Maths Core WMA01/WMA02: INEQUALITIES Topical Past Paper Questions

The straight line $l$ has equation $y = mx - 2$, where $m$ is a constant. The curve C has equation $ y = 2x^{2} + x + 6 $ The line l does not cross or touch the curve C. (a) Show that m satisfies the inequality $$ m^{2}-2m-63 (4)

The equation $ (p - 2)x^{2} + 8x + (p + 4) = 0, $ where $ p $ is a constant has no real roots. (a) Show that $p$ satisfies $p^{2} + 2p - 24 > 0$ (3) (b) Hence find the set of possible values of $p$. (4)

Find the range of values of x for which $$ \begin{array}{l}(a)\ 4(x-2)\leqslant2x+1\\ (b)\ (2x-3)(x+5)>0\\ (c)\ \text{both}4(x-2)\leqslant2x+1\text{and}(2x-3)(x+5)>0 \end{array} $$