Prove that x2+4x>2x−4x^2 + 4x > 2x - 4x2+4x>2x−4 for all real values of xxx.
A student claims: "If I add 2 to a number and then square the sum, the result is always greater than the square of the original number." State, giving a reason, whether this claim is always true, sometimes true or never true.
132 exam-style questions on OCR (MEI) A Level Maths 1.1 Proof, covering 1.1.1 Structure of mathematical proof, 1.1.2 Disproof by counter example, 1.1.3 Proof by contradiction (A-level only), and 1.1 Proof. Each one has a worked solution and a mark scheme showing where the marks go.