Why complete the square when the quadratic formula always works?
Because the formula gives you the roots and nothing else. Completing the square gives you the turning point, the line of symmetry, the range, and whether there are…
Worked answers
Additional Mathematics questions, worked through
A bridging qualification taken alongside IGCSE Maths that introduces calculus, functions and more demanding algebra a year early. Schools use it to prepare students for A Level; students often experience it as the moment maths stopped being easy.
- 1 worked answers
- 1 topics
Quadratic functions
Where Additional Mathematics marks actually go
These answers are written around the failure modes below rather than around the topic list. That is deliberate: most students who are stuck in this subject know more content than their grade suggests, and lose marks to one of these instead.
- Differentiation and integration learned as procedures without any sense of what they mean, which collapses at A Level
- Weak surd, indices and logarithm manipulation making otherwise straightforward questions unmanageable
- Underestimating it because it runs alongside the IGCSE, then discovering the standard is close to AS
- Trigonometric identities treated as memorisation rather than as tools to be selected
More on how we teach Additional Mathematics, or browse questions in other subjects.
Who these are written for
Strong IGCSE mathematicians heading for A Level Maths, Further Maths, engineering or physics. It is not a subject to take for the extra grade: it is genuinely harder than the IGCSE it sits beside.
How to get something out of a worked answer
Reading one of these is worth very little on its own, which is true of any explanation and is the reason revision by rereading feels productive and mostly is not. The method that works is slightly uncomfortable and takes about ten minutes per question.
Read the question, close the page, and attempt it on paper. Get it wrong if that is what happens: being wrong and then finding out why is the part that sticks. Then read the worked answer and, rather than checking whether your final answer matched, find the exact step where your version diverged from ours. That step is the thing to practise, and it is usually one specific decision rather than a whole topic.
Then find two similar questions from your own materials and do them cold. If the same step goes wrong again, you have found a genuine gap. If it does not, you have just fixed something. The wider method is here.
Why we publish these at all
Because we do not publish reviews or testimonials, and a parent choosing a tutor needs something to judge. Review widgets are cheap and star ratings are unfalsifiable, so we would rather hand you the actual teaching and let you decide whether it is any good. If these explanations are clear, that is the most honest sample of what you would be paying for that we can give you. More on that policy here.