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IB Maths AI SL Mock Paper (Paper 1): 80 Marks of Modelling with Answers
TUTORZONE ORIGINAL MOCK PAPER · IB MATHEMATICS AI (APPLICATIONS AND INTERPRETATION) SL PAPER 1
Written to the IBO subject brief (first assessment 2021): every AI paper allows the graphic display calculator (Papers 1 and 2 alike), so drilling centres on modelling, tool choice and interpretation. SL Paper 1 short-response is 40% over 1.5 hours, Paper 2 extended-response 40%, and the exploration 20%. This paper has 10 short-response modelling questions (80 marks) with answers, model statements and interpretation.
What is in IB Maths AI SL Paper 1?
Direct answer: IB Maths AI (Applications and Interpretation) SL Paper 1 is short-response, 40% of the subject over 1.5 hours; Paper 2 extended-response is 40% over 1.5 hours and the exploration is 20%. Unlike AA, both AI papers allow the graphic display calculator, so drilling centres on modelling, tool choice and interpretation, not hand arithmetic.
Assessment at a glance (2027)
| Component | Content | Weighting | Duration |
|---|---|---|---|
| Paper 1 (short-response, technology allowed) | Compulsory short-response questions; SL 1.5 h / 40% | SL 40% | 1.5 h |
| Paper 2 (extended-response, technology allowed) | Compulsory extended-response questions; SL 1.5 h / 40% | SL 40% | 1.5 h |
| Mathematical exploration (IA) | Independent investigation; 15 recommended hours; 20% at both levels | 20% (SL and HL) | 15 recommended hours |
Ten short-response questions in 90 minutes is about 8-9 minutes each. AI marks are rarely lost to computation but to ‘calculator output only, no model and no interpretation’ – keep two or three lines for the model and the interpretation in every answer.
How this paper was built
This is a TutorZone original mock paper: the questions follow the IBO subject brief (first assessment 2021) structure (SL Paper 1 at 40% in 1.5 hours, technology allowed), and the answers are our own model answers, not IBO past papers or official marking references.
Ten short-response questions for 80 marks; every numerical answer was recomputed programmatically. Each answer is split into model, computation and interpretation, matching IB marking habits.
Pacing
| Section | Marks | Suggested time | What to do first |
|---|---|---|---|
| Paper 1 (short-response, technology allowed) | SL 40% | about 85 min with 5 min checking | Model first: variables, model, reason, then the GDC |
| Paper 2 (extended-response, technology allowed) | SL 40% | real-context modelling | extract the data, choose a function or distribution, justify it |
| Mathematical exploration (IA) | 20% (SL and HL) | four stages: topic, model, computation, interpretation | choose a real context you can model with data |
How many questions does this paper have, and how should the time be split?
Direct answer: 10 short-response questions for 80 marks; aim for 85 minutes with 5 to check (about 8-9 minutes each). Keep two or three lines for the model and the interpretation in every answer – the part IB marks separately.
Paper 1: short-response modelling questions (10 questions, 80 marks)
All compulsory; aim for 85 minutes with 5 to check. State the model and variables before computing.
Question 1 (8 marks)
$5000 is deposited at 4% per annum, compounded annually. Find the amount after three years (to the cent) and name the type of model used.
Question 2 (8 marks)
A city has 200 000 people and is expected to grow 2.5% per year. Assuming the rate stays constant, find the population after five years (to the nearest whole number) and comment on one limitation of the model.
Question 3 (8 marks)
For the sample data 12, 15, 18, 20, 22, find the mean and the sample standard deviation (3 significant figures), and explain what the standard deviation measures.
Question 4 (8 marks)
A bag contains 4 red and 6 blue balls. Two balls are drawn without replacement. Find the probability of drawing at least one red ball.
Question 5 (8 marks)
A line passes through (2, 5) and (6, 13). Find its equation and explain what the gradient represents.
Question 6 (8 marks)
From a point 20 m from the base of a building, the angle of elevation of its top is 40°. Find the height of the building (3 significant figures).
Question 7 (8 marks)
A radioactive substance has a half-life of 5 years and an initial mass of 80 g. After how many years will 10 g remain?
Question 8 (8 marks)
A company’s profit (in thousands) is P(x) = −x² + 12x − 20, where x is output in hundreds of units. Find the maximum profit and the output that gives it.
Question 9 (8 marks)
You save monthly: $100 in the first month, then $10 more each month. Find the amount saved in month 12 and the total saved over the first 12 months.
Question 10 (8 marks)
Find the distance between A(1, 2) and B(4, 6).
Where are the answers, and do they show the working?
Direct answer: every question is followed by an answers-and-interpretation block split into model / computation / interpretation with the marks for each part (e.g. the compound-interest item: 2 for the model, 4 for the computation, 2 for the interpretation) – not just the final number.
Paper 1 answers and interpretation
Question 1
(1) Model: compound interest is a geometric sequence, multiplying by 1.04 each year (2 marks); (2) compute 5000 × 1.04³ = $5624.32 (4 marks); (3) interpretation: interest earns interest, so the amount exceeds simple interest ($5600) (2 marks).
Question 2
(1) Model: exponential growth P = 200 000 × 1.025^t (2 marks); (2) compute 200 000 × 1.025⁵ ≈ 226 282 people (4 marks); (3) limitation: a growth rate rarely stays constant long-term, as migration, policy or resources bend the model away from reality (2 marks).
Question 3
(1) Mean: 87 ÷ 5 = 17.4 (2 marks); (2) sample standard deviation √(Σ(x−μ)²/(n−1)) = √(63.2 ÷ 4) = √15.8 ≈ 3.97 (4 marks); (3) it measures how spread out the data are around the mean (2 marks). Use the GDC’s sx (divide by n−1), not σx (divide by n).
Question 4
(1) Method: use the complement, P(at least one red) = 1 − P(both blue) (2 marks); (2) compute 1 − 6/10 × 5/9 = 1 − 30/90 = 2/3 (4 marks); (3) without replacement the second denominator becomes 9 (2 marks).
Question 5
(1) Gradient: (13 − 5) ÷ (6 − 2) = 2 (3 marks); (2) equation y − 5 = 2(x − 2), i.e. y = 2x + 1 (3 marks); (3) a gradient of 2 means y rises by 2 for every unit of x (2 marks).
Question 6
(1) Model: a right-angled triangle with tan 40° = h/20 (2 marks); (2) compute h = 20 × tan 40° ≈ 20 × 0.8391 = 16.8 m (4 marks); (3) the angle of elevation, distance and height form a trig relation solved with tangent (2 marks).
Question 7
(1) Model: exponential decay M = 80 × (1/2)^(t/5) (2 marks); (2) compute 10 = 80 × (1/2)^(t/5) → (1/2)^(t/5) = 1/8 = (1/2)³ → t/5 = 3 → t = 15 years (4 marks); (3) from 80 to 10 is three halvings, i.e. three half-lives (2 marks).
Question 8
(1) Method: differentiate for the turning point, P′(x) = −2x + 12 (3 marks); (2) P′(x) = 0 → x = 6; P(6) = −36 + 72 − 20 = 16 (thousand) (4 marks); (3) output 600 units maximises profit at $16 000, beyond which marginal profit turns negative (1 mark).
Question 9
(1) Model: an arithmetic sequence with first term 100 and common difference 10 (2 marks); (2) month 12: T₁₂ = 100 + 11 × 10 = $210 (3 marks); (3) total S₁₂ = 12/2 × (100 + 210) = $1860 (3 marks).
Question 10
(1) Method: the distance formula d = √((x₂−x₁)² + (y₂−y₁)²) (2 marks); (2) compute √((4−1)² + (6−2)²) = √(9 + 16) = √25 = 5 units (6 marks).
Where are AI paper marks most easily lost?
Direct answer: calculator output with no model or interpretation; an implausible model left unchecked; and missing units or significant figures. All three are method and interpretation marks, a large share of every question.
Where these marks are usually lost
| Mistake | What it looks like | What it costs | Instead |
|---|---|---|---|
| Calculator output only | Pressing buttons and writing the answer | IB marks method and interpretation separately | Write the variables and model, then the computation, then the interpretation |
| No model check | Stopping once a number appears | No verification or limitations, so the top band is lost | Test the model by graph or order of magnitude and state its limits |
| Units and accuracy | Bare numbers | IB marks units and significant figures | Check units and significant figures at the end of every answer |
How to use this paper
First sit: no references, the full 90 minutes, no formula booklet.
Mark it: check the model / computation / interpretation split – count which part you omitted, since that is where IB marks are lost.
Second sit: redo the paper three to seven days later, aiming for shorter and more complete working.
What should I do after finishing this paper?
Direct answer: log every question where the model or interpretation was missed and name the part; redo the paper three to seven days later with fuller working; then drill Paper 2 extended-response and the exploration by context type (finance, population, statistics).
FAQ
Is this an IBO paper?
No. The questions, answers and mark allocation are TutorZone originals; only the framework figures come from the IBO subject brief (first assessment 2021).
Does AI Paper 1 really allow a calculator?
Yes. The IBO subject brief for AI lists technology as allowed in Papers 1 and 2 (AA’s Paper 1 does not).
This is only Paper 1 – where is Paper 2?
This paper demonstrates Paper 1 short-response modelling; Paper 2 extended-response and the exploration are separate components to drill.
Official references
| Resource | What to check |
|---|---|
| IBO Mathematics AI subject brief (first assessment 2021) | Confirm SL Paper 1’s 40% in 1.5 hours and the technology policy |
| https://www.tutorzone.com.hk/en-ib-math-ai-past-paper-drill-guide/ | IB Maths AI drilling guide: modelling and a 12-week plan |
| https://www.tutorzone.com.hk/en-ib-math-aa-sl-mock-paper/ | IB Maths AA SL mock paper (no-technology Paper 1) |
Related: IB practice area · IB Maths AI drilling guide · IB Maths AA SL mock · IB Maths AI HL mock · IB Maths AI SL Paper 2 (GDC)
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