CAIE IGCSE Mathematics E2.5.1 Equations

Practise forming and solving equations, from factorised quadratics to simultaneous line-curve systems and rearranged formulae.

Exam points

show a contextual equation simplifies to a given quadratic by clearing fractions correctly
solve quadratics by factorisation or formula, giving decimal answers when requested
rearrange formulae with algebraic denominators by collecting the required variable

[Maximum number: 4]

Antonio travels 100 km at an average speed of $x \mathrm{~km} / \mathrm{h}$ .

He then travels a further 150 km at an average speed of (x+10) km / h.
The time taken for the whole journey is 4 hours 20 minutes.

Show that $13x^2-620x-3000=0$ .

$\frac{100}{x}+\frac{150}{x+10}=4\frac13$ oe or $150=\left(\frac{13}{3}-\frac{100}{x}\right)(x+10)$
M1
$\frac{100(x+10)+150x}{x(x+10)}$ or better
M1
$300x+3000+450x=13x^2+130x$ oe or better
B1
Allow correct multiples of $13x^2-620x-3000=0$

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E2.5.1 Construct expressions, equations and formulas question 1