Proof by contradiction

A question is this type if and only if it explicitly requires using proof by contradiction to establish a result (typically involving irrationality, stationary points, or number properties).

3 questions · Standard +0.5

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Edexcel P4 2022 January Q6

5 marks Moderate -0.5

Three consecutive terms in a sequence of real numbers are given by

$$k , 1 + 2 k \text { and } 3 + 3 k$$ where \(k\) is a constant. Use proof by contradiction to show that this sequence is not a geometric sequence.

Edexcel P4 2024 January Q8

4 marks Standard +0.8

Use proof by contradiction to prove that the curve with equation

$$y = 2 x + x ^ { 3 } + \cos x$$ has no stationary points.

OCR MEI Paper 3 2018 June Q15

3 marks Challenging +1.2

15 It is given in lines \(31 - 32\) that the square has the smallest perimeter of all rectangles with the same area. Using this fact, prove by contradiction that among rectangles of a given perimeter, \(4 L\), the square with side \(L\) has the largest area. \section*{END OF QUESTION PAPER}