At the beginning of her sports career, Kučerová was an alpine ski racer . She took part in FIS races from November 2004 and won a total of eleven times at this level in the following five years. At three Junior World Championships she did not get beyond a 37th place and in the European Cup she never placed in the points. She took part in the 2009 World Championships in Val-d'Isère , where she was eliminated in the first run of the slalom.
Kučerová turned to ski cross. She made her debut in the Freestyle World Cup on January 5, 2010 and finished 35th in St. Johann in Tirol . She won her first World Cup points two months later with 19th place in Branäs . Her breakthrough to the top of the world came on December 18, 2010 in San Candido , where she came third. In the course of the 2010/11 season, two more top 10 placements were added so far.
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