中文（繁體）
中文（简体）
English
IB Maths AA HL Past Papers & Drilling (Paper 1): 10 No-Calculator Exact-Value Questions
TUTORZONE ORIGINAL MOCK PAPER · IB MATHEMATICS AA (ANALYSIS AND APPROACHES) HL PAPER 1
The big difference between IB Maths AA (Analysis and Approaches) and AI is that AA Paper 1 bans the calculator, so answers must be exact (surds, fractions, pi) and drilling centres on algebraic derivation and proof. AA HL: Paper 1 (no technology) 110 marks in 2 h at 30%, Paper 2 (technology) 110 marks in 2 h at 30%, Paper 3 (no technology) 55 marks in 1 h at 20%, and the exploration 20%. This set has 10 no-calculator practice questions written to the Paper 1 style (80 marks in this set) with exact answers.
What is in IB Maths AA HL Paper 1?
Direct answer: IB Maths AA (Analysis and Approaches) HL Paper 1 has no calculator: 110 marks, 2 hours, 30% of the subject; Paper 2 has technology at 110 marks, 2 hours, 30%; Paper 3 (HL only) has no technology at 55 marks, 1 hour, 20%; and the exploration is 20%. AA Paper 1’s answers must be exact (surd, fraction, pi) – the contrast with AI, where every paper allows the GDC.
Assessment at a glance (2027)
| Component | Content | Weighting | Duration |
|---|---|---|---|
| Paper 1 (no technology) | Compulsory short-response; HL 110 marks, 2 h, 30% | HL 30% / SL 40% | 2 h |
| Paper 2 (technology allowed) | Compulsory extended-response; HL 110 marks, 2 h, 30% | HL 30% / SL 40% | 2 h |
| Paper 3 (HL only, no technology) | Two compulsory extended problem-solving questions; 55 marks, 1 h, 20% | HL 20% (HL only) | 1 h |
| Mathematical exploration (IA) | 20% at both levels; 15 recommended hours | 20% (SL and HL) | 15 recommended hours |
The official HL Paper 1 runs 120 minutes for 110 marks; this set’s 10 questions work out at about 11 minutes each. No-calculator marks are rarely lost to slow arithmetic but to leaving a decimal where an exact value is wanted – AA answers are surds, fractions or pi, not approximations.
How this paper was built
This is a TutorZone original mock paper: the questions follow the AA structure (HL Paper 1, no calculator, 30% over 2 hours) and the answers are our own exact computations, not IBO past papers or official marking references.
Ten short-response questions for 80 marks in this set (the official HL Paper 1 runs 110 marks over 2 hours); every answer was recomputed programmatically and is given as an exact value (surd, fraction or pi), as AA Paper 1 requires.
Pacing
| Section | Marks | Suggested time | What to do first |
|---|---|---|---|
| Paper 1 (no technology) | HL 30% / SL 40% | about 110 min with 10 min checking | answers must be exact (surd, fraction, pi), not decimals |
| Paper 2 (technology allowed) | HL 30% / SL 40% | extended-response with the GDC | state the method before computing |
| Paper 3 (HL only, no technology) | HL 20% (HL only) | about 26 min per question | write the route and assumptions first |
| Mathematical exploration (IA) | 20% (SL and HL) | topic, derivation, computation, interpretation | choose a question open to mathematical investigation |
How many questions does this paper have, and how should the time be split?
Direct answer: 10 short-response questions for 80 marks in this set (the official HL Paper 1 is 110 marks in 2 hours); aim for 110 minutes with 10 to check (about 11 minutes each). Give every answer as an exact value (surd, fraction, pi).
Paper 1: no-calculator short-response (10 questions, 80 marks)
All compulsory; aim for 110 minutes with 10 to check. Answers must be exact.
Question 1 (8 marks)
Let the complex number z = 2 + 3i. Find z² and |z| (in surd form).
Question 2 (8 marks)
Let a = 3i − 4j and b = i + 2j. Find the dot product a·b and |a|.
Question 3 (8 marks)
A geometric sequence has first term 2 and common ratio 3. Find the sum of the first 5 terms.
Question 4 (8 marks)
Solve sin x = 1/2 for 0 ≤ x ≤ 2π, giving your answers in terms of π.
Question 5 (8 marks)
Let f(x) = x³ − 3x² + 2. Find f′(x) and f′(1).
Question 6 (8 marks)
Evaluate the definite integral ∫₁³ (2x + 3) dx.
Question 7 (8 marks)
Solve log₂(x) = 5.
Question 8 (8 marks)
Solve 2^(x+1) = 8.
Question 9 (8 marks)
Let f(x) = 2x + 1. Find the inverse function f⁻¹(x).
Question 10 (8 marks)
A bag contains 3 red and 5 blue balls. Two balls are drawn without replacement. Find the probability that both are red.
Where are the answers, and do they show the working?
Direct answer: every question is followed by an exact-answer block giving each step of the derivation with its marks (e.g. the complex-number item: 4 for the expansion, 4 for the modulus) plus the usual losses. Not just final answers.
Paper 1 exact answers
Question 1
(1) z² = (2+3i)² = 4 + 12i + 9i² = 4 + 12i − 9 = −5 + 12i (4 marks); (2) |z| = √(2² + 3²) = √13 (4 marks). i² = −1; expand the product term by term.
Question 2
(1) a·b = 3×1 + (−4)×2 = 3 − 8 = −5 (4 marks); (2) |a| = √(3² + (−4)²) = √25 = 5 (4 marks).
Question 3
S₅ = 2(3⁵ − 1) ÷ (3 − 1) = 2(243 − 1) ÷ 2 = 242 (8 marks). Use Sₙ = a(rⁿ − 1)/(r − 1).
Question 4
sin x = 1/2 on [0, 2π] gives x = π/6 and x = 5π/6 (4 marks each). Sine is also positive in the second quadrant: include π − π/6.
Question 5
(1) f′(x) = 3x² − 6x (4 marks); (2) f′(1) = 3 − 6 = −3 (4 marks). Differentiate term by term.
Question 6
∫(2x+3)dx = x² + 3x (4 marks); [x² + 3x]₁³ = (9 + 9) − (1 + 3) = 18 − 4 = 14 (4 marks).
Question 7
log₂(x) = 5 ⇔ x = 2⁵ = 32 (8 marks). Logarithm and exponential are inverse: log₂(x) = 5 means x = 2⁵.
Question 8
8 = 2³, so 2^(x+1) = 2³ (4 marks); x + 1 = 3 → x = 2 (4 marks). Make the base equal, then compare exponents.
Question 9
Let y = 2x + 1; swap x and y to get x = 2y + 1 (4 marks); solving gives y = (x − 1) ÷ 2, i.e. f⁻¹(x) = (x − 1)/2 (4 marks).
Question 10
P = 3/8 × 2/7 = 6/56 = 3/28 (8 marks). Without replacement the second denominator becomes 7.
Where are no-calculator marks most easily lost?
Direct answer: leaving a decimal where an exact value is wanted (1.41 instead of √2); comparing exponents before making the bases equal; and not changing the denominator in without-replacement probability. All three are exactness and method marks.
Where these marks are usually lost
| Mistake | What it looks like | What it costs | Instead |
|---|---|---|---|
| Leaving decimals | Writing 1.41 | AA Paper 1 wants surds, fractions or pi | Write √2, 3/28, π/6 as exact values |
| Different bases | Comparing exponents directly | Different bases cannot be equated directly | Make the base equal first, then compare exponents |
| Replacement probability | Dividing by 8 again | Without replacement the denominator drops each time | Use 7 for the second draw |
How to use this paper
First sit: no references, the full 120 minutes, no calculator.
Mark it: check every step, especially whether you replaced an exact value with a decimal.
Second sit: redo the paper three to seven days later, aiming for less time and fully exact answers.
What should I do after finishing this paper?
Direct answer: log every question where an exact value was missed; redo the paper three to seven days later aiming for fully exact answers; then drill Paper 2 and Paper 3 extended questions and the exploration by topic.
FAQ
Is this an IBO paper?
No. The questions, answers and mark allocation are TutorZone originals, not IBO past papers or marking references.
Does AA Paper 1 really ban the calculator?
Yes. AA Paper 1 has no technology and answers must be exact – the key contrast with AI, where every paper allows the GDC.
How many papers does AA HL have?
Three: Paper 1 (no technology) 30%, Paper 2 (technology) 30%, Paper 3 (no technology) 20%, plus the exploration at 20%.
Official references
| Resource | What to check |
|---|---|
| IBO Mathematics AA subject brief (first assessment 2021) | Confirm the SL/HL weightings, durations and the no-technology policy |
| https://www.tutorzone.com.hk/en-ib-math-aa-past-paper-drill-guide/ | IB Maths AA drilling guide: algebra and no-calculator answering |
| https://www.tutorzone.com.hk/en-ib-math-ai-sl-mock-paper/ | IB Maths AI SL mock (every paper allows the GDC) |
Related: IB practice area · IB Maths AA drilling guide · IB Maths AI SL mock · IB Maths AI HL mock · IB Maths AA SL Paper 2 (GDC)
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.
