 learners. Expect a single rule with realistic distractors, longer sentences, and contexts where you have to think before answering rather than reading off the obvious choice.
Filter by Medium when you're past the absolute basics and ready to consolidate. It's the level where most lasting progress happens — easy enough that you can finish without exhausting concentration, hard enough that getting it right means you've actually understood.