CAIE IGCSE Additional Math 4 Equations Inequalities and Graphs Topic Practice

$2 x^{2}+x-10=5$

leading to $2 x^{2}+x-15=0$ with a valid attempt to solve to obtain 2 values for x M1
$x=\frac{5}{2}, \quad-3$ A1 For both
Mark final answer for this equation,
A0 if - 3 is rejected
$$x^{2}+x-10=-5$$

leading to $2 x^{2}+x-5=0$ M1 Must be a correct 3-term quadratic
equated to zero
$x=\frac{-1 \pm \sqrt{41}}{4}$ oe 2 Dep M1 for a valid method of
solution to obtain 2 values for x.
Mark final answer for this equation,
A0 if negative root is rejected
Denominator of final answer must be positive

Correct graph of y=|x-2| and $x \leqslant -2.5,\ x \geqslant -0.25$
B1 for correct graph of y=|x-2|.
B1 for $x \leqslant -2.5$ or $x \geqslant -0.25$.
B1 STRICT FT for their critical values from the two intersections of their straight-line section of graph, providing it has negative gradient.

$\pm 3(x+4)(2 x-1)(x-2)$

B1 for ±
B1 for 3, may be implied by a linear
factor
B1 for (x+4)(2 x-1)(x-2) and no
extra terms;
may be implied if 3 is
included