Moderate -0.3 This is a straightforward Further Maths question requiring calculation of a 2×2 determinant and solving a quadratic inequality. While it involves algebraic manipulation across multiple steps, the techniques are routine: expand det(M) = (3x)(2-x) - (7)(4x+1), simplify to get a quadratic, and solve the inequality. The 5 marks reflect the working required rather than conceptual difficulty. Slightly easier than average A-level standard due to being a direct application of standard procedures.
$$\mathbf{M} = \begin{pmatrix} 3x & 7 \\ 4x + 1 & 2 - x \end{pmatrix}$$
Find the range of values of \(x\) for which the determinant of the matrix \(\mathbf{M}\) is positive.
[5]
$$\mathbf{M} = \begin{pmatrix} 3x & 7 \\ 4x + 1 & 2 - x \end{pmatrix}$$
Find the range of values of $x$ for which the determinant of the matrix $\mathbf{M}$ is positive.
[5]
\hfill \mbox{\textit{Edexcel F1 2022 Q1 [5]}}