Common Add Math question structures

Add Math questions are built from a small set of recurring shapes. Once you can name the shape in front of you, a 'show that' that feeds a 'hence', a linked (a)(b)(c) build-up, a 'find the range of values' problem, or a graph you must sketch and then read, you stop meeting each question cold and start recognising the plan it wants.

This guide sets out the structures our teachers see most often across Paper 1 and Paper 2, the command words that signal each one, and how to decode a structure quickly so your time goes into solving rather than staring. We describe the shapes in general terms with our own short illustrations only, never a real past-year question, so you learn the pattern, not a memorised answer.

Across topics as different as functions, quadratics, differentiation and statistics, the same structural moves reappear. Recognising them is half the work: the shape tells you where the marks sit and roughly how long the answer should be.

• Linked build-up: a question in parts where (a) fixes a value or a result and (b), (c) reuse it. The whole thing is one chain, so a slip in (a) can cost the parts after it, check (a) before you build on it.
• 'Show that … hence …': a part hands you a target result to derive, then a follow-up part uses that exact result. The marks in the 'show that' are all in the working; the 'hence' expects you to reuse what you just proved rather than start again.
• 'Hence or otherwise': you may use the previous result, or a fresh method if you spot one. 'Hence' is usually the shorter route the setter intended, so try it first.
• Range-of-values problems: you solve an inequality or apply a condition and state a set of values. For example, $x^{2}+kx+4=0$ has two distinct real roots only when $k^{2}>16$, i.e. $k<-4$ or $k>4$.
• Express-in-terms-of: you change the subject of a relation, then substitute it elsewhere. If $3x+y=7$ then $y=7-3x$, and that expression drops into the next line.
• Graph or diagram based: you sketch a curve or read a given figure, then pull information from it, an intercept, a gradient, a point of intersection, an area under a curve.
• Contextual word problem: a described situation you must translate into equations first, then solve like any other question. Defining your variables clearly is where these start to score.

The command word tells you what kind of answer earns the marks. Reading it before you touch the numbers stops you from doing the wrong sort of work.

1. 1

   Spot the verb

   'Solve' wants a value or values; 'find' or 'determine' wants a specific quantity; 'evaluate' wants a number; 'sketch' wants a labelled shape, not a plotted table; 'show that' and 'prove' want a full derivation to a stated target.

2. 2

   Notice the linking words

   'Hence' means reuse the previous result; 'hence or otherwise' allows a fresh method but hints the previous one is quicker; 'given that' hands you a condition you must apply somewhere in the working.

3. 3

   Underline what is asked for

   Circle the unknown or the phrase 'range of values', 'in terms of', 'the coordinates of', so your final line answers exactly that. Many marks are lost by solving correctly but stopping one step short of what was asked.

4. 4

   Estimate the shape of the answer

   From the command word and the marks, picture the answer before working: a range problem ends in an inequality, an express-in-terms-of ends in an equation, a sketch ends in a labelled curve. Knowing the destination keeps your working pointed at it.

The two papers use the same shapes but weight them differently, so knowing which paper you are in changes how long an answer should run.

• Paper 1 is 2 hours for 80 marks in Sections A and B. Section A gathers shorter, single-idea questions across many topics; Section B has longer questions worth more marks each. The linked build-up and short 'solve'/'find' shapes dominate here.
• Paper 2 is 2 hours 30 minutes for 100 marks in Sections A, B and C. Questions run longer and are built in more parts, so the 'show that … hence', extended build-up and graph-based shapes carry more weight, and a single question can hold a long chain of method marks.
• There is no Paper 3, the two papers together cover the whole subject, so every shape you meet in practice belongs to one of these two.
• You may use a non-programmable scientific calculator, and marking is analytic, so clear working in the recurring shapes is what banks the method marks stage by stage.

It is easy to know every topic and still lose marks by misreading the shape of a question, treating a 'show that' like a normal solve, missing that a 'hence' wanted the previous result, or stopping before the range was fully stated. In our one-to-one sessions we work through your practice with you and name the structure of each question out loud, so you build the habit of decoding before diving in.

We show you how the command words map to the marks, drill the shapes you misread most, and set your next practice around those structures across several topics. The aim is simple: you should recognise the plan of a question before you write a line.