The 5 and 6 mark questions at the end of each GCSE Maths paper are where grades are genuinely won and lost. These extended questions appear on all three papers — AQA 8300, Edexcel 1MA1, and OCR J560 — and they reward students who show clear, logical working over those who just write down an answer. The good news: you can earn marks at every stage of your working, even if the final answer is wrong. Getting the structure right is the most reliable way to pick up those extra marks.
What You Need to Know First
- The difference between method marks (M marks) and accuracy marks (A marks) — method marks are awarded for correct process even with arithmetic errors
- That a correct answer with no working shown earns zero marks on most 5 and 6 mark questions
- How to identify the number of stages in a question before you start — a 5-mark question usually has 3 to 4 distinct steps
- What "show that" and "hence" mean in a question stem (covered below)
- How to use the mark scheme logic: marks are awarded at specific checkpoints, not just at the end
The Structure That Gets Full Marks
Every extended question on the GCSE Maths paper follows the same principle: the examiner awards marks at specific stages of the working. This means you must write down every step, even if it feels obvious. A student who writes every line of working can earn 4 out of 5 marks even with a wrong final answer. A student who jumps to the answer — even correctly — may earn nothing.
Here is the method to use every time you face a 5 or 6 mark question:
- Read the whole question before you start. Identify how many separate calculations the question requires. Circle or underline key numbers and the final thing being asked.
- Write down any formula you are using. Before substituting numbers, state the formula. "Volume of cylinder = πr²h" at the top of your working earns you a mark on AQA and Edexcel papers where the method mark is linked to a correct formula being seen.
- Show substitution as a separate line. Do not jump straight to a numerical answer. Write "V = π × 5² × 12" before you write "= 942.5 cm³". That substitution line is often worth a mark in itself.
- Label each stage clearly. If the question has two parts — say, finding an angle and then using it to find a length — write "Step 1: Find angle" and "Step 2: Find length" so the examiner can follow your logic without guessing.
- Keep full decimals until the final step. Rounding intermediate answers causes errors that lose the accuracy mark at the end. Use your calculator memory or write out all decimal places, then round only in the final line.
- Write a concluding statement. Always end with a sentence that directly answers what was asked. "The volume of the remaining solid is 829 cm³" is much better than a bare number.
Worked Example 1
A cylinder has radius 5 cm and height 12 cm. A sphere of radius 3 cm is removed from inside it. Calculate the remaining volume. Give your answer to 3 significant figures. (5 marks)
Step 1: Volume of cylinder
Formula: V = πr²h
V = π × 5² × 12 = π × 300 = 942.477... cm³
Step 2: Volume of sphere
Formula: V = ⁴⁄₃πr³
V = ⁴⁄₃ × π × 3³ = ⁴⁄₃ × π × 27 = 113.097... cm³
Step 3: Remaining volume
942.477... − 113.097... = 829.380... cm³
Step 4: Round to 3 significant figures
= 829 cm³
The mark scheme awards marks at Steps 1, 2, 3, and 4. Even if you make an arithmetic slip in Step 3, you can still earn 3 or 4 marks for correct methods in the earlier steps. That is the power of showing every line.
"Show That" and "Hence" Questions
These two question types appear regularly in the higher-mark questions on all three boards, and they trip up students who do not know the specific rules.
"Show that" means the final answer is given to you in the question. Your job is to prove it by working logically from start to finish. The marks are all in the process. Never start from the given answer and work backwards — examiners recognise this approach and award zero marks for it, no matter how neat it looks.
"Hence" means you must use the result from the previous part of the question. If part (a) asked you to factorise an expression and part (b) says "hence solve the equation", you must use the factorised form from part (a). Starting fresh with a different method — for example, using the quadratic formula instead — will usually lose you all the method marks in part (b), even if you get the right answer.
Worked Example 2
(a) Show that x² − 5x + 6 = 0 can be written as (x − 2)(x − 3) = 0. (2 marks)
(b) Hence solve the equation x² − 5x + 6 = 0. (2 marks)
Part (a): Show that
Expand (x − 2)(x − 3):
= x² − 3x − 2x + 6
= x² − 5x + 6 ✓
This matches the left-hand side of the equation, so the factorisation is correct.
Notice: you must show the expansion fully. Writing "(x − 2)(x − 3) = x² − 5x + 6" in one line is not sufficient — the examiner needs to see the intermediate step to award the marks.
Part (b): Hence solve
Using the result from part (a):
(x − 2)(x − 3) = 0
Either x − 2 = 0, which gives x = 2
Or x − 3 = 0, which gives x = 3
Solution: x = 2 or x = 3
Part (b) earns marks for using the factorised form and stating both solutions clearly with the word "or" between them. Writing only x = 2 is a common error that loses a mark.
Common Mistakes Students Make
- Skipping the formula statement. Jumping straight to substitution loses the method mark linked to writing the correct formula first. Always state it — it takes two seconds and is worth a mark.
- Rounding too early. Rounding 942.477 to 942 before subtracting will give a wrong final answer and lose the accuracy mark. Keep full calculator values until the very last line.
- Starting "show that" questions from the answer. Working backwards from a given result earns nothing. The marks are in the forward working — always start from the left-hand side or the given information.
- Not giving both solutions. Quadratic equations have two solutions. Writing only one loses a mark every time, yet students do it repeatedly in exams.
- Giving up on harder questions. Many students see a 6-mark question, feel unsure, and leave it blank. Even starting with a correct formula or a correct first step earns 1 or 2 marks. Partial credit adds up — two 6-mark questions left blank is 12 marks lost before the paper is even marked.
- Forgetting units. A volume answer of "829" without "cm³" can cost the final accuracy mark on questions where units are explicitly required. Re-read the question — if the data has units, your answer needs them too.
Exam Tips for 5 and 6 Mark Questions
- Time budget correctly. Allow roughly 1 minute per mark, plus 1 extra minute for reading. A 5-mark question deserves 6 minutes. Do not rush these questions — they carry the most marks per question on the paper.
- M marks are your safety net. AQA 8300 awards the M1 mark for a correct method even if arithmetic errors follow in the same line. Write your method explicitly and the method mark is usually safe, regardless of the final answer.
- Draw a diagram for geometry questions. Sketch the shape, label it with the numbers from the question, and mark on any angles or lengths you calculate along the way. This makes the working clearer for the examiner and helps you spot missing steps.
- Answer the question that was asked. Before writing your concluding statement, re-read the final sentence of the question. Students frequently calculate the wrong quantity — surface area instead of volume, angle A instead of angle B — and lose the final mark even with perfect working.
- Do not cross out correct working unless you are replacing it. Crossed-out working can sometimes still be awarded marks if it is legible and correct. If you change approach, write "New method below" and leave the original visible rather than scribbling it out entirely.
Practise Now
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