No.Grand PrixCircuitPoleWinner
1Monaco Monaco Stirling Moss • Cooper Jack Brabham • Cooper
2Indianapolis Indianapolis Johnny Thomson • Lesovsky Rodger Ward • Watson
3Netherlands Zandvoort Jo Bonnier • BRM Jo Bonnier • BRM
4France Reims Tony Brooks • Ferrari Tony Brooks • Ferrari
5Britain Aintree Jack Brabham • Cooper Jack Brabham • Cooper
6Germany Avus Tony Brooks • Ferrari Tony Brooks • Ferrari
7Portugal Monsanto Stirling Moss • Cooper Stirling Moss • Cooper
8Italy Monza Stirling Moss • Cooper Stirling Moss • Cooper
9USA Sebring Stirling Moss • Cooper Bruce McLaren • Cooper

Engines

2.5 L atmospheric or 0.75 L supercharged.
4.5 L atmospheric or 3.0 L supercharged engines were allowed at Indianapolis 500.

Points System

8-6-4-3-2 points for the top 5 places and 1 point for the fastest lap.
Best 5 results count toward championship.
The point is shared equally between drivers who set the same fastest lap time.
Only the points of the highest-scoring driver for each constructor at each race (including privateer entries) are counted towards the Constructors' Championship.
The points in Indianapolis 500 race are only awarded to drivers, not constructors.
The point for fastest lap is only awarded to drivers, not constructors.

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This season on Wikipedia.