{
  "text": "How many numbers are there in the sequence 67, 82, 97, ..., 997? (assuming equal increments)",
  "image": null,
  "answers": [
    {
      "points": 0,
      "text": "60"
    },
    {
      "points": 0,
      "text": "62"
    },
    {
      "points": 5,
      "text": "63"
    },
    {
      "points": 0,
      "text": "65"
    },
    {
      "points": 0,
      "text": "78"
    }
  ]
}
{
  "text": "Assuming that every question in this 20-question test has only 1 right answer and you choose to answer each question randomly, what is the chance that you're so bad that you only get 4 questions right or less?",
  "image": null,
  "answers": [
    {
      "points": 5,
      "text": "Between 0.5 and 1"
    },
    {
      "points": 0,
      "text": "Between 0.1 and 0.5 (not including 0.5)"
    },
    {
      "points": 0,
      "text": "Between 0.01 and 0.1 (not including 0.1)"
    },
    {
      "points": 0,
      "text": "Between 0.001 and 0.01 (not including 0.01)"
    },
    {
      "points": 0,
      "text": "Less than 0.001"
    }
  ]
}
{
  "text": "When the base of the logarithm is 0.5, (log x)² < (log y)² means that:",
  "image": null,
  "answers": [
    {
      "points": 0,
      "text": "x < y"
    },
    {
      "points": 0,
      "text": "x > y"
    },
    {
      "points": 0,
      "text": "x ≤ y"
    },
    {
      "points": 0,
      "text": "x ≥ y"
    },
    {
      "points": 5,
      "text": "None of the above applies"
    }
  ]
}
{
  "text": "The dot product operation on vectors is:",
  "image": null,
  "answers": [
    {
      "points": 0,
      "text": "Associative, commutative and distributive on addition"
    },
    {
      "points": 5,
      "text": "Non-associative, commutative and distributive on addition"
    },
    {
      "points": 0,
      "text": "Non-associative, non-commutative and distributive on addition"
    },
    {
      "points": 0,
      "text": "Non-associative, non-commutative and non-distributive on addition"
    },
    {
      "points": 0,
      "text": "None of the above"
    }
  ]
}
{
  "text": "2020 is not divisible by 13 because...",
  "image": null,
  "answers": [
    {
      "points": 0,
      "text": "It ends with an even digit"
    },
    {
      "points": 0,
      "text": "The sum of its digits is not divisible by 13"
    },
    {
      "points": 0,
      "text": "The number comprising of its three rightmost digits is not divisible by 13"
    },
    {
      "points": 5,
      "text": "The number 2020 - 150×13 = 70 is not divisible by 13"
    },
    {
      "points": 0,
      "text": "The number 7×(2+0+2+0) - 1 = 27 is not divisible by 13"
    }
  ]
}
{
  "text": "Given two everywhere-differentiable real-valued functions f and g that are inverses of each other with f(3)=-5, if f'(3) = 15, then f'(3) + g'(-5) would be:",
  "image": null,
  "answers": [
    {
      "points": 0,
      "text": "15"
    },
    {
      "points": 0,
      "text": "-5"
    },
    {
      "points": 0,
      "text": "308/15"
    },
    {
      "points": 5,
      "text": "226/15"
    },
    {
      "points": 0,
      "text": "Cannot be determined from the information given above"
    }
  ]
}
{
  "text": "If x > y, then:",
  "image": null,
  "answers": [
    {
      "points": 0,
      "text": "1/(1+x²) > 1/(1+y²)"
    },
    {
      "points": 5,
      "text": "x² + y² > 2xy"
    },
    {
      "points": 0,
      "text": "sin²x > cos²x"
    },
    {
      "points": 0,
      "text": "x² - y² > 0"
    },
    {
      "points": 0,
      "text": "None of the above applies"
    }
  ]
}
{
  "text": "A standard deck of cards has 13 cards for each of the 4 suits (spade, club, heart, diamond). With that in mind, how many hands of 5 cards involve exactly 2 suits?",
  "image": null,
  "answers": [
    {
      "points": 0,
      "text": "7895"
    },
    {
      "points": 0,
      "text": "36744"
    },
    {
      "points": 5,
      "text": "379236"
    },
    {
      "points": 0,
      "text": "394680"
    },
    {
      "points": 0,
      "text": "None of the above"
    }
  ]
}
{
  "text": "Assuming that every question in this 20-question test has only 1 right answer and you choose to guess the answer of each question randomly, then in terms of the number of correctly-guessed answers, approximately 68% of them will fall between:",
  "image": null,
  "answers": [
    {
      "points": 5,
      "text": "2.2 and 5.8"
    },
    {
      "points": 0,
      "text": "0.8 and 7.2"
    },
    {
      "points": 0,
      "text": "6.8 and 12.5"
    },
    {
      "points": 0,
      "text": "7 and 13"
    },
    {
      "points": 0,
      "text": "None of the above"
    }
  ]
}
{
  "text": "If x is an irrational number, then:",
  "image": null,
  "answers": [
    {
      "points": 0,
      "text": "x² is also an irrational number"
    },
    {
      "points": 0,
      "text": "x + e is also an irrational number"
    },
    {
      "points": 0,
      "text": "ex is also an irrational number"
    },
    {
      "points": 0,
      "text": "ln(x) is also an irrational number"
    },
    {
      "points": 5,
      "text": "None of the above is true"
    }
  ]
}
{
  "text": "You go for a walk and casually ask people about their birth dates, what's the chance that among the first 3 people you meet, exactly 2 of them were born on February 29th?",
  "image": null,
  "answers": [
    {
      "points": 0,
      "text": "Between 1/100 and 1"
    },
    {
      "points": 0,
      "text": "Between 1/1000 and 1/100 (not including 1/100)"
    },
    {
      "points": 0,
      "text": "Between 1/10,000 and 1/1000 (not including 1/1000)"
    },
    {
      "points": 5,
      "text": "Between 1/1,000,000 and 1/10,000 (not including 1/10,000)"
    },
    {
      "points": 0,
      "text": "Less than 1/1,000,000"
    }
  ]
}
{
  "text": "If a unit circle is inscribed within an equilateral triangle, what would be the area of the said triangle?",
  "image": {
    "url": "https://mathvault.ca/wp-content/uploads/Circle-Inscribed-Within-Equilateral-Triangle.png",
    "width": 248,
    "height": 241,
    "orientation": "landscape"
  },
  "answers": [
    {
      "points": 0,
      "text": "1"
    },
    {
      "points": 0,
      "text": "2√2"
    },
    {
      "points": 5,
      "text": "3√3"
    },
    {
      "points": 0,
      "text": "6√3"
    },
    {
      "points": 0,
      "text": "Impossible to determine from the information given above"
    }
  ]
}
{
  "text": "(1+i)¹⁰⁰⁰ is equal to",
  "image": null,
  "answers": [
    {
      "points": 5,
      "text": "2⁵⁰⁰"
    },
    {
      "points": 0,
      "text": "16¹²⁶"
    },
    {
      "points": 0,
      "text": "4²⁵¹"
    },
    {
      "points": 0,
      "text": "32¹²⁰"
    },
    {
      "points": 0,
      "text": "None of the above"
    }
  ]
}
{
  "text": "If two functions f, g are such that the composition g○f is defined and is bijective, then it must mean that:",
  "image": null,
  "answers": [
    {
      "points": 0,
      "text": "(A) g is injective"
    },
    {
      "points": 2,
      "text": "(B) g is surjective"
    },
    {
      "points": 2,
      "text": "(C) f is injective"
    },
    {
      "points": 0,
      "text": "A and B"
    },
    {
      "points": 5,
      "text": "B and C"
    }
  ]
}
{
  "text": "Three friends are back at a round table to play a game where each person chooses a number randomly from 1 to 50. What's the chance that the numbers won't be chosen such that one is the square of another, which in turn is the square of the other?",
  "image": null,
  "answers": [
    {
      "points": 0,
      "text": "58769/125000"
    },
    {
      "points": 5,
      "text": "124993/125000"
    },
    {
      "points": 0,
      "text": "124987/125000"
    },
    {
      "points": 0,
      "text": "123757/125000"
    },
    {
      "points": 0,
      "text": "None of the above"
    }
  ]
}
{
  "text": "If D is a statement which is true precisely when exactly two of the statements A, B and C are false, then the falsity of D would imply that:",
  "image": null,
  "answers": [
    {
      "points": 0,
      "text": "If A and B are true, then C is true."
    },
    {
      "points": 0,
      "text": "If A and B are true, then C is false."
    },
    {
      "points": 0,
      "text": "If A and B are false, then C is true."
    },
    {
      "points": 5,
      "text": "If A and B are false, then C is false."
    },
    {
      "points": 0,
      "text": "The set of statements {C, D} is inconsistent."
    }
  ]
}
{
  "text": "How many real roots does the function f(x)=x³ + x - 8 have?",
  "image": null,
  "answers": [
    {
      "points": 0,
      "text": "0"
    },
    {
      "points": 5,
      "text": "1"
    },
    {
      "points": 0,
      "text": "2"
    },
    {
      "points": 0,
      "text": "3"
    },
    {
      "points": 0,
      "text": "4 or more"
    }
  ]
}
{
  "text": "What is the area enclosed by the function f(x) = sin²x - x²(sin³x)(cos²x) and the x-axis — between -π/4 and π/4?",
  "image": null,
  "answers": [
    {
      "points": 0,
      "text": "0"
    },
    {
      "points": 0,
      "text": "e + 1"
    },
    {
      "points": 5,
      "text": "(π -2)/4"
    },
    {
      "points": 0,
      "text": "π/4 - 2"
    },
    {
      "points": 0,
      "text": "None of the above"
    }
  ]
}
{
  "text": "If x and y are integers satisfying the equations 3x ≡ 4 (mod 50) and 7y ≡ 5 (mod 50), what is the expression x+y congruent to in mod 50?",
  "image": null,
  "answers": [
    {
      "points": 5,
      "text": "33"
    },
    {
      "points": 0,
      "text": "25"
    },
    {
      "points": 0,
      "text": "7"
    },
    {
      "points": 0,
      "text": "45"
    },
    {
      "points": 0,
      "text": "None of the above"
    }
  ]
}
{
  "text": "What is the 100ᵗʰ derivative of the function f(x) = sin(2x)?",
  "image": null,
  "answers": [
    {
      "points": 0,
      "text": "5sin(3x)"
    },
    {
      "points": 0,
      "text": "2⁵⁰cos(2x)"
    },
    {
      "points": 0,
      "text": "0"
    },
    {
      "points": 0,
      "text": "100sin(2x)"
    },
    {
      "points": 5,
      "text": "2¹⁰⁰sin(2x)"
    }
  ]
}