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"I don't understand how I could make so many mistakes," said Kovalainen.
Adrian Sutil will line up in P17 after a technical issue hampered his chances.
Pastor Maldonado's qualifying was hindered by traffic in Q1 which meant that he just missed out on Q2.
It was the 44th pole of the newly-crowned champion’s career and his eighth of the season.
The Spaniard is in sixth place on the grid, starting alongside the Mercedes of Lewis Hamilton.
Sergio Perez: “I’ll be really hoping to put on a great show for all my Mexican fans”
Daniel Ricciardo: "Now I’m looking forward to the race: I’m just outside the top ten, I’m on the clean side of the track and I get a free tyre choice.”
This afternoon saw Lewis Hamilton and Nico Rosberg qualify in fifth and 14th places respectively for the United States Grand Prix.
Sebastian Vettel now has 44 career Formula One pole positions.
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The E21 demonstrated strong potential using both tyre compounds. Heikki was quickly up to speed.
Dr Vijay Mallya: "The engineers have lots of data to analyse tonight to make sure we get the most from the tyres in qualifying and the race.”
The quickest driver of the day was Red Bull’s Sebastian Vettel, who set a time of 1m37.305s on the medium compound tyres halfway through FP2.
Nico Hulkenberg: "The car was ok and the performance is looking good too."
Daniil Kvyat: "...we still did 20 laps which is important mileage for me and we also managed to do some aero measurements."
Sebastian Vettel: "Ferrari looked quick this morning and McLaren could be a surprise here, and Lotus and Mercedes will be strong as normal."
Pastor Maldonado: "It was a difficult session today, particularly trying to get the most out of the tyres."
The Mercedes drivers completed a total of 118 laps today, more than a full race distance each.
Sebastian Vettel set a best time of 1m 37.305 on the medium compound tyre to finish 0.115s ahead of his Australian team mate Mark Webber on 1m37.420s.
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Sergio Perez will be hoping to build on his consecutive points finishes in India and Abu Dhabi, while Jenson Button will be looking to score points for the 13th time this year.