CAIE IGCSE Mathematics Extended E2.5.1 Construct Expressions Equations and Formulas Questions

Practise Extended CAIE IGCSE Mathematics by modelling rates, costs and areas with equations, then simplifying them into the required quadratic or cubic form.

Exam points

Translate rates, costs, areas or other worded relationships into a correct Extended algebraic equation or formula, including simultaneous relationships.
Rearrange or simplify the constructed equation to show the required quadratic or cubic form while preserving the context and variables.

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

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CAIE IGCSE Mathematics Extended E2.5.1 Construct Expressions Equations and Formulas Questions question 1