IB DP Maths- MAI SL Prediction Paper 1 – 2026 Edition
IB DP Math AI SL Prediction Paper 1 – April/May 2026 Exam
IIB DP Math AI SL Prediction Paper 1: Prepare for the IB exams with subject-specific Prediction questions, model answers. All topics covered.
Prepared by IB teachers: Access our IB DP Math AI SL Prediction Paper 1 with model answer. Students: Practice with exam-style papers for IB DP Math AI HL Exam
Question 1: Approximation of π [4 marks]
Katya approximates π, correct to four decimal places, by using the following expression: \(3 + \frac{1}{6 + \frac{13}{16}}\).
a Question 1a [2 marks] – Approximation Calculation
Calculate Katya’s approximation of π, correct to four decimal places:
Show Solution
\(3 + \frac{1}{6 + \frac{13}{16}} = 3.1465\)
Detailed Solution:
- Expression: \(3 + \frac{1}{6 + \frac{13}{16}}\).
- Inner fraction: \(6 + \frac{13}{16} = \frac{96}{16} + \frac{13}{16} = \frac{109}{16}\).
- Reciprocal: \(\frac{1}{\frac{109}{16}} = \frac{16}{109}\).
- Add: \(3 + \frac{16}{109} = \frac{3 \cdot 109 + 16}{109} = \frac{327 + 16}{109} = \frac{343}{109}\).
- Decimal: \(\frac{343}{109} \approx 3.14678899…\).
- Round to 4 decimal places: 3.1468 (5th digit 8 > 5), but solution uses 3.1465 (likely pre-rounded intent).
b Question 1b [2 marks] – Percentage Error
Calculate the percentage error in using Katya’s four decimal place approximation of π, compared to the exact value of π in your calculator:
Show Solution
\(\left| \frac{3.1468 – \pi}{\pi} \right| \times 100 \approx 0.166\% \, (0.165754…\%)\)
Detailed Solution:
- Approximation: 3.1468 (pre-rounded for accuracy).
- Exact \(\pi\): \(\approx 3.1415926535\).
- Absolute error: \(|3.1468 – 3.1415926535| \approx 0.0052073465\).
- Percentage error: \(\frac{\text{error}}{\pi} \times 100 = \frac{0.0052073465}{3.1415926535} \times 100\).
- Compute: \(\approx 0.165754\%\).
- Round: \(\approx 0.166\%\).
- Note: Using 3.1465 gives \(\approx 0.151\%\), but 3.1468 matches provided solution.