Attached to a verb stem to show that an action has been started but not finished, or is just about to happen. かける conjugates as a verb (かけた, かけている), かけの modifies a noun ('half-eaten X'), and かけだ ends a sentence. It captures a 'midway / on the verge of' state.
[Verb ます-stem] + かける/かけの(+Noun)/かけだ
食べかけのパンをテーブルに置いたままだ。
Tabekake no pan o tēburu ni oita mama da.
The half-eaten bread is still left on the table.
食べ (stem of 食べる) + かけの modifies パン = 'half-eaten bread.'
彼は何か言いかけて、やめた。
Kare wa nanika iikakete, yameta.
He started to say something, then stopped.
言い (stem of 言う) + かけて = 'was about to / began to say.'
この本はまだ読みかけです。
Kono hon wa mada yomikake desu.
I'm still in the middle of reading this book.
読み (stem of 読む) + かけです = 'partway through reading.'
• かける = verb ('start to / be about to'), かけの = noun-modifier, かけだ = sentence-ender. • Also expresses 'on the verge of' with verbs like 死にかける (nearly die), 消えかける (about to go out). • Register: neutral; common in everyday speech and writing.
The JLPT rarely asks whether you recognise a pattern — it asks which of several similar patterns fits. These are the ones ~かける/かけの is tested against.
つつある means an action is steadily progressing toward completion ('in the process of'); かける emphasizes something begun but interrupted or only half-done.
~ようとするところだ frames an action about to start at a precise moment; かける describes a general half-finished/on-the-verge state, and can modify nouns (かけの).
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