中文（繁體）
中文（简体）
English
IB Maths AA SL Past Papers & Drilling (Paper 2): GDC Extended-Response Questions with Answers
TUTORZONE ORIGINAL DRILLING MOCK · IB MATHS AA (ANALYSIS AND APPROACHES) SL PAPER 2 GDC PAPER
Written to the IBO subject brief (first assessment 2021): AA Paper 2 requires the graphic display calculator, with a short-response Section A and an extended-response Section B; SL runs 1 h 30 min for 80 marks and 40%. Paper 1 is the no-technology paper, also 80 marks. This mock has 10 questions (6 in Section A, 4 in Section B, 80 marks) with GDC method notes, answers and drilling technique.
What is in IB Maths AA SL Paper 2?
Direct answer: 1 h 30 min, 80 marks, 40%, with the graphic display calculator required: a compulsory short-response Section A and an extended-response Section B. Paper 1 carries the same 80 marks but bans technology.
Assessment at a glance (2027)
| Component | Content | Weighting | Duration |
|---|---|---|---|
| Paper 1 (no technology) | Compulsory short- and extended-response questions; 80 marks | SL 40% | 1.5 h |
| Paper 2 (this paper, GDC required) | Short-response Section A + extended-response Section B; 80 marks | SL 40% | 1.5 h |
| Exploration (internal assessment) | 15 recommended hours within the 150-hour course | 20% | during the course |
IB Maths AA SL Paper 2 drilling technique: decide first whether the question wants the GDC or algebra – roots, intersections, definite integrals, normal probabilities and inverse functions go to the GDC; proofs, simplification and exact values still need written steps. Give every numerical answer to three significant figures (one decimal place for angles) with units. Check Section A before moving on, because Section B builds on it.
How this paper was built
This is a TutorZone original drilling mock: the questions follow the IB Maths AA SL Paper 2 format and the answers are our own, not IB past papers, marking references or IB publications.
Every numerical answer here was computed and cross-checked independently – normal probabilities, regression predictions and the total-distance kinematics answer included – so no key can drift from the question data.
Pacing
| Section | Marks | Suggested time | What to do first |
|---|---|---|---|
| Paper 1 (no technology) | SL 40% | analytic work: exact surds, fractions and algebra | tests hand manipulation and proof |
| Paper 2 (this paper, GDC required) | SL 40% | about 40 min on Section A, 45 min on Section B, 5 min to check | sketch or model first, then GDC and interpretation |
| Exploration (internal assessment) | 20% | work in stages, never in the last two weeks | own topic, modelling and reflection |
Should I start with Section A or Section B?
Direct answer: Section A first (short response, 8 marks each) in about 40 minutes, then Section B (extended response, 32 marks) in about 45, leaving 5 minutes to check. Section B often uses Section A results, so working in order saves time.
Section A: short-response questions (6 questions, 48 marks)
8 marks each, about 40 minutes; decide GDC or algebra before you start.
Question 1 (8 marks)
Let x² − 6x + 4 = 0. Use your graphic display calculator to find both roots, correct to three significant figures.
Question 2 (8 marks)
Let f(x) = x³ − 9x² + 24x − 16. (a) Find f′(x). (b) Find the coordinates of the local maximum and the local minimum, and state which is which.
Question 3 (8 marks)
Find the area of the region enclosed by the curves y = 2x and y = x². (Hint: find the intersections on the GDC first.)
Question 4 (8 marks)
A geometric sequence has third term 12 and sixth term 96. Find the common ratio r, the first term u₁ and the sum of the first eight terms S₈.
Question 5 (8 marks)
In triangle ABC, AB = 7 cm, AC = 9 cm and angle BAC = 52°. Find BC and the area of the triangle, correct to three significant figures.
Question 6 (8 marks)
The random variable X follows a normal distribution with mean 50 and standard deviation 8. (a) Find P(X > 60). (b) Find the value that only 10% of observations exceed.
Section B: extended-response questions (4 questions, 32 marks)
8 marks each, about 45 minutes; write the model, the working and the interpretation.
Question 1 (8 marks)
The temperature T (°C) of a hot drink t minutes after it is poured is modelled by T(t) = 20 + 60e^(−0.05t). (a) Find the temperature when t = 10. (b) Find how long it takes to cool to 30 °C.
Question 2 (8 marks)
A school relates weekly drilling hours x to mock-exam marks y with the least-squares regression line y = 2.4x + 1.3, for x between 2 and 10 hours. (a) Predict the mark for 12 hours a week. (b) Interpret the gradient 2.4 and comment on the reliability of the prediction in (a).
Question 3 (8 marks)
For two events A and B, P(A) = 0.6, P(B) = 0.5 and P(A ∩ B) = 0.3. (a) Find P(A | B). (b) Find P(A ∪ B). (c) Determine whether A and B are independent, giving a reason.
Question 4 (8 marks)
A particle moves in a straight line so that its displacement in metres is s(t) = t³ − 6t² + 9t, with t in seconds. (a) Find the velocity and acceleration at t = 2. (b) Find the total distance travelled in the first 2 seconds.
Which topics does this paper drill?
Direct answer: GDC roots and the discriminant, derivatives and extrema, definite integrals and areas, geometric sequences, the cosine rule, the normal and inverse-normal distributions, exponential models, least-squares regression, conditional probability and independence, and kinematics total distance.
Section A answers and GDC methods
Question 1
(1) GDC method: use the polynomial root finder, or graph y = x² − 6x + 4 and read the x-intercepts (4 marks); (2) roots: x = 5.24 and x = 0.764 (4 marks). Check: 5.236 + 0.764 = 6.000 = −b/a, and the discriminant 36 − 16 = 20 > 0, so there are two real roots.
Question 2
(a) f′(x) = 3x² − 18x + 24 (3 marks). (b) f′(x) = 0 gives 3(x − 2)(x − 4) = 0, so x = 2 or x = 4 (2 marks); f(2) = 4 and f(4) = 0 (2 marks); f″(x) = 6x − 18, so f″(2) = −6 < 0 makes (2, 4) the local maximum and f″(4) = 6 > 0 makes (4, 0) the local minimum (1 mark).
Question 3
(1) Intersections: 2x = x² gives x(x − 2) = 0, so x = 0 or x = 2 (2 marks); (2) set up: area = ∫₀² (2x − x²) dx (2 marks); (3) evaluate: [x² − x³/3]₀² = 4 − 8/3 = 4/3 ≈ 1.33 (4 marks). The GDC will evaluate the definite integral, but the method marks need the integral written down.
Question 4
(1) u₆ ÷ u₃ = r³ = 96 ÷ 12 = 8, so r = 2 (3 marks); (2) u₁ = u₃ ÷ r² = 12 ÷ 4 = 3 (2 marks); (3) S₈ = 3(2⁸ − 1) ÷ (2 − 1) = 3 × 255 = 765 (3 marks).
Question 5
(1) Cosine rule: BC² = 7² + 9² − 2 × 7 × 9 × cos 52° = 130 − 126 cos 52° (4 marks); (2) BC = 7.24 cm (2 marks); (3) area = ½ × 7 × 9 × sin 52° = 24.8 cm² (2 marks). Check the angle mode is DEG before you start; a radian-mode GDC gets the cosine of 52° wrong.
Question 6
(a) Standardise: z = (60 − 50) ÷ 8 = 1.25 (2 marks), so P(X > 60) = 0.106 (2 marks). (b) Use the GDC inverse normal with area 0.9 to get x = 60.3 (4 marks). The normal functions take the standard deviation 8, not the variance 64.
Section B answers and marking points
Question 1
(a) T(10) = 20 + 60e^(−0.5) = 56.4 °C (4 marks). (b) 20 + 60e^(−0.05t) = 30 gives e^(−0.05t) = 1/6 (2 marks), so t = ln 6 ÷ 0.05 = 35.8 minutes (2 marks). Simplify to e^(−0.05t) = 1/6 before solving on the GDC – twice as fast as graphing.
Question 2
(a) y = 2.4 × 12 + 1.3 = 30.1 (2 marks). (b) Each extra hour of drilling raises the mark by 2.4 marks on average (3 marks); but x = 12 lies outside the data range 2-10 hours, so it is extrapolation and the relationship may not continue – the prediction is unreliable (3 marks).
Question 3
(a) P(A | B) = P(A ∩ B) ÷ P(B) = 0.3 ÷ 0.5 = 0.6 (3 marks). (b) P(A ∪ B) = 0.6 + 0.5 − 0.3 = 0.8 (2 marks). (c) P(A | B) = 0.6 = P(A), so knowing B does not change the probability of A and the events are independent (3 marks).
Question 4
(a) v(t) = s′(t) = 3t² − 12t + 9 (2 marks), so v(2) = 12 − 24 + 9 = −3 m/s (1 mark); a(t) = 6t − 12, so a(2) = 0 (1 mark). (b) s(1) = 4 and s(2) = 2, and the particle turns round at t = 1, so total distance = 4 + 2 = 6 metres (4 marks). Total distance needs both stages: add |s(1) − s(0)| and |s(2) − s(1)|. Writing s(2) − s(0) alone gives 2 m.
How many figures should answers carry?
Direct answer: Three significant figures (one decimal place for angles) unless an exact value is asked for, and always with units – 7.24 cm, 35.8 minutes, 6 metres.
Where these marks are usually lost
| Mistake | What it looks like | What it costs | Instead |
|---|---|---|---|
| Trigonometry without DEG mode | Evaluating cos 52° straight away | A radian-mode GDC gives a completely wrong side length | Set DEG or RAD first, then enter the angle |
| Calculator answer only | Copying the screen output | All method marks are lost, keeping only the answer mark | Write the formula, the substitution and the integral |
| Too many decimal places | Roots written to five or six decimals | IB wants three significant figures, so marks are deducted | Give every answer to three significant figures |
| Total distance as a displacement | Writing s(2) − s(0) | The return leg cancels out and removes half the distance | Add the absolute values of each stage |
How to use this paper
First drill: the full 1 h 30 min – 40 minutes on Section A, 45 on Section B – with no notes and only your own GDC model.
Mark it: check three-significant-figure answers and units, and confirm each solution shows a formula.
Second drill: redo three to seven days later, aiming to finish inside 1 h 20 min, and log the GDC steps you missed.
What should I do after drilling this paper?
Direct answer: Log the three classic slips (radian mode, calculator answer only, total distance written as a displacement); redo the paper in three to seven days inside 1 h 20 min; then drill the sibling GDC paper (AI SL Paper 2) or the AA HL hand-algebra paper.
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 AA SL Paper 2?
1 h 30 min, 80 marks, 40%, GDC required: a short-response Section A and an extended-response Section B, with numerical answers to three significant figures.
How do Papers 1 and 2 differ?
Paper 1 bans technology and tests hand manipulation and proof; Paper 2 requires the GDC and tests modelling, tool choice and interpretation.
Which GDC skills should I drill?
Polynomial roots, graph intersections, definite integrals, normal and inverse-normal, and statistics or regression – practised until you never open the manual.
Official references
| Resource | What to check |
|---|---|
| IB mathematics curriculum page (IBO) | Confirm the Paper 1-2 marks and weighting |
| IB Maths AA SL Paper 1 mock | no-technology hand algebra |
| IB Maths AI SL Paper 2 mock | the same-level GDC paper |
| Practice area | index of IB subject mocks |
Related: practice area · IB Maths AA SL Paper 1 · IB Maths AA HL · IB Maths AI SL Paper 2
Next step: find a tutor / register as a tutor
After drilling, the hard part is telling a conceptual error from a writing error. Tell us the year group, the school and your available times, and TutorZone will match you with a tutor who knows the HKEAA assessment requirements.
Demand for tutors in this subject is steady, and those who can explain the marking scheme and where marks are won are especially sought after. Register free; you pay only when a match succeeds.
