Diagram 1, Both just finished a joseki and Black move-5 protects its corner and White move-6 kicks intended to aim for A later and B jumps. In this diagram, Black has the choice of tenuki to allow White to A in exchange of a bigger sente.
Diagram 2, If Black protects at move-1, White simply jumps at move-2. Black has sente.
Diagram 3, Black move-1 is correct and White must connects move-2 because atari at A and Black B helps Black thicken. White invades move-6 after Black gote move-5. So how should Black move next?
Diagram 4, If Black covers at move-1, White can hane move-2 and tesuji move-4 and move-6. Black A atari next result KO, If Black covers at move-2, White lives the corner at A.
Diagram 5, If Black tries to avoid KO from Diagram 4, the result is terrible for Black.
Diagram 6, Black move-1 is the correct answer here. White atari move-2 and ended at move-8 is a capturing race. Black next move is crucial.
Diagram 7, Black move-1 here is the correct killing move, White is short of liberty.
Diagram 8, White pincer at move-1, Black must extends at move-2. If Black connects at A. White can connects at move-2 which is really bad for Black.
Diagram 9, White connects at move-3 and ended up at move-5. Black to kill White next.
Diagram 10, Black point move-1 then thrust at move-3 is the key move. White move-6 is not KO. White is dead.
Diagram 11, to be informed that if Black starting joseki is at forth-line move-1, White can move-2 stays alive.
Note: Xinwen concerns about Kyu-Players life and death; thus all this elementary lectures provide certain amount of real-game life and death. Hope you all like it.