TMUA Style, Mastery (Paper 1)

TMUA Style Questions · Mathematical Knowledge · Mastery

This free ExamAlly page is a full TMUA Style practice question for students preparing for the TMUA (Test of Mathematics for University Admission). It mirrors the multi-topic style of the real exam: you choose a method, work through every option, and review a step-by-step solution—no account required.

Independent practice material, not affiliated with official TMUA organisers.

Let $f$ and $g$ be real-valued functions with, for all real $x$ , $g(x)=2f(x)^2-6f(x)+1$ and $g(x)=3\sin x-4\cos x+k$ , where $k\ge \tfrac{3}{2}$ .
What is the minimum value of $f(x)$ ?

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