International Olympiad problems

9 problems for International Olympiad practice, in Physics, Chemistry, Mathematics and Biology, each with a worked solution. Try each one on paper first, then check your answer.

All SubjectsPhysicsChemistryMathematicsBiologyPython ProgrammingStatistics & Data Science

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1.

A radio antenna stands on the edge of a cliff, at a height h = 120 m above a calm sea, and points… New

High School (11–12) · Wave OpticsOlympiad, International OlympiadStemPy Lab

Advanced

2.

Triangle ABC has sides BC = 36, CA = 29 and AB = 25… New

High School (11–12) · TrianglesOlympiad, International OlympiadStemPy Lab

Advanced

3.

A large flat coil of 500 turns and radius R = 20 cm carries a steady current of 4.0 A… New

High School (11–12) · Electromagnetic InductionOlympiad, International OlympiadStemPy Lab

Advanced

4.

Let x, y and z be real numbers with x, y, z ≥ 0 and x + y + z = 6, and put E = x²y + y²z + z²x… New

High School (11–12) · Algebraic Identities and FactorisationOlympiad, International OlympiadStemPy Lab

Advanced

5.

In a vacuum chamber there is a uniform electric field of 2.0 × 10⁴ V/m along +y and a uniform… New

High School (11–12) · Magnetic Effects of CurrentOlympiad, International OlympiadStemPy Lab

Advanced

6.

In a round-robin tournament every two teams play each other exactly once, and every match has a… New

High School (11–12) · Permutations and CombinationsOlympiad, International OlympiadStemPy Lab

Advanced

7.

Two equal capacitors, each of C = 100 µF, and two equal resistors, each of R = 10 kΩ, make a… New

High School (11–12) · Current ElectricityOlympiad, International OlympiadStemPy Lab

Advanced

8.

A 7 × 7 board has its rows numbered 0 to 6 from the top and its columns numbered 0 to 6 from the… New

High School (11–12) · Permutations and CombinationsOlympiad, International OlympiadStemPy Lab

Advanced

9.

A metal sphere of radius R = 10.0 cm stands on an insulating stand in a large empty room… New

High School (11–12) · ElectrostaticsOlympiad, International OlympiadStemPy Lab

Advanced