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.

For real $x$ and $k$ with $-3\le k\le 1$ , let $y_k=\left(x+\frac{3k-1}{5}\right)^2+3k^2-12k+11$ .
Over all real $x$ and all allowed $k$ , what is the smallest possible value of $y_k$ ?

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