CAIE A-Level Mathematics 1.1.5 Equations in Quadratic Form

$\left(x^{2}-2\right)^{2}=9$ leading to $x^{2}-2= \pm 3$

M1

Must be $x^{2}$ unless substitution is clear.

$x^{2}=-1$ or $x^{2}=5$

M1

Marking guidance:

Allow omission of -1 if $\pm 3$ seen.

$x= \pm \sqrt{5}$

A1

B1 SC if M1M1 not awarded. Ignore $\pm \mathrm{i}, \mathrm{i},-\mathrm{i}, \sqrt{ }-1$.
Use of calculator with no working scores 0/3.

Alternative method for Question 1(b)

$3 x^{4}-12 x^{2}-15=0$ leading to $3\left(x^{2}-5\right)\left(x^{2}+1\right)[=0]$

(M1)

$x^{2}=-1$ or $x^{2}=5$

(M1)

Allow omission of -1 if factors seen. Factorising or other
valid method.

$x= \pm \sqrt{5}$

(A1)

B1 SC if M1M1 not scored. Ignore $\pm \mathrm{i}, \mathrm{i},-\mathrm{i}, \sqrt{ }-1$.
Use of calculator with no working scores 0/3.