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.
302 exam-style questions on WJEC A Level Maths 1.2 Algebra and Functions, covering 1.2.1 Algebra and Functions, 1.2.2 Algebra and Functions, 1.2.3 Algebra and Functions, 1.2.4 Algebra and Functions, 1.2.5 Algebra and Functions, 1.2.6 Algebra and Functions, 1.2.7 Algebra and Functions, 1.2.8 Algebra and Functions, 1.2.9 Algebra and Functions, 1.2.10 Algebra and Functions, 1.2.11 Algebra and Functions, and 1.2.12 Algebra and Functions. Each one has a worked solution and a mark scheme showing where the marks go.