Edexcel P2 2023 June — Question 8

Exam BoardEdexcel
ModuleP2 (Pure Mathematics 2)
Year2023
SessionJune
TopicProof

  1. (i) A student writes the following statement:
    "When \(a\) and \(b\) are consecutive prime numbers, \(a ^ { 2 } + b ^ { 2 }\) is never a multiple of 10 "
    Prove by counter example that this statement is not true.
    (ii) Given that \(x\) and \(y\) are even integers greater than 0 and less than 6 , prove by exhaustion, that
$$1 < x ^ { 2 } - \frac { x y } { 4 } < 15$$