Cambridge O Level Mathematics (Syllabus D) · Syllabus 4024 · Algebra and Graphs
Equations
What is Equations?
A statement that two expressions are equal, true only for particular values of the unknown, which solving is the process of finding. Linear equations are solved by inverse operations, fractional equations by clearing denominators after recording their excluded values, simultaneous linear equations by elimination or substitution, and quadratic equations by factorisation, by completing the square or by the quadratic formula. Changing the subject rearranges a formula so that a different letter stands alone, and any solution that makes an original denominator zero must be rejected.
This definition is part of the Algebra and Graphs chapter in Cambridge O Level Mathematics (Syllabus D).
Equations in context
An equation asks “which value?”; an inequality asks “which values?”. Almost everything you know about solving equations carries over unchanged. The single genuine difference is the reversal rule, and it exists because multiplying by a negative number flips the order of the number line: \(2<5\), but \(-2>-5\).
A drawn graph is a solving machine. Once the curve \(y=f(x)\) is on the paper, you can read off the solution to \(f(x)=0\) (where it crosses the \(x\)-axis), to \(f(x)=k\) (where it crosses the horizontal line \(y=k\)), and to a whole family of rearranged equations, by adding the right straight line. That last idea is the most powerful thing in this section, and the least obvious.