With queens on the board, checks decide almost everything. A queen stops a pawn on the seventh rank only with help from its king, queen against rook wins by separating the rook from its king, and queen and pawn endings are often drawn by perpetual check.
Verdict Draw. The pawn is a bishop pawn and the black king is close.
Stop a pawn on the seventh rank with the queen, and know when the queen cannot win.
The black pawn on f2 is a bishop pawn, one step from queening, and the black king on g1 stands next to it. The white king is too far away to help. Each queen check only sends the king to the corner, and if the queen takes the pawn there, it is stalemate. With a central pawn the queen wins.
1. ♕g6+ ♚h2 2. ♕b1 ♚g2 3. ♕e4+ ♚g1
Taking the pawn at the wrong moment. After 1. ♕g8+ ♚h2 2. ♕g3+ ♚h1 3. ♕xf2?? it is stalemate.
White to move. Win or draw? (The pawn is now a central pawn.)
White wins. A central pawn cannot be saved by stalemate tricks, and the queen wins the pawn with check.
1. ♕d1+ ♚a2 2. ♕xd2+ ♚b3 3. ♕d3+ ♚b4 4. ♔f6 ♚c5 5. ♔e7 ♚c6 6. ♕c4+ ♚b6 7. ♔d7 ♚a5 8. ♕b3 ♚a6
♕d1+ drives the king away from the pawn, and ♕xd2+ wins it with check. Queen and king then mate.
Copy the position into any board or engine to practice it:
4Q3/8/5K2/8/8/8/5p2/6k1 w - - 0 1
Verdict White wins. A check separates the rook from its king.
Win the rook with a check that makes its king leave, or mate the king. Queen against rook is usually a win, but it takes many accurate moves.
The rook on e7 is protected by its king on f7, but the white king on d8 attacks it. The check ♕f5+ forces the black king away, the rook loses its protector, and ♔xe7 wins it. With queen and king against a bare king, mate follows.
1. ♕f5+ ♚g7 2. ♔xe7 ♚h8 3. ♔f6 ♚g8 4. ♕g4+ ♚f8 5. ♕c8#
Chasing the rook with the queen while the king is far away. The rook stays protected by its king, and the queen only gives checks that lead nowhere.
White to move. Find the winning check.
White wins. The same position mirrored: ♕c5+ separates the rook from its king.
1. ♕c5+ ♚b7 2. ♔xd7 ♚b8 3. ♕b4+ ♚a8 4. ♔c7 ♚a7 5. ♕a4#
After ♕c5+ ♚b7 the white king takes the rook with ♔xd7, and the queen mates three moves later.
Copy the position into any board or engine to practice it:
3K4/4rk2/8/8/8/3Q4/8/8 w - - 0 1
Verdict Draw by perpetual check.
Know that queen endings are often drawn by perpetual check, even against an advanced pawn, and use a safe king to win them.
White has a pawn on e7, one step from queening, but the white king stands exposed on h4. The black queen checks without end, and White cannot push the pawn. With the white king on g5, out of reach of the checks, White wins.
1... ♛f6+ 2. ♔h5 ♛f5+ 3. ♔h6 ♛f6+ 4. ♔h5 ♛f5+ 5. ♔h6 ♛f6+
Pushing the pawn with the king exposed. The checks never stop, and the pawn on the seventh rank cannot queen.
Black to move. Win or draw?
Draw. Black checks and then takes the h-pawn.
1... ♛a5+ 2. ♔f2 ♛f5+ 3. ♔g3 ♛xh7 4. ♕e6 ♚b8
After ... ♛xh7 the pawn is gone and only the queens remain, so the position is a draw.
Copy the position into any board or engine to practice it:
8/1k2P3/2q5/8/7K/8/8/4Q3 b - - 0 1