Core Pure -as Year 1- Unit Test 5 Algebra And Functions Info

She felt a small smile. But the test wasn't done.

Unit Test 5 wasn't just about algebra. It was about precision. About checking every assumption. About remembering that a square can never be negative. core pure -as year 1- unit test 5 algebra and functions

was the killer. The one that separated the A from the B. The function ( p(x) = x^4 - 8x^2 + 16 ). Find all real roots. Hence solve the inequality ( p(x) < 0 ). She factorised: let ( u = x^2 ). Then ( u^2 - 8u + 16 = (u-4)^2 ). So ( p(x) = (x^2 - 4)^2 = (x-2)^2 (x+2)^2 ). She felt a small smile

She wrote the final answer: ( \sqrt{x^2+3} ), domain ( [0, \infty) ). It was about precision

But the domain of ( h \circ k ) is ( { x \in \text{dom}(k) \mid k(x) \in \text{dom}(h) } ). ( x \geq 0 ) and ( x^2 - 1 \geq -4 ) — which is always true. So the domain is simply ( x \geq 0 ).

On her desk lay . The front cover was deceptively calm, featuring only the exam board’s logo and the instruction: Attempt all questions. Use algebraic methods unless otherwise stated.