Questions & Answers about Bu testi çözer misin?
Why use the aorist tense (-er) here when the English translation says 'Will you'?
While the aorist tense is used for general facts and habits, asking a question in the 2nd person aorist (like çözer misin?) is the standard way to make a polite request in Turkish. It's the equivalent of asking 'Would you...?' or 'Will you...?' in English.
Why is there an -i at the end of testi?
The word test takes the accusative case ending -i because it is the specific direct object of the verb. Whenever you use a demonstrative word like bu (this), the object becomes specific, so bu test must become bu testi.
How do we know to use -er for the aorist suffix on çöz- instead of -ür?
For most verbs with only one syllable, the aorist suffix follows 2-way vowel harmony, meaning it will be either -ar or -er. Since çöz- has the vowel ö, it takes -er. Only a specific list of exception single-syllable verbs take the 4-way endings like -ür.
Why does the personal ending -sin attach to mi instead of the verb?