IGCSE Mathematics (0580)

Algebraic manipulation

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 collecting like terms, combine their coefficients (including negative signs) without changing the variable's power.
Common mistake: Students often add or subtract incorrectly with negatives, or mistakenly change p to p² when combining p terms.
When expanding two binomials, multiply each term in the first bracket by each in the second (four products), and combine like terms correctly.
Common mistake: Students often miss a middle term or add coefficients instead of combining all like terms.
To factorise fully, identify and factor out the highest common factor from both the numerical and variable parts of each term.
Common mistake: Students often miss a variable or do not take the largest possible factor, leaving the answer only partially factorised.
Completing the square requires halving the x coefficient to find a, then subtracting a² (not just a) from the constant term.
Common mistake: A common mistake is to use the full coefficient or subtract a instead of a².
To rewrite a product involving a squared bracket as a cubic polynomial, expand the squared term first, then distribute and combine like terms.
Common mistake: Students often skip steps or misapply the distributive law, leading to missing or incorrect terms.
When equating a completed square form to an expanded quadratic, match the coefficients of x and the constant terms separately.
Common mistake: Students often forget to expand (x - a)² fully or misalign terms when comparing.

Simplify. $3p - t - p - 4t$

Try it first, then show the working

Answer: 2p - 5t

28 exam-style questions on Algebraic manipulation, each marked to the scheme.