{
 "version": 1,
 "note": "IGCSE Jeopardy boards, generated by scripts/build-igcse-jeopardy.js from verified repo content only (4MA1 worked examples and verified 4MA1 bank questions; the verified Cambridge 0580 bank). Each cell's src is its question id. Do not edit by hand.",
 "tiers": [
  100,
  200,
  300,
  400,
  500
 ],
 "courses": {
  "4ma1": {
   "label": "Edexcel IGCSE 4MA1 · Higher",
   "categories": [
    {
     "title": "Number",
     "cells": [
      {
       "q": "Write \\(0.\\dot{4}\\) as a fraction.",
       "a": "\\(\\tfrac{4}{9}\\)",
       "src": "u1l17-gap-q01"
      },
      {
       "q": "Expand \\((2+\\sqrt{7})^2\\). Give your answer in the form \\(a+b\\sqrt{7}\\), where \\(a\\) and \\(b\\) are integers.",
       "a": "\\(11+4\\sqrt{7}\\)",
       "src": "u1l16-gap-q05"
      },
      {
       "q": "A price rises from £64 to £80. Find the percentage increase.",
       "a": "25%",
       "src": "igcse-we-u1l12"
      },
      {
       "q": "Write \\(2.1\\dot{3}\\dot{6}\\) as an improper fraction in its simplest form.",
       "a": "\\(\\tfrac{47}{22}\\)",
       "src": "u1l17-gap-q06"
      },
      {
       "q": "A rectangle has area \\((7-\\sqrt{5})\\,\\text{cm}^2\\). The length of the rectangle is \\((4+\\sqrt{5})\\) cm. Find the width of the rectangle. Give your answer in the form \\((a+b\\sqrt{5})\\) cm, where \\(a\\) and \\(b\\) are integers.",
       "a": "\\(3-\\sqrt{5}\\) cm",
       "src": "u1l16-gap-q09"
      }
     ]
    },
    {
     "title": "Algebra",
     "cells": [
      {
       "q": "Factorise \\(x^2 - 81\\).",
       "a": "\\((x+9)(x-9)\\)",
       "src": "u3l19-gap-q03"
      },
      {
       "q": "Expand \\((x+1)(x+2)(x+3)\\).",
       "a": "\\(x^3+6x^2+11x+6\\)",
       "src": "igcse-we-u2l13"
      },
      {
       "q": "Find the sum of the first 25 terms of \\(5+8+11+\\cdots\\).",
       "a": "1025",
       "src": "igcse-we-u3l21"
      },
      {
       "q": "Find the minimum value of \\(x^2+3x+5\\) and the value of \\(x\\) at which it occurs.",
       "a": "Minimum value \\(\\tfrac{11}{4}\\) when \\(x=-\\tfrac{3}{2}\\)",
       "src": "u3l22-gap-q07"
      },
      {
       "q": "The sum of the first 10 terms of an arithmetic series is 185. The sum of the first 20 terms of the same series is 670. Find the first term and the common difference.",
       "a": "first term 5, common difference 3",
       "src": "u3l21-gap-q10"
      }
     ]
    },
    {
     "title": "Graphs & calculus",
     "cells": [
      {
       "q": "State the value of \\( x \\) that must be excluded from the domain of \\( \\mathrm{f}(x) = \\dfrac{5}{x + 4} \\).",
       "a": "\\( x = -4 \\)",
       "src": "u4l15-refill-q01"
      },
      {
       "q": "Find the points on \\(y=2x-3\\) for \\(x=0,\\ 1,\\ 2\\).",
       "a": "\\((0,-3),\\ (1,-1),\\ (2,1)\\)",
       "src": "igcse-we-u4l2"
      },
      {
       "q": "The point \\((2,\\ 3)\\) lies on \\(y=\\mathrm{f}(x)\\). Find its image on \\(y=-\\mathrm{f}(x)+1\\).",
       "a": "\\((2,\\ -2)\\)",
       "src": "igcse-we-u4l23"
      },
      {
       "q": "Solve \\(3\\tan x+4=0\\) for \\(0^\\circ\\le x\\le360^\\circ\\). Give your answers to 1 decimal place.",
       "a": "\\(x=126.9^\\circ,\\ 306.9^\\circ\\)",
       "src": "u4l27-gap-q08"
      },
      {
       "q": "A particle moves along a straight line. Its displacement, \\(s\\) metres, from a fixed point O at time \\(t\\) seconds is \\(s = t^3 - 9t^2 + 24t + 2\\). Find the displacement of the particle from O at each time when it is instantaneously at rest.",
       "a": "22 m (t = 2) and 18 m (t = 4)",
       "src": "u8l6-gap-q07"
      }
     ]
    },
    {
     "title": "Geometry & vectors",
     "cells": [
      {
       "q": "Write down the order of rotational symmetry of a regular hexagon.",
       "a": "6",
       "src": "u5l39-gap-q01"
      },
      {
       "q": "Triangle T has vertices (2, 1), (5, 1) and (5, 3). T is rotated 90° anticlockwise about the point (1, 1). Find the coordinates of the vertices of the image.",
       "a": "(1, 2), (1, 5), (−1, 5)",
       "src": "u5l38-gap-q04"
      },
      {
       "q": "Two triangles each have sides 5 cm and 8 cm with an included angle of \\(70^\\circ\\). Are they congruent?",
       "a": "Yes (SAS)",
       "src": "igcse-we-u5l40"
      },
      {
       "q": "A bicycle wheel has diameter 65 cm. How many complete turns does the wheel make when the bicycle travels 1 km?",
       "a": "489 complete turns",
       "src": "u5l41-gap-q07"
      },
      {
       "q": "A sector of a circle has radius \\(r\\) cm and angle \\(\\theta°\\). The area of the sector, in cm², is numerically equal to 3 times the length of its arc, in cm. The arc length is \\(5\\pi\\) cm. Find the value of \\(r\\) and the value of \\(\\theta\\).",
       "a": "\\(r=6,\\ \\theta=150\\)",
       "src": "u5l35-gap-q11"
      }
     ]
    },
    {
     "title": "Statistics & probability",
     "cells": [
      {
       "q": "A sports centre asked 50 of its members which facilities they use. 27 use the gym, 21 use the pool and 6 use both the gym and the pool. How many of these members use neither the gym nor the pool?",
       "a": "8",
       "src": "u6l12-refill-q01"
      },
      {
       "q": "Values 1, 2, 3, 4 have frequencies 3, 5, 8, 4. Find the mean.",
       "a": "2.65",
       "src": "igcse-we-u6l4"
      },
      {
       "q": "Frequencies of four classes are 4, 9, 15, 12. Write the cumulative frequencies.",
       "a": "4, 13, 28, 40",
       "src": "igcse-we-u6l6"
      },
      {
       "q": "A bag has 3 red and 7 blue balls. Two are taken without replacement. Find P(both blue).",
       "a": "\\(\\tfrac{7}{15}\\)",
       "src": "igcse-we-u6l19"
      },
      {
       "q": "A dice is rolled 120 times and shows six 23 times. Estimate P(six) and the expected number of sixes in 600 rolls.",
       "a": "\\(\\tfrac{23}{120}\\); 115",
       "src": "igcse-we-u6l15"
      }
     ]
    }
   ]
  },
  "0580e": {
   "label": "Cambridge IGCSE 0580 · Extended",
   "categories": [
    {
     "title": "Number",
     "cells": [
      {
       "q": "The population of a village is 8500. It increases by 2% each year. Find the population after 3 years.",
       "a": "\\(9020\\)",
       "src": "cie0580-1.17-q03"
      },
      {
       "q": "Use your calculator to work out \\(\\dfrac{5}{\\frac{1}{3} + \\frac{1}{7}}\\).",
       "a": "\\(10.5\\)",
       "src": "cie0580-1.14-q07"
      },
      {
       "q": "Sara invests \\(\\$2400\\) at \\(3.5\\%\\) per year simple interest. Work out the total interest after 4 years.",
       "a": "\\(\\$336\\)",
       "src": "cie0580-1.13-c05"
      },
      {
       "q": "A trader buys 40 T-shirts for \\(\\$6.25\\) each. She sells 32 of them for \\(\\$12\\) each and the rest for \\(\\$8\\) each. Work out her profit.",
       "a": "\\(\\$198\\)",
       "src": "cie0580-1.16-q08"
      },
      {
       "q": "Lin earns \\(\\$38\\,400\\) per year. She pays no tax on the first \\(\\$12\\,000\\). She pays 20% tax on the rest. How much does she take home each month after tax?",
       "a": "\\(\\$2760\\)",
       "src": "cie0580-1.16-q12"
      }
     ]
    },
    {
     "title": "Algebra & graphs",
     "cells": [
      {
       "q": "Find the length of the line joining \\((1, 2)\\) and \\((7, 10)\\).",
       "a": "\\(10\\)",
       "src": "cie0580-3.4-q02"
      },
      {
       "q": "Write \\(2y = 6x - 8\\) in the form \\(y = mx + c\\) and write down the gradient.",
       "a": "\\(y = 3x - 4\\), gradient \\(3\\)",
       "src": "cie0580-3.5-c05"
      },
      {
       "q": "Find the equation of the line parallel to \\(y = -\\frac{1}{2}x + 4\\) that passes through \\((4, 5)\\).",
       "a": "\\(y = -\\frac{1}{2}x + 7\\)",
       "src": "cie0580-3.6-c05"
      },
      {
       "q": "Find an expression for the \\(n\\)th term of the sequence \\(3, \\ 7, \\ 15, \\ 31, \\ 63, \\ \\ldots\\)",
       "a": "\\(2^{n+1} - 1\\)",
       "src": "cie0580-2.7-q13"
      },
      {
       "q": "\\(A\\) is the point \\((2, 1)\\) and \\(B\\) is the point \\((6, 5)\\). The point \\(P\\) lies on the \\(y\\)-axis and is the same distance from \\(A\\) as from \\(B\\). Find the coordinates of \\(P\\).",
       "a": "\\((0, 7)\\)",
       "src": "cie0580-3.4-q12"
      }
     ]
    },
    {
     "title": "Geometry & mensuration",
     "cells": [
      {
       "q": "Convert \\(60\\,000\\text{ cm}^3\\) to \\(\\text{m}^3\\).",
       "a": "\\(0.06\\text{ m}^3\\)",
       "src": "cie0580-5.1-c04"
      },
      {
       "q": "\\(AB\\) is a diameter of a circle and \\(C\\) is on the circle. Angle \\(CAB = x^\\circ\\) and angle \\(CBA = 2x^\\circ\\). Find \\(x\\).",
       "a": "\\(x = 30\\)",
       "src": "cie0580-4.7-c04"
      },
      {
       "q": "A triangle has sides 5 cm, 7 cm and 9 cm. A similar triangle has longest side 22.5 cm. Find the length of its shortest side.",
       "a": "\\(12.5\\) cm",
       "src": "cie0580-4.4-c06"
      },
      {
       "q": "Five of the interior angles of a hexagon are \\(110^\\circ\\), \\(125^\\circ\\), \\(130^\\circ\\), \\(118^\\circ\\) and \\(102^\\circ\\). Find the sixth angle.",
       "a": "\\(135^\\circ\\)",
       "src": "cie0580-4.6-c05"
      },
      {
       "q": "A cube has one corner cut off by a flat cut, leaving a small triangular face where the corner was. The cut does not reach any other corner. Write down the number of faces, edges and vertices of the new solid.",
       "a": "7 faces, 15 edges, 10 vertices",
       "src": "cie0580-4.1-q12"
      }
     ]
    },
    {
     "title": "Trigonometry & vectors",
     "cells": [
      {
       "q": "Without using a calculator, find the exact value of \\(\\sin 30^\\circ + \\cos 60^\\circ\\).",
       "a": "\\(1\\)",
       "src": "cie0580-6.3-q04"
      },
      {
       "q": "In triangle \\(ABC\\), angle \\(B = 90^\\circ\\), angle \\(C = 60^\\circ\\) and \\(AC = 8\\) cm. Without using a calculator, find the exact length of \\(AB\\).",
       "a": "\\(4\\sqrt{3}\\) cm",
       "src": "cie0580-6.3-q07"
      },
      {
       "q": "In triangle \\(PQR\\), angle \\(Q = 90^\\circ\\), angle \\(P = 30^\\circ\\) and \\(PQ = 9\\) cm. Without using a calculator, find the exact length of \\(QR\\). Give your answer in its simplest form.",
       "a": "\\(3\\sqrt{3}\\) cm",
       "src": "cie0580-6.3-q08"
      },
      {
       "q": "In triangle \\(ABC\\), angle \\(B = 90^\\circ\\), \\(AB = 4\\sqrt{3}\\) cm and \\(BC = 4\\) cm. Without using a calculator, find angle \\(ACB\\).",
       "a": "\\(60^\\circ\\)",
       "src": "cie0580-6.3-q11"
      },
      {
       "q": "In triangle \\(ABC\\), angle \\(B = 45^\\circ\\) and angle \\(C = 30^\\circ\\). \\(D\\) is the point on \\(BC\\) such that \\(AD\\) is perpendicular to \\(BC\\), and \\(AD = 6\\) cm. Without using a calculator, find the exact length of \\(BC\\).",
       "a": "\\(6 + 6\\sqrt{3}\\) cm",
       "src": "cie0580-6.3-q14"
      }
     ]
    },
    {
     "title": "Probability & statistics",
     "cells": [
      {
       "q": "Give one example of categorical data that could be collected about a car.",
       "a": "e.g. colour (or make, or type of fuel)",
       "src": "cie0580-9.1-q03"
      },
      {
       "q": "Find the mean of \\(12, \\ 15, \\ 9, \\ 14\\).",
       "a": "\\(12.5\\)",
       "src": "cie0580-9.3-c02"
      },
      {
       "q": "The probability that Leo wins a game is 0.15. He plays the game 40 times. How many games should he expect to win?",
       "a": "\\(6\\)",
       "src": "cie0580-8.2-c02"
      },
      {
       "q": "The mean of six numbers is 8. Five of the numbers are \\(5, \\ 9, \\ 11, \\ 6, \\ 7\\). Find the sixth number.",
       "a": "\\(10\\)",
       "src": "cie0580-9.3-c06"
      },
      {
       "q": "A pie chart shows how 240 people voted for three candidates, A, B and C. The angle for A is \\(105^\\circ\\) and the angle for B is \\(150^\\circ\\). How many people voted for C?",
       "a": "\\(70\\)",
       "src": "cie0580-9.4-q12"
      }
     ]
    }
   ]
  },
  "0580c": {
   "label": "Cambridge IGCSE 0580 · Core",
   "categories": [
    {
     "title": "Number",
     "cells": [
      {
       "q": "Write \\(\\frac{7}{40}\\) as a percentage.",
       "a": "\\(17.5\\%\\)",
       "src": "cie0580-1.4-c03"
      },
      {
       "q": "A recipe for 6 people uses 450 g of rice. How much rice is needed for 10 people?",
       "a": "\\(750\\) g",
       "src": "cie0580-1.11-c03"
      },
      {
       "q": "Find the lowest common multiple (LCM) of 18 and 30.",
       "a": "\\(90\\)",
       "src": "cie0580-1.1-c04"
      },
      {
       "q": "The length of a rope is \\(l\\) metres. \\(l = 7.6\\), correct to 1 decimal place. Complete the statement: \\(\\ldots \\le l \\lt \\ldots\\)",
       "a": "\\(7.55 \\le l \\lt 7.65\\)",
       "src": "cie0580-1.10-c04"
      },
      {
       "q": "Lin earns \\(\\$38\\,400\\) per year. She pays no tax on the first \\(\\$12\\,000\\). She pays 20% tax on the rest. How much does she take home each month after tax?",
       "a": "\\(\\$2760\\)",
       "src": "cie0580-1.16-q12"
      }
     ]
    },
    {
     "title": "Algebra & graphs",
     "cells": [
      {
       "q": "Solve \\(5x - 7 = 18\\).",
       "a": "\\(x = 5\\)",
       "src": "cie0580-2.5-c01"
      },
      {
       "q": "Write down the gradient and the \\(y\\)-intercept of the line \\(y = 4x - 7\\).",
       "a": "gradient \\(4\\), \\(y\\)-intercept \\(-7\\)",
       "src": "cie0580-3.5-c01"
      },
      {
       "q": "Factorise completely \\(12x^2y - 18xy\\).",
       "a": "\\(6xy(2x - 3)\\)",
       "src": "cie0580-2.2-c06"
      },
      {
       "q": "Find an expression for the \\(n\\)th term of the sequence \\(5, \\ 12, \\ 31, \\ 68, \\ 129, \\ \\ldots\\)",
       "a": "\\(n^3 + 4\\)",
       "src": "cie0580-2.7-q07"
      },
      {
       "q": "The angles of a triangle are \\(x^\\circ\\), \\(2x^\\circ\\) and \\((x + 20)^\\circ\\). Write an equation in \\(x\\) and solve it.",
       "a": "\\(4x + 20 = 180\\), \\(x = 40\\)",
       "src": "cie0580-2.5-c06"
      }
     ]
    },
    {
     "title": "Geometry & mensuration",
     "cells": [
      {
       "q": "A net is made from 6 identical squares. Write down the name of the solid it folds to make.",
       "a": "cube",
       "src": "cie0580-4.2-q01"
      },
      {
       "q": "\\(AB\\) is a diameter of a circle, and \\(C\\) is a point on the circle. \\(AB = 13\\) cm and \\(AC = 5\\) cm. Find \\(BC\\).",
       "a": "\\(12\\) cm",
       "src": "cie0580-4.7-c03"
      },
      {
       "q": "A closed box is a cuboid measuring 6 cm by 4 cm by 3 cm. Find the total area of its net.",
       "a": "\\(108\\text{ cm}^2\\)",
       "src": "cie0580-4.2-q07"
      },
      {
       "q": "A pyramid has a square base of side 6 cm and a perpendicular height of 10 cm. The volume of a pyramid is \\(\\frac{1}{3} \\times\\) base area \\(\\times\\) height. Find its volume.",
       "a": "\\(120\\text{ cm}^3\\)",
       "src": "cie0580-5.4-c06"
      },
      {
       "q": "A cube has one corner cut off by a flat cut, leaving a small triangular face where the corner was. The cut does not reach any other corner. Write down the number of faces, edges and vertices of the new solid.",
       "a": "7 faces, 15 edges, 10 vertices",
       "src": "cie0580-4.1-q12"
      }
     ]
    },
    {
     "title": "Trigonometry & vectors",
     "cells": [
      {
       "q": "The two shorter sides of a right-angled triangle are 6 cm and 8 cm. Find the length of the hypotenuse.",
       "a": "\\(10\\) cm",
       "src": "cie0580-6.1-c01"
      },
      {
       "q": "A right-angled triangle has hypotenuse 13 cm and one other side 5 cm. Find the length of the third side.",
       "a": "\\(12\\) cm",
       "src": "cie0580-6.1-c02"
      },
      {
       "q": "The points \\((4, 6)\\) and \\((8, 2)\\) are enlarged with scale factor \\(\\frac{1}{2}\\), centre the origin. Write down their images.",
       "a": "\\((2, 3)\\) and \\((4, 1)\\)",
       "src": "cie0580-7.1-c05"
      },
      {
       "q": "A triangle has vertices \\((1, 1)\\), \\((2, 1)\\) and \\((1, 3)\\). It is enlarged with scale factor 3, centre the origin. Write down the vertices of the image.",
       "a": "\\((3, 3), (6, 3), (3, 9)\\)",
       "src": "cie0580-7.1-c04"
      },
      {
       "q": "In a right-angled triangle, the sides next to the right angle are 5.2 cm and 8.1 cm. Find the angle opposite the 5.2 cm side. Give your answer correct to 1 decimal place.",
       "a": "\\(32.7^\\circ\\)",
       "src": "cie0580-6.2-c05"
      }
     ]
    },
    {
     "title": "Probability & statistics",
     "cells": [
      {
       "q": "Give one example of categorical data that could be collected about a car.",
       "a": "e.g. colour (or make, or type of fuel)",
       "src": "cie0580-9.1-q03"
      },
      {
       "q": "Find the mean of \\(12, \\ 15, \\ 9, \\ 14\\).",
       "a": "\\(12.5\\)",
       "src": "cie0580-9.3-c02"
      },
      {
       "q": "The probability that Leo wins a game is 0.15. He plays the game 40 times. How many games should he expect to win?",
       "a": "\\(6\\)",
       "src": "cie0580-8.2-c02"
      },
      {
       "q": "The mean of six numbers is 8. Five of the numbers are \\(5, \\ 9, \\ 11, \\ 6, \\ 7\\). Find the sixth number.",
       "a": "\\(10\\)",
       "src": "cie0580-9.3-c06"
      },
      {
       "q": "A pie chart shows how 240 people voted for three candidates, A, B and C. The angle for A is \\(105^\\circ\\) and the angle for B is \\(150^\\circ\\). How many people voted for C?",
       "a": "\\(70\\)",
       "src": "cie0580-9.4-q12"
      }
     ]
    }
   ]
  }
 }
}