Choose a Math Topic to Learn — 15-year-old (ACARA Year 10, AoPS Pre-Algebra/Intro to Algebra, Beast Academy)

Pick a focused math topic for a 15-year-old with AoPS/Beast Academy background — algebra, geometry, number theory, functions, or modelling (including medieval infrastructure). Step-by-step lessons and practice available.

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Hi — before I teach a specific topic, tell me which one you want. Based on your background (ACARA Year 10, AoPS Pre-Algebra & Intro to Algebra, Beast Academy), here are good choices and what I can do for each. Pick one, or suggest your own.

  • Linear equations & systems — solving single-variable equations, two-variable systems (substitution/elimination), slope-intercept form, modeling rates. Good for algebra fluency.
  • Quadratics — factoring, completing the square, quadratic formula, graph shape and vertex. Builds toward higher algebra.
  • Exponents & radicals — laws of exponents, scientific notation, simplifying roots. Useful for working with large/small numbers and later polynomials.
  • Polynomials & factoring — polynomial arithmetic, factoring techniques, using factoring to solve equations.
  • Functions & graphs — function notation, domain/range, interpreting graphs, linear vs. quadratic behavior.
  • Number theory & modular arithmetic — divisibility, prime factors, remainders (useful for contest-style problems).
  • Geometry (plane) — similar triangles, circle basics, area/volume, coordinate geometry.
  • Problem modelling (medieval infrastructure) — turn historical/real-world scenarios into math problems (e.g., designing walls, water flow rates, resource allocation). Great if you like history and applied math.

How I can teach each topic (choose one or more formats):

  1. Step-by-step explanation with simple examples.
  2. Guided practice: try problems with hints, then full solutions.
  3. Challenge problems (AoPS-style), with solutions and strategy notes.
  4. Real-world modelling (I can make a medieval infrastructure problem to model mathematically).

Quick warm-up (diagnostic) — pick the solution method you prefer (I show steps):

Problem: Solve 2(x + 3) = 5x - 4

Step-by-step solution:

  1. Distribute on the left: 2x + 6 = 5x - 4.
  2. Collect x-terms on one side: subtract 2x from both sides: 6 = 3x - 4.
  3. Isolate 3x: add 4 to both sides: 10 = 3x.
  4. Divide by 3: x = 10/3 ≈ 3.333... .

If that felt easy, we can move to harder problems in your chosen topic. If it felt tricky, we can review prerequisite ideas first.

Tell me: which topic do you want to learn now, and which format (step-by-step, guided practice, AoPS-style challenges, or applied modelling)? Also say how fast you want to go (quick overview, normal pace, or slow with lots of practice).

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