Explaining, convincing and proving

  • t for Tan
    problem
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    T for Tan

    Age
    16 to 18
    Challenge level
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    Can you find a way to prove the trig identities using a diagram?

  • Stats statements
    problem
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    Stats Statements

    Age
    16 to 18
    Challenge level
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    Are these statistical statements sometimes, always or never true? Or it is impossible to say?

  • Contrary Logic
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    Contrary Logic

    Age
    16 to 18
    Challenge level
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    Can you invert the logic to prove these statements?

  • Direct logic
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    Direct Logic

    Age
    16 to 18
    Challenge level
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    Can you work through these direct proofs, using our interactive proof sorters?

  • Dangerous driver?
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    Dangerous Driver?

    Age
    16 to 18
    Challenge level
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    Was it possible that this dangerous driving penalty was issued in error?

  • Areas and Ratios
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    Areas and Ratios

    Age
    16 to 18
    Challenge level
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    Do you have enough information to work out the area of the shaded quadrilateral?

  • Shape and territory
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    Shape and Territory

    Age
    16 to 18
    Challenge level
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    If for any triangle ABC tan(A - B) + tan(B - C) + tan(C - A) = 0 what can you say about the triangle?

  • Binomial
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    Binomial

    Age
    16 to 18
    Challenge level
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    By considering powers of (1+x), show that the sum of the squares of the binomial coefficients from 0 to n is 2nCn

  • Orthogonal Circle
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    Orthogonal Circle

    Age
    16 to 18
    Challenge level
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    Given any three non intersecting circles in the plane find another circle or straight line which cuts all three circles orthogonally.

  • Mechanical Integration
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    Mechanical Integration

    Age
    16 to 18
    Challenge level
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    To find the integral of a polynomial, evaluate it at some special points and add multiples of these values.