IGCSE Mathematics (0580)

Equations

What this topic tests, the mistakes that cost marks, and one exam-style question worked through step by step.

Key ideas and common mistakes

When solving linear equations with the unknown on both sides, collect all variable terms on one side and constants on the other.
Common mistake: A common mistake is to incorrectly add or subtract terms, leading to sign errors or incorrect grouping.
To solve a linear equation with a variable term and a constant, first isolate the variable term by undoing addition or subtraction before dividing by the coefficient.
Common mistake: Students often mistakenly divide before moving the constant.
To eliminate a variable in simultaneous equations, add or subtract the equations so that the coefficients of one variable are opposites.
Common mistake: Students often mistakenly subtract when addition cancels the variable, or vice versa.
When the coefficients of one variable are equal and opposite in simultaneous equations, adding (not subtracting) the equations eliminates that variable immediately.
Common mistake: Students often subtract instead, which does not eliminate the variable.
To find intersection points, set the line and curve equations equal and rearrange all terms to one side before factorising.
Common mistake: Students often forget to substitute both x-values back to get full coordinate pairs, not just the x-values.
When solving a quadratic for a physical quantity like length, both roots must be found by factorisation, but only the positive root is valid.
Common mistake: Students often forget to reject the negative root that is not physically meaningful.

Solve the equation. $7 - h = 3 - 5h$

Try it first, then show the working

Answer: -1

24 exam-style questions on Equations, each marked to the scheme.