{
  "version": 1,
  "note": "Sample A-Level Jeopardy boards. Two courses: ial (Edexcel IAL, 6 units) and uk (Edexcel UK 9MA0). Same shape as /jeopardy_boards.json. Back-fill via the Gemini pipeline once real content lands.",
  "tiers": [100, 200, 300, 400, 500],
  "courses": {
    "ial": {
      "label": "IAL (Edexcel International A-Level)",
      "categories": [
        {
          "title": "Algebra & Series (P1/P2)",
          "cells": [
            { "q": "Solve $2x + 5 = 13$.",                                                    "a": "x = 4" },
            { "q": "Expand $(x + 3)(x - 5)$.",                                                "a": "x^2 - 2x - 15" },
            { "q": "Sum of the first 20 terms of an AP with $a = 3$, $d = 4$.",              "a": "820" },
            { "q": "Solve $\\log_3(x) - \\log_3(2) = 4$.",                                    "a": "x = 162" },
            { "q": "Sum to infinity of a GP with $a = 8$, $r = 1/4$.",                       "a": "32/3" }
          ]
        },
        {
          "title": "Coordinate Geometry (P1)",
          "cells": [
            { "q": "Midpoint of $(2, 3)$ and $(8, 11)$.",                                     "a": "(5, 7)" },
            { "q": "Gradient of the line through $(-1, 2)$ and $(3, 10)$.",                  "a": "2" },
            { "q": "Equation of line through $(4, 5)$ perpendicular to $y = 2x + 1$.",       "a": "y = -1/2 x + 7" },
            { "q": "Distance between $(1, 2)$ and $(4, 6)$.",                                 "a": "5" },
            { "q": "Equation of circle centre $(3, -2)$ radius $\\sqrt{13}$.",                "a": "(x-3)^2 + (y+2)^2 = 13" }
          ]
        },
        {
          "title": "Calculus (P1/P3)",
          "cells": [
            { "q": "Differentiate $y = 4x^3$.",                                                "a": "12x^2" },
            { "q": "$\\int (6x^2 + 2)\\,dx =$ ?",                                              "a": "2x^3 + 2x + C" },
            { "q": "Stationary point of $y = x^2 - 6x + 5$.",                                  "a": "(3, -4)" },
            { "q": "$\\dfrac{d}{dx}\\left[e^{3x}\\right] =$ ?",                                "a": "3 e^{3x}" },
            { "q": "$\\int_0^{\\pi} \\sin x\\,dx =$ ?",                                        "a": "2" }
          ]
        },
        {
          "title": "Trigonometry (P1/P2)",
          "cells": [
            { "q": "Value of $\\sin 30°$.",                                                    "a": "1/2" },
            { "q": "$\\cos^2\\theta + \\sin^2\\theta =$ ?",                                    "a": "1" },
            { "q": "Convert $\\pi/6$ rad to degrees.",                                          "a": "30°" },
            { "q": "Arc length: radius 5, angle 1.2 rad.",                                     "a": "6" },
            { "q": "Solve $2\\cos\\theta = \\sqrt{3}$ for $0 \\le \\theta \\le 2\\pi$.",       "a": "π/6, 11π/6" }
          ]
        },
        {
          "title": "Stats & Mechanics (S1/M1)",
          "cells": [
            { "q": "Mean of $2, 4, 6, 8, 10$.",                                                "a": "6" },
            { "q": "$X \\sim N(20, 3^2)$. $z$ for $X = 26$?",                                 "a": "2" },
            { "q": "P(A) = 0.3, P(B) = 0.5, independent. P(A and B)?",                        "a": "0.15" },
            { "q": "SUVAT: $u = 0$, $a = 4$, $t = 3$. Displacement $s$?",                     "a": "18 m" },
            { "q": "Force 12 N on mass 3 kg. Acceleration?",                                   "a": "4 m/s^2" }
          ]
        }
      ]
    },
    "uk": {
      "label": "UK 9MA0 (Edexcel A-Level Maths)",
      "categories": [
        {
          "title": "Pure Algebra (Y1)",
          "cells": [
            { "q": "Simplify $\\dfrac{x^2 - 9}{x - 3}$.",                                       "a": "x + 3" },
            { "q": "Solve $|2x - 3| = 5$.",                                                   "a": "x = 4, x = -1" },
            { "q": "Discriminant of $2x^2 + 3x + 1$.",                                        "a": "1" },
            { "q": "Coefficient of $x^3$ in $(1 + x)^{10}$.",                                 "a": "120" },
            { "q": "Solve $3^{x+1} = 27$.",                                                    "a": "x = 2" }
          ]
        },
        {
          "title": "Calculus (Y1/Y2)",
          "cells": [
            { "q": "Differentiate $y = x^5$.",                                                 "a": "5x^4" },
            { "q": "$\\int 4x\\,dx =$ ?",                                                      "a": "2x^2 + C" },
            { "q": "Chain rule: $\\dfrac{d}{dx}\\left[(3x+1)^4\\right]$.",                     "a": "12(3x+1)^3" },
            { "q": "Product rule: $\\dfrac{d}{dx}[x^2 \\ln x]$.",                              "a": "2x ln x + x" },
            { "q": "$\\int \\dfrac{1}{x}\\,dx =$ ?",                                           "a": "ln|x| + C" }
          ]
        },
        {
          "title": "Trigonometry & Radians",
          "cells": [
            { "q": "Value of $\\tan 45°$.",                                                    "a": "1" },
            { "q": "Solve $\\sin\\theta = 0.5$ for $0 \\le \\theta < 360°$.",                  "a": "30°, 150°" },
            { "q": "Sector area: radius 4, angle $\\pi/3$ rad.",                               "a": "8π/3" },
            { "q": "$\\sec^2\\theta - \\tan^2\\theta =$ ?",                                    "a": "1" },
            { "q": "Solve $2\\sin^2\\theta - \\sin\\theta - 1 = 0$ for $0 \\le \\theta < 2\\pi$.", "a": "π/2, 7π/6, 11π/6" }
          ]
        },
        {
          "title": "Statistics (Y1/Y2)",
          "cells": [
            { "q": "Mean of $5, 8, 12, 15, 20$.",                                              "a": "12" },
            { "q": "$X \\sim B(10, 0.3)$. $E(X)$?",                                            "a": "3" },
            { "q": "Median of $3, 7, 8, 12, 15, 20$.",                                         "a": "10" },
            { "q": "$X \\sim N(100, 16)$. $P(X < 108)$ (approx to 3 d.p.).",                   "a": "0.977" },
            { "q": "In a hypothesis test, $H_0: p = 0.5$ vs $H_1: p > 0.5$. This test is:",   "a": "one-tailed" }
          ]
        },
        {
          "title": "Mechanics (Y1/Y2)",
          "cells": [
            { "q": "SUVAT: $u = 10$, $v = 0$, $a = -2$. Time $t$?",                            "a": "5 s" },
            { "q": "Weight of a 5 kg mass on Earth (use $g = 9.8$).",                          "a": "49 N" },
            { "q": "Two forces: 6 N east, 8 N north. Resultant magnitude?",                    "a": "10 N" },
            { "q": "Moment of a 20 N force at 3 m perpendicular distance.",                     "a": "60 N·m" },
            { "q": "Friction coefficient 0.4, mass 2 kg on horizontal surface. Max friction (use $g = 10$).", "a": "8 N" }
          ]
        }
      ]
    }
  }
}