IB Mathematics SL 1.6 Approximation decimal places, significant figures AI SL Paper 1- Exam Style Questions- New Syllabus
Question
Most appropriate topic codes (IB Mathematics: applications and interpretation):
• SL 1.6: Degree of accuracy and calculation of measurement errors — entire question
▶️ Answer/Explanation
Step 1 – Bounds on time:
Time \(t = 1.2\) s (to nearest \(0.1\) s) ⇒ bounds:
\(t_{\min} = 1.15\) s, \(t_{\max} = 1.25\) s.
Step 2 – Calculate speed bounds:
Speed = distance ÷ time.
Minimum speed = \(\frac{10}{1.25} = 8.0\ \text{m s}^{-1}\).
Maximum speed = \(\frac{10}{1.15} \approx 8.696\ \text{m s}^{-1}\).
Step 3 – Compare with speed limit:
Possible speeds range from \(8.0\) to \(8.696\ \text{m s}^{-1}\).
Since \(8.0 < 8.3 < 8.696\), the car’s speed could be either below or above \(8.3\ \text{m s}^{-1}\), depending on the exact time.
Step 4 – Certainty?
If the actual time were \(1.25\) s, speed = \(8.0\ \text{m s}^{-1}\) (< limit).
Therefore, it is not certain that the car exceeded the speed limit.
✅ Answer:
\(\boxed{\text{It is not certain that the car was exceeding the speed limit.}}\)
Justification: The maximum possible time (1.25 s) gives a speed of \(8.0\ \text{m s}^{-1}\), which is below the limit, so exceeding is not guaranteed from the given rounded measurement.