Students taking science GCSEs in Wales, England and Northern Ireland are going to need more maths, regulators say.
Responding to scientists' complaints, regulators Ofqual, DCells and Ccea say greater maths knowledge, understanding and skills will be needed.
They have set out what should be in each GCSE: science, additional science, physics, chemistry and biology.
The awarding bodies - who devise the actual courses of study and exams - must come up with suitable materials.
Ofqual: GCSE sciences criteria
The regulators said they would consult further on the specific maths requirements for each of the subjects.
But they would have to be satisfied these were "requiring candidates to demonstrate a greater degree of mathematical knowledge, understanding and skills than is typically used in current GCSE sciences examinations".
These latest changes to secondary school science follow an Ofqual report that was critical of the way standards had fallen.
Ofqual made exam boards take immediate action after finding there was "clearly a cause for concern" in science GCSEs.
Among the criticisms of the current content, the Royal Society of Chemistry said entire exam papers contained no maths and some questions no science.
It said a new, more independent regulator with more clout was needed to prevent standards from such "dumbing down".
The assistant director of the lobby group the Campaign for Science and Engineering (Case), Dr Hilary Leevers, said: "Awarding bodies compete for custom among schools, and the schools, in turn, compete in the league tables, so there has been a driving down of standards.
"Ofqual's intervention, with the help of many science and mathematics organisations, should improve standards.
"New mathematical content in science GCSEs will help give future scientists and engineers the skills they will need, as well as boosting the rigour of exams."
Dr Leevers also said all students should have the chance to study for these qualifications - as many state schools do not offer separate biology, chemistry and physics courses.
Most state schools do the basic science GCSE. The regulators' new criteria for this do not include, for example, the chemical properties of elements or periodic table, photosynthesis or Newton's laws of motion.
Those are reserved for the "additional science" GCSE, which a majority of pupils in state schools do also take.
The separate GCSEs in physics, chemistry and biological sciences are the norm in grammar schools and independent schools.
The Tories have called it "truly shocking" that last year there were whole areas of England where not a single child had the opportunity to study them.
The government has now made it an entitlement for pupils who are making sufficient progress to be able to study the three sciences, so take-up may rise.
But it has not placed any equivalent obligation on schools to offer the three subjects.
Last month Case called on politicians to impose a statutory duty on all schools to offer interested and able students the three separate biology, physics and chemistry GCSEs.