Number and Algebra Strategies

Flashcards covering key concepts, problem-solving techniques, and common pitfalls in number and algebra topics.

Add or subtract when coefficients line up

A technique used when coefficients mirror each other or when a question only asks for a sum or difference: add the equations for $x + y$ or subtract for $x - y$ (halving a perimeter first if applicable) instead of solving fully for both variables separately.

Identity

A mathematical statement joined by $\equiv$ that holds true for every value of $x$; solved by comparing the coefficients of each power on both sides and solving the resulting system.

Equation

A mathematical statement that holds true only for particular values of a variable, which is solved by finding those specific values.

Identity substitution trap

The mistake of substituting one convenient value into two expressions and concluding an identity holds, which only demonstrates that both sides agree at that single point.

Unit conversion method

A procedure used when an answer requires a different unit than the provided data: convert only the incorrect unit and carry units through multiplication so that they cancel.

Linear factor conversion trap

The error of using a linear conversion factor for an area or volume calculation, where the conversion factor must instead be squared or cubed.

Difference of two squares

An expression featuring one square subtracted from another, simplified by factorising to $(a - b)(a + b)$ rather than expanding large numbers in full under time pressure.

Factorise before cancelling

A technique for algebraic fractions (such as a quadratic over a quadratic) where all expressions are factorised first and only whole brackets are cancelled.

Compound denominator

A denominator within a fraction that is itself a sum of fractions; it must be combined into a single fraction before inverting.

Reciprocal sum trap

The common algebraic error of cancelling individual terms inappropriately or incorrectly assuming that $\frac{1}{a + b} = \frac{1}{a} + \frac{1}{b}$.