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IB Maths AI SL Past Papers & Drilling (Paper 2): Modelling Questions with Answers
TUTORZONE ORIGINAL DRILLING MOCK · IB MATHS AI (APPLICATIONS AND INTERPRETATION) SL PAPER 2 GDC PAPER
Written to the IBO subject brief (first assessment 2021): AI Paper 2 is extended-response and requires the graphic display calculator; SL runs 1 h 30 min for 80 marks and 40% (Paper 1 carries the same 80 marks and 40%). This mock has 10 real-context modelling questions (80 marks) with answers, model assumptions and interpretation.
What is in IB Maths AI SL Paper 2?
Direct answer: 1 h 30 min, 80 marks, 40% of compulsory extended-response questions with the GDC required, all set in real contexts. Paper 1 is also 80 marks and 40% but is short-response.
Assessment at a glance (2027)
| Component | Content | Weighting | Duration |
|---|---|---|---|
| Paper 1 (short-response, technology allowed) | Compulsory short-response questions; 80 marks | SL 40% | 1.5 h |
| Paper 2 (this paper, GDC required) | Compulsory extended-response questions in real contexts; 80 marks | SL 40% | 1.5 h |
| Exploration (internal assessment) | 15 recommended hours within the 150-hour course | 20% | during the course |
IB Maths AI SL Paper 2 drilling technique: write down what you need and which GDC function you will use before touching the keys, and always translate the answer back into the context (36.2 years becomes “about 36 years”; 0.292 becomes “29.2% take neither”). Percentage change, conditional probability and sample standard deviation are the three most common mark losses – three significant figures and units every time.
How this paper was built
This is a TutorZone original drilling mock: the questions follow the IB Maths AI SL Paper 2 format and the answers are our own, not IB past papers, marking references or IB publications.
Every numerical answer was computed and cross-checked independently (compound interest, depreciation, normal probabilities, exponential models, trigonometry, statistics, probability and solid geometry) so the key always matches the data.
Pacing
| Section | Marks | Suggested time | What to do first |
|---|---|---|---|
| Paper 1 (short-response, technology allowed) | SL 40% | short, single-step questions | core skills and graph reading |
| Paper 2 (this paper, GDC required) | SL 40% | 10 questions at about 8 min each, 10 min to check | state the model and assumptions, then compute and interpret |
| Exploration (internal assessment) | 20% | work in stages: fix the topic before collecting data | model real data and reflect on the limits |
How does AI Paper 2 differ from AA Paper 2?
Direct answer: Both require the GDC and both are 80 marks / 40% at SL. AA splits into a short-response Section A and an extended Section B and rewards hand algebra; AI is modelling throughout and rewards assumptions and interpretation.
Paper 2 (10 questions, 80 marks, 8 marks each)
All extended response: state the model and assumptions, compute, then interpret in context.
Question 1 (8 marks)
USD 8000 is invested at 3.2% per year compounded quarterly for 5 years. (a) Find the value after 5 years, to the nearest dollar. (b) Find the overall percentage increase over the 5 years.
Question 2 (8 marks)
A machine worth HKD 260 000 depreciates by 15% each year. (a) Find its value after 4 years, to three significant figures. (b) Find the first year in which its value falls below HKD 100 000.
Question 3 (8 marks)
Systolic blood pressure (mmHg) of adults in a city follows a normal distribution with mean 120 and standard deviation 15. (a) Find the probability that a reading is below 100. (b) Find the probability that a reading lies between 100 and 140.
Question 4 (8 marks)
The population of an island is modelled by P(t) = 25000e^(0.013t), with t in years. (a) Find the population after 20 years. (b) Find the time taken for the population to reach 40000.
Question 5 (8 marks)
A wheelchair ramp is 8 m long and rises at 12° to the horizontal. (a) Find the height and the horizontal length of the ramp, to three significant figures. (b) If the regulations require a height of 2 m, find the angle the ramp makes with the horizontal.
Question 6 (8 marks)
A ball is thrown vertically upwards so that its height in metres is h(t) = −4.9t² + 18t + 1.2, with t in seconds. (a) Find the maximum height above the ground and when it occurs. (b) Find when the ball hits the ground.
Question 7 (8 marks)
Five students drill for 12, 15, 18, 20 and 22 hours a week. (a) Find the mean, the median and the interquartile range. (b) Find the standard deviation to three significant figures and state which value to use.
Question 8 (8 marks)
Of 120 students, 70 take mathematics, 45 take physics and 30 take both. One student is chosen at random. (a) Find the probability that they take both. (b) Given that they take mathematics, find the probability that they also take physics. (c) Find the probability that they take neither.
Question 9 (8 marks)
The amount of a drug in the blood (mg) is modelled by A(t) = 200 × 0.88^t, with t in hours. (a) Find the amount 6 hours after the dose. (b) Find how long it takes for the amount to fall below 50 mg for the first time.
Question 10 (8 marks)
A cone has base radius 5 cm and slant height 13 cm. (a) Find the height of the cone. (b) Find its volume and total surface area, to three significant figures.
Which topics does this paper drill?
Direct answer: Compound interest and depreciation, normal probabilities, exponential growth and decay, trigonometry of ramps and gradients, quadratic projectile models, summary statistics and standard deviation, conditional probability, and cone volume and surface area.
Paper 2 answers and modelling points
Question 1
(a) Quarterly rate = 0.032 ÷ 4 = 0.008 with 4 × 5 = 20 periods (3 marks); value = 8000(1.008)²⁰ = USD 9382 (3 marks). (b) Increase = (9382 − 8000) ÷ 8000 × 100% = 17.3% (2 marks).
Question 2
(a) V(4) = 260000 × 0.85⁴ = HKD 136 000 (3 marks). (b) 0.85^t < 100000 ÷ 260000 = 0.3846 (2 marks), so t > ln 0.3846 ÷ ln 0.85 = 5.88 (2 marks), which makes year 6 the first year below HKD 100 000 (1 mark).
Question 3
(a) Standardise: z = (100 − 120) ÷ 15 = −1.33 (2 marks), so the probability is 0.0912 (2 marks). (b) P(100 < X < 140) = 0.818 (4 marks). Standardise both bounds and subtract, and sketch the normal curve with the required area shaded – far safer than memorising formulae.
Question 4
(a) P(20) = 25000e^0.26 = 32400 people (3 marks). (b) 25000e^(0.013t) = 40000 gives e^(0.013t) = 1.6 (2 marks), so t = ln 1.6 ÷ 0.013 = 36.2 years (3 marks).
Question 5
(a) Height = 8 sin 12° = 1.66 m and horizontal length = 8 cos 12° = 7.83 m (4 marks). (b) sin θ = 2 ÷ 8 = 0.25 (2 marks), so θ = 14.5° (2 marks).
Question 6
(a) Vertex at t = 18 ÷ (2 × 4.9) = 1.84 s (2 marks) with maximum height 17.7 m (2 marks). (b) Solve −4.9t² + 18t + 1.2 = 0 and take the positive root: t = 3.74 s (4 marks). The GDC returns both roots; the negative one is meaningless, so state why you keep the positive root.
Question 7
(a) Mean = 87 ÷ 5 = 17.4 hours, median = 18 hours, interquartile range = 20 − 15 = 5 hours (4 marks). (b) 1-Var Stats gives s = 3.97 (sample) alongside σ = 3.56 (population); these five students are a sample, so take s = 3.97 (4 marks). Tell s from σ when you copy the GDC output – it is the classic AI Paper 2 slip.
Question 8
(a) P(both) = 30 ÷ 120 = 0.25 (2 marks). (b) P(physics | mathematics) = 30 ÷ 70 = 0.429 (3 marks). (c) Neither = 120 − 70 − 45 + 30 = 35 students, so the probability is 35 ÷ 120 = 0.292 (3 marks). A conditional probability divides by the given group only: 30/70, never 30/120.
Question 9
(a) A(6) = 200 × 0.88⁶ = 92.9 mg (3 marks). (b) 200 × 0.88^t < 50 gives 0.88^t < 0.25 (2 marks), so t > ln 0.25 ÷ ln 0.88 = 10.84 (2 marks): about 11 hours (1 mark).
Question 10
(a) Height = √(13² − 5²) = 12 cm (2 marks). (b) Volume = ⅓π(5²)(12) = 100π = 314 cm³ (3 marks); total surface area = πr(r + l) = π(5)(5 + 13) = 90π = 283 cm² (3 marks). Total surface area is the base plus the curved surface: πr² + πrl = πr(r + l). Do not drop the base.
Why is copying the GDC output so often penalised?
Direct answer: AI Paper 2 demands interpretation: taking σ instead of s, giving a ratio instead of a percentage change, dividing a conditional by the wrong total, or omitting units all count as unfinished. Write every answer as a meaningful sentence.
Where these marks are usually lost
| Mistake | What it looks like | What it costs | Instead |
|---|---|---|---|
| Answer not returned to context | Writing just 36.2 or 0.292 | All interpretation marks vanish | “about 36 years”, “29.2% take neither” |
| Wrong standard deviation | Copying σ from the GDC | Sample data needs s, so the number disagrees | Tell s from σ and use s for samples |
| Percentage change error | Writing 9382 ÷ 8000 | Answers 1.17 instead of 17.3% | Subtract the original, divide by the original, times 100% |
| Wrong denominator for a conditional | P(physics | maths) as 30 ÷ 120 | Understates the probability by more than half | Divide by the given group only: 30 ÷ 70 |
How to use this paper
First drill: the full 1 h 30 min, all 10 questions in order, keeping each to 8 minutes.
Mark it: check three-significant-figure answers, units and the interpretation sentence, then the four classic slips one by one.
Second drill: redo three to seven days later inside 1 h 20 min, then sit an AA SL Paper 2 and compare what each paper demands.
What should I do after drilling this paper?
Direct answer: Log the four recurring faults (no interpretation, wrong standard deviation, percentage-change error, wrong conditional denominator); redo in three to seven days inside 1 h 20 min; then drill AA SL Paper 2 (the sibling GDC paper) or AI SL Paper 1 (short response).
FAQ
Is this an IB past paper?
No. The questions and answers are TutorZone originals, not IB past papers, marking references or IB publications.
What is in IB Maths AI SL Paper 2?
1 h 30 min, 80 marks, 40%: all extended-response questions with the GDC required, every one set in a real context.
How do AI and AA Paper 2 differ?
Both use the GDC and carry 80 marks, but AA adds a short-response Section A and rewards hand algebra and proof, while AI is modelling throughout and rewards interpretation.
Why must answers carry units and context?
AI is built on the modelling cycle: turn the context into mathematics, compute, then translate the result back – the last step carries the interpretation marks.
Official references
| Resource | What to check |
|---|---|
| IB mathematics curriculum page (IBO) | Confirm the Paper 1-2 marks and weighting |
| IB Maths AI SL Paper 1 mock | short-response modelling |
| IB Maths AA SL Paper 2 mock | the same-level GDC paper |
| Practice area | index of IB subject mocks |
Related: practice area · IB Maths AI SL Paper 1 · IB Maths AI HL · IB Maths AA SL Paper 2
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