IB Maths AI SL Topic 1 — Number & Algebra Paper 1 & 2 Exam-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).
Choose accuracy by context: people → whole numbers, money (USD/EUR/GBP) → 2 d.p., engineering → s.f., default IB answer → 3 s.f.
Keep extra precision in working, round only at the end — early rounding causes wrong final answers.
Estimates are never the final answer — they just check the order of magnitude.
Symbol: ≈ means “approximately equal to”. Use it whenever you’ve rounded.

How to estimate quickly

The estimation rule Round each number to 1 s.f. → do the mental sum → answer ≈ your estimate

Estimation isn’t about being exactly right — it’s about being in the right ballpark, fast.

🧭 Recipe — estimate & check

Round each value to 1 s.f. (e.g. 47 → 50, 0.038 → 0.04, 218 → 200).
Do the mental sum with the rounded values.
Compute the exact answer on your GDC.
Compare: if exact is the same order of magnitude as estimate (within ~50%), you’re fine.
If WAY off, recheck the GDC input — usually a typo, missing bracket, or wrong button.

Worked examples

WE 1

Estimate a product

Estimate 4783 × 218.

Round each to 1 s.f. 4783 ≈ 5000 218 ≈ 200 Multiply 5000 × 200 = 1 000 000 ≈ 1 000 000 exact = 1 042 694 — estimate is within 5%.

WE 2

Estimate a quotient

Estimate 597 ÷ 31.

Round each to 1 s.f. 597 ≈ 600 31 ≈ 30 Divide 600 ÷ 30 = 20 ≈ 20 exact = 19.26 — very close.

WE 3

Estimate a multi-step expression

Estimate (38.4 + 61.2) × 19.7.

Round each 38.4 ≈ 40, 61.2 ≈ 60, 19.7 ≈ 20 Bracket first, then multiply (40 + 60) × 20 = 100 × 20 = 2000 ≈ 2000 exact = 1962.12 — estimate within 2%.

WE 4

Choosing appropriate accuracy

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 standard 142.7 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 cm match 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 ≈ 8 3 × 8² = 3 × 64 = 192 Compare with 1910.84 1910.84 is ~10× too big — error! Recompute 3.14 × 7.8² = 3.14 × 60.84 = 191.04 correct 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 m³ V = 25 × 12 × 1.5 = 300 × 1.5 = 450 m³ Convert to litres 450 × 1000 = 450 000 L Round to 1 s.f. for estimate ≈ 500 000 L good 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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