MathCompass

Methodology

How MathCompass measures difficulty, maps curricula to competitions, and helps you find the right mathematical path β€” from IGCSE foundations to olympiad-level problem solving.

⏱ Time

Time constraint can alter difficulty significantly and requires different strategies to cope with the problem. Faster pacing demands quicker pattern recognition.

πŸ“ Difficulty-Range

It's always good to know what sort of things you are going to be tested for. The range coefficient captures the breadth and depth of mathematical topics covered.

🧩 Difficulty-Solving

The problem itself remains a key factor. That is, how familiar you have to be with your knowledge to work out the problem β€” creativity and insight beyond rote learning.

The H-Value Formula

Combining all three coefficients into a unified difficulty score that works across competitions, curricula, and year groups.

\[ H = \frac{1}{6+\sqrt{t}} \cdot \ln(r) \cdot d \]
t = average time per problem (min)  |  r = range coefficient  |  d = problem-solving difficulty

H-Values by Competition

CompetitiontrdH

Average H-Value by Year Group

Although age is not a perfect indicator of ability, the average H-value for each year group gives a useful benchmark. An H-value means a student will find problems challenging but manageable.

YearH-Value (average student)

Example: If you're roughly at the Year 12 level (H β‰ˆ 5.0), try AMC 10 problems (H = 5.01)!

The Six-Level System

Rather than matching one course to one competition, MathCompass uses six ability levels. Each level maps to specific curricula, competitions, and university pathways.

Curriculum Systems

The four major international high school math curricula, mapped to levels and competitions.

Competitions by Country

Major mathematics competitions across the USA, UK, Canada, Australia, and international olympiads β€” all on the same H-value scale.

Find Your Perfect Match

Tell us your curriculum and level β€” get personalized competition recommendations instantly.

Try Pathfinder β†’