CAIE IGCSE Additional Math 4.1 Solve Modulus Equations Questions

Practise Cambridge IGCSE Additional Mathematics by solving absolute-value equations case by case and analysing distinct real roots.

Exam points

Solve absolute-value equations by considering the relevant positive and negative cases.
Determine parameter values from the number of distinct real roots of an absolute-value equation.
Check all candidate solutions and report the required distinct real values.

[Maximum number: 5]

the equation $\left|2 x^{2}+x-10\right|=5$ .

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

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

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CAIE IGCSE Additional Math 4.1 Solve Modulus Equations Questions question 1