IB Maths AI SLTopic 1 — Number & AlgebraPaper 1 & 2Exam-saver skill~5 min read
Accuracy & Estimation
Round each number to 1 s.f., do the easy mental sum — that’s your estimate. Use it to (a) sanity-check calculator answers and (b) pick how many s.f. or d.p. to give in your final answer.
📘 What you need to know
Estimation method: round every value to 1 s.f., then compute in your head.
Use estimates to catch errors: if your calculator says 1910 but the estimate is 192, something’s wrong (probably forgot to square or pressed the wrong key).
A length is calculated as 142.7385 cm. State it to an accuracy suitable for (a) a sewing pattern, (b) a school report.
(a) sewing — mm precision is standard142.7 cm (1 d.p., or 1427 mm)(b) school report — IB default is 3 s.f.143 cm (3 s.f.)(a) 142.7 cm (b) 143 cmmatch accuracy to context — over-precise looks silly, under-precise loses marks.
WE 5
Use estimation to catch a calculator error
A student computes 3.14 × 7.8² and writes 1910.84. Use estimation to check whether this is reasonable.
Estimate (round to 1 s.f.)3.14 ≈ 3, 7.8 ≈ 83 × 8² = 3 × 64 = 192Compare with 1910.841910.84 is ~10× too big — error!Recompute3.14 × 7.8² = 3.14 × 60.84 = 191.04correct answer ≈ 191 (3 s.f.)student probably squared 7.8 then multiplied by 31.4 (typo) instead of 3.14.
WE 6
Estimate a real-world quantity
A swimming pool measures roughly 25 m × 12 m × 1.5 m deep. Estimate its volume in litres. (1 m³ = 1000 L)
Volume in m³V = 25 × 12 × 1.5 = 300 × 1.5 = 450 m³Convert to litres450 × 1000 = 450 000 LRound to 1 s.f. for estimate≈ 500 000 Lgood for a rough idea (water bill, refill time). For precise capacity you’d measure properly.
💡 Top tips
Always estimate big calculations before trusting the calculator — catches typos and bracket errors.
1 s.f. is enough — don’t try to round to 2 or 3 s.f. mentally, you’ll lose the speed advantage.
For π, use 3; for √2, use 1.4; for e, use 3 — quick mental shortcuts.
Match accuracy to context: money 2 d.p., people whole numbers, IB default 3 s.f.
⚠ Common mistakes
Skipping the estimate and trusting whatever the calculator shows — even a digit out of place gives a wildly wrong answer that’s easy to miss.
Rounding too precisely: estimating 4783 ≈ 4800 isn’t easier than 4783 itself. Stick to 1 s.f.
Giving the estimate as the final answer: 1 000 000 is an estimate, not the answer to 4783 × 218.
Rounding mid-calculation in the exact answer: keep full precision until the very last step.
Up next: Solving Equations using a GDC. Once you can estimate, you’ll spot when the GDC’s “solver” gives a sensible answer (one root in range) versus when it’s missed others — a key Paper 2 skill.
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