IB DP Maths AA · Exam special · AA and AI · SL & HL · how examiners award every mark · ~9 min read
IB Maths Command Terms and Markscheme Codes (M1, A1, R1, AG, FT)
What every IB Maths command term asks for, and how examiners award marks: M1, A1, R1, AG, FT, implied marks, misreads, "hence" vs "hence or otherwise", accuracy and the presentation rules that cost students marks.
Command termsWrite down vs findShow thatHenceJustify & proveM, A, R, AG marksFollow throughMisreads
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No tag = SL and HLHL ONLY HL students onlyFORMULA BOOKLET given in the examM1A1 how marks are awardedhighlight = comes up again and againHANDY worth memorisingTest yourself at the end
In 30 seconds
- The command term tells you how much to write. "Write down" needs only the answer; "show that" needs every step; "justify" needs a reason. Misreading it loses marks even when the mathematics is right.
- Markschemes split marks into types. M marks reward a method, A marks a correct answer, R marks reasoning. A correct final answer without working doesn't automatically get full marks.
- This note explains both, in plain words, using the conventions of the IB Maths markschemes (AA and AI share them).
By the end you can
- Know what each command term requires.
- Understand M1, A1, R1, AG, FT and implied marks.
- Avoid the presentation habits that lose marks.
1Command terms
Short-answer terms
| Command term | What it asks for | Working needed? |
|---|---|---|
| Write down | The answer, with little or no calculation | No; it is usually 1 mark |
| State | A value, fact or name | No |
| Find / Calculate / Determine | An answer, with the method that gets it | Yes |
| Solve | All the values that satisfy an equation or inequality | Yes, and check the domain |
| Estimate | An approximate value | Show what it is based on |
| Draw / Plot | An accurate diagram or graph, to scale | Points marked accurately |
| Sketch | The shape, with the key features labelled (intercepts, turning points, asymptotes, endpoints) | No scale needed; features are |
| Label | Names or values added to a diagram | No |
Reasoning terms
| Command term | What it asks for | How it is marked |
|---|---|---|
| Show that | Every step from the information given to the stated result | You must work towards the answer, not from it |
| Verify | Substitute a value and check that it works | Substitution is expected here (unlike "show that") |
| Prove | A complete, rigorous argument for all cases | Each step and the conclusion carry marks |
| Justify | A valid reason or evidence for your answer | Usually an R1 mark |
| Explain | Reasons or causes | One mark per valid point |
| Deduce | A conclusion that follows from earlier results | Use what you've just found |
| Hence | Use the previous result to answer | Other methods score zero |
| Hence or otherwise | The previous result is the intended route, but any correct method is fine | Full marks for any valid method |
| Interpret / Comment | What the result means in the context | Context and numbers both needed |
| Suggest | A sensible idea or explanation (more than one might be right) | Must be plausible and relevant |
Common mistakeAnswering a "write down" question with a page of algebra. If it is worth 1 mark, the answer is either obvious or on your calculator.
"Show that" done right
- Start from one side (or from the given facts) and work to the other side. Finish with the given result as the last line.
- Don't manipulate both sides at once. Moving terms across an equation you're asked to prove is treated as assuming the result: AA markschemes typically cap this at the first method mark.
- Don't substitute the answer to check it, unless the command term is "verify".
Worked example
Show that (x + 3)² − (x − 3)² = 12x.
- LHS = (x² + 6x + 9) − (x² − 6x + 9) [M1 expanding both]
- = x² + 6x + 9 − x² + 6x − 9 A1
- = 12x = RHS AG
- Numerical "show that": give one more significant figure than the stated value. To show x ≈ 2.4, write x = 2.4495… ≈ 2.4.
- Use it anyway. Even if you couldn't show the result, use the given value in later parts; you can still earn those marks.
"Hence" done right
Worked example
(a) Show that x = 2 is a root of p(x) = x³ − 3x² + 4. (b) Hence factorise p(x) fully.
- (a) p(2) = 8 − 12 + 4 = 0 A1
- (b) "Hence": use x = 2, so (x − 2) is a factor M1
- p(x) = (x − 2)(x² − x − 2) = (x − 2)²(x + 1) [A1A1]
Common mistakeIgnoring "hence" and starting again from scratch. Even a correct answer then scores nothing, unless the question says "hence or otherwise".
2How the marks work
Mark types
| Code | Awarded for | Key rule |
|---|---|---|
| M | Attempting a correct method (e.g. substituting into the right formula) | A marks that follow usually need this M mark first |
| A | A correct answer or accurate working | No A without the M before it (M0 A1 is generally impossible) |
| R | Clear reasoning or justification | Often only available if earlier marks were earned |
| AG | The answer was given in the question | No mark for writing it; the marks come from the steps |
| (M1), (A1) | Implied marks, in brackets | Earned if a correct later answer implies the step |
| FT | Follow through | A wrong earlier answer used correctly later still scores |
Rules worth knowing
- A correct answer can lose marks without working. Marks are awarded for what you write, and many A marks depend on a method being seen.
- Implied marks rescue you on a GDC paper: if the final answer is correct, bracketed marks for the steps are implied. On Paper 1 (no GDC) the working is expected.
- Follow through needs working. With a wrong value from part (a), you can still get full marks in part (b), but usually only if the examiner can see your method.
- No follow through for impossible answers. A probability above 1, sin θ = 1.4, or a non-integer where an integer is needed loses the answer mark.
- No follow through after a failed "show that" if you then use your own (wrong) value instead of the given one. Use the value printed in the question.
- Misreads are penalised once. If you copy a number wrongly from the question, you lose the first mark but can earn the rest.
- Only the first answer is marked if you give two. Crossed-out work isn't marked at all, so don't cross anything out until you have something better.
- Correct, then wrong: once a correct answer is seen, later wrong working is usually ignored, unless you use the wrong version in a later part.
3Accuracy and form
- Exact or 3 s.f.: unless the question says otherwise, give numerical answers exactly or to 3 significant figures.
- Simplify what simplifies to an integer: write 2, not 10/5. A fraction such as 10/4 is acceptable as long as top and bottom are integers.
- Finish the arithmetic: 4e2x × e3x must become 4e5x. Factorising or expanding isn't required unless asked.
- No calculator notation in final answers: write 3.2 × 10⁻⁴, not 3.2E−4.
- Degrees or radians: an answer in the wrong unit usually loses the final A mark.
- Extra solutions: a wrong extra answer (often outside the domain) can cost the final A1. Check each solution against the domain.
4Habits from the markscheme notes
- Line equations need "r =". A vector equation written without r = typically loses a mark.
- Probability in context: write P(late ∣ rain), not just P(A∣B), to earn the method mark.
- Induction: "let n = k" or "n = k is true" isn't an assumption. Write "assume the statement is true for n = k".
- Final reasoning marks need earlier marks. In proofs, the concluding R1 is often only awarded if most previous marks were earned, so a lucky conclusion doesn't score.
- Sketches: put multiple curves on the same axes when asked; show intercepts, turning points and asymptotes with their values.
- Transformations: name the type, the direction and the factor or vector ("vertical stretch, scale factor 3"; "translation by the vector (2, 0)").
Linking questionSee these rules in action in the AA exam traps, the AI exam traps and the AI answer templates.
Test yourself — cover the answers first
Quick check
- What does AG mean in a markscheme?
- Can you get an A mark without the M mark before it?
- What is the difference between "hence" and "hence or otherwise"?
- Should you substitute the given answer in a "show that"?
- You give two different answers to one part. Which is marked?
- Is 3.2E−4 acceptable as a final answer?
Show answers
- the answer is given in the question, so no mark is awarded for writing it
- generally no
- "hence" requires the previous result; "or otherwise" allows any valid method
- no, only in a "verify" question
- only the first
- no; write 3.2 × 10⁻⁴
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