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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 termWhat it asks forWorking needed?
Write downThe answer, with little or no calculationNo; it is usually 1 mark
StateA value, fact or nameNo
Find / Calculate / DetermineAn answer, with the method that gets itYes
SolveAll the values that satisfy an equation or inequalityYes, and check the domain
EstimateAn approximate valueShow what it is based on
Draw / PlotAn accurate diagram or graph, to scalePoints marked accurately
SketchThe shape, with the key features labelled (intercepts, turning points, asymptotes, endpoints)No scale needed; features are
LabelNames or values added to a diagramNo

Reasoning terms

Command termWhat it asks forHow it is marked
Show thatEvery step from the information given to the stated resultYou must work towards the answer, not from it
VerifySubstitute a value and check that it worksSubstitution is expected here (unlike "show that")
ProveA complete, rigorous argument for all casesEach step and the conclusion carry marks
JustifyA valid reason or evidence for your answerUsually an R1 mark
ExplainReasons or causesOne mark per valid point
DeduceA conclusion that follows from earlier resultsUse what you've just found
HenceUse the previous result to answerOther methods score zero
Hence or otherwiseThe previous result is the intended route, but any correct method is fineFull marks for any valid method
Interpret / CommentWhat the result means in the contextContext and numbers both needed
SuggestA 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.

  1. LHS = (x² + 6x + 9) − (x² − 6x + 9) [M1 expanding both]
  2. = x² + 6x + 9 − x² + 6x − 9 A1
  3. = 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.

  1. (a) p(2) = 8 − 12 + 4 = 0 A1
  2. (b) "Hence": use x = 2, so (x − 2) is a factor M1
  3. 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

CodeAwarded forKey rule
MAttempting a correct method (e.g. substituting into the right formula)A marks that follow usually need this M mark first
AA correct answer or accurate workingNo A without the M before it (M0 A1 is generally impossible)
RClear reasoning or justificationOften only available if earlier marks were earned
AGThe answer was given in the questionNo mark for writing it; the marks come from the steps
(M1), (A1)Implied marks, in bracketsEarned if a correct later answer implies the step
FTFollow throughA 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

  1. What does AG mean in a markscheme?
  2. Can you get an A mark without the M mark before it?
  3. What is the difference between "hence" and "hence or otherwise"?
  4. Should you substitute the given answer in a "show that"?
  5. You give two different answers to one part. Which is marked?
  6. Is 3.2E−4 acceptable as a final answer?
Show answers
  1. the answer is given in the question, so no mark is awarded for writing it
  2. generally no
  3. "hence" requires the previous result; "or otherwise" allows any valid method
  4. no, only in a "verify" question
  5. only the first
  6. no; write 3.2 × 10⁻⁴
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Independent notes written by Riyaz Sir. Not produced, endorsed or approved by the International Baccalaureate Organization. Syllabus codes refer to the IB DP subject guides.