The pair qualified for their first-ever Olympic final in ninth place and will now seek to improve on their tenth place finish at last year's World Championships in Shanghai.
"It was a good swim but there are still a few things to improve on and we need to get them fixed," said former Hurst Lodge school pupil Randall.
"Some of the technical aspects weren't quite perfect, there were a few things that were a little bit off and hopefully we can correct those with a bit more work."
Randall and Federici have one of the most demanding training schedules of any British athlete at the Games, spending 45 hours a week training - much of it in the pool at their training base in Hampshire.
While most taper - or ease up - before major championships, they increase their training intensity, ramping up the hours in a sport where endless repetition is the only key to success.
"We train eight hours a day in the water working on these routines and this is the one we want to get absolutely right," added Randall, 23.
"The last four years have been lots of hard, hard work and many hours training. We've gone from being 22nd in the world five years ago to hopefully being in the top eight or nine here.
"Synchro is a very judged sport, we can only do our best performance and hope that the judges reward us with good marks.
"Our reputation as a country is improving. We'd still like higher marks and there are countries that we think we can move ahead of in the future.
"But it's great the public are seeing our sport and seeing how hard it is."
The final will see the top 12 pairs compete again and repeat the same free program they performed yesterday, with the score added to their performance from the technical routine.
Russia's Natalia Ishchenko, a 15-time world champion, and Svetlana Romashina looked a lock for gold with China and Spain expected to contest the other podium positions.
Radall's younger sister, Asha, will be involved in the synchro team event later in the week.
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