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GCSE/Mathematics/Edexcel

N14Estimate answers; check using approximation and estimation

Notes

Estimation and checking calculations

Edexcel 1MA1 tests estimation across both tiers, especially Paper 1F and 1H non-calculator sections. The skill is rounding each input to 1 significant figure (1 s.f.), then computing.

Method

  1. Round each value to 1 s.f.
  2. Carry out the simpler calculation.
  3. State the estimate clearly.
  4. Optionally compare the estimate to the actual answer to spot input errors.

Worked example

Estimate 593 × 0.214 ÷ 7.83.

  • 593 ≈ 600
  • 0.214 ≈ 0.2
  • 7.83 ≈ 8

Estimate: 600 × 0.2 ÷ 8 = 120 ÷ 8 = 15.

Actual = 16.207..., so 15 is a good ballpark.

Useful rounding rules

  • Numbers ≥ 1: round to first non-zero digit, replacing rest with zeros (593 → 600).
  • Numbers < 1: round to first non-zero digit (0.0247 → 0.02).
  • Halves traditionally round up (4.5 → 5).

Why estimate?

  • To spot calculator key-press errors.
  • To "sanity-check" a final answer.
  • To do quick calculations when a precise value is unnecessary.

Common Edexcel mark-scheme phrasing

  • M1 for at least two values rounded to 1 s.f.
  • M1 for the simpler calculation set out.
  • A1 for the correct estimate.
  • B1 for stating whether the estimate is bigger or smaller than the actual.

Common mistakesCommon errors

  • Rounding inconsistently (some to 1 s.f., others to 2 s.f.).
  • Rounding 0.214 to 0 instead of 0.2 (forgetting the leading-zero rule).
  • Not simplifying enough — defeating the purpose of estimation.
  • Computing exactly and calling it an estimate.

AI-generated · claude-opus-4-7 · v3-edexcel-maths-leaves

Practice questions

Try each before peeking at the worked solution.

  1. Question 15 marks

    Basic estimate — Foundation

    Edexcel Paper 1F (non-calculator)

    (a) By rounding each number to 1 significant figure, estimate the value of (213 × 4.78) ÷ 19.6. (3 marks)
    (b) Without computing the exact answer, state whether your estimate is likely to be larger or smaller than the actual value. Justify briefly. (2 marks)

    Ask AI about this

    AI-generated · claude-opus-4-7 · v3-edexcel-maths-leaves

  2. Question 24 marks

    Estimating a square root

    Edexcel Paper 1H — Higher

    Estimate the value of √(48.7) × (3.92)² ÷ 9.76, showing each value rounded to 1 s.f. (4 marks)

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    AI-generated · claude-opus-4-7 · v3-edexcel-maths-leaves

  3. Question 34 marks

    Estimate involving small numbers

    Edexcel Paper 1F (non-calculator)

    Estimate 0.0287 × 411 ÷ 5.93 by rounding each to 1 s.f. (4 marks)

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    AI-generated · claude-opus-4-7 · v3-edexcel-maths-leaves

Flashcards

N14 — Estimate answers; check using approximation and estimation

7-card SR deck for Edexcel GCSE Mathematics (1MA1) — Leaves Batch 4 topic N14

7 cards · spaced repetition (SM-2)