Skip to content

Math Gym

Factor out board for 49 times 3 plus 51 times 3
All guides
competitionsolympiadAMCpreparation

Math Competitions: A Beginner's Roadmap

Start competition prep with the right first week.

Competition base

Factor shared structure before calculating

Many contest prompts hide a short path inside an expression that looks busy.

Factor out board for 49 times 3 plus 51 times 3
  1. 1Scan for shared factors.
  2. 2Group into a friendly sum.
  3. 3Multiply only after the structure is simple.
Roadmap use

Train structure spotting before speed drills; it pays off across algebra and number theory.

Matrix habit

Pick the least-work determinant route

Zeros and triangular structure should change the method before calculation starts.

Determinant speed tips board
  1. 1Look for a zero row, zero column, or triangle.
  2. 2Choose the shortest route.
  3. 3Check signs before arithmetic.
Competition habit

Method selection often saves more time than faster arithmetic.

Competitions reward flexible problem solving, but the base is still calm arithmetic and clean review.

Promise

Start with reusable skills: factors, primes, fractions, percentages, simple equations, and careful counting.

Worked Example

If a problem hides 49 x 3 + 51 x 3, factor first: (49 + 51) x 3 = 100 x 3 = 300.

Mistake to Avoid

Do not turn preparation into a giant checklist. A scattered pile of solved questions is weaker than one reviewed pattern.

Practice Drill

Pick one past set. Solve for 20 minutes. For every miss, write two lines: what it asked, and what move unlocked it.

Recap

The first roadmap is simple: build the base, study one topic at a time, practice short timed sets, and review honestly.