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0580/32 Feb/Mar 2023, Question 4: Estimation

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 7 marks

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The question, in short

Six short items: round 6479 to the nearest 100, find a multiple of 13 in a range, take a reciprocal, evaluate an expression, give an irrational number, and estimate a division using 1 significant figure.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 1 mark

Round 6479 to the nearest 100.

  1. 16479 is between 6400 and 6500; the tens digit 7 rounds up
  2. 26479 ≈ 6500

Answer6500

Part (b) · 1 mark

State the multiple of 13 lying between 100 and 110.

  1. 113 × 8 = 104, which is between 100 and 110
  2. 2Multiple of 13 = 104

Answer104

Part (c) · 1 mark

Find the reciprocal of 0.6.

  1. 1Reciprocal of 0.6 = 1 ÷ 0.6 = 10/6 = 5/3
  2. 2= 1 2/3

Answer1 2/3

Part (d) · 1 mark

Work out 3 + 4 × 2.

  1. 1Multiply first: 4 × 2 = 8
  2. 23 + 8 = 11

Answer11

Part (e) · 1 mark

Give an irrational number whose value lies between 15 and 20.

  1. 115² = 225 and 20² = 400, so √n lies between 15 and 20 for 225 < n < 400
  2. 2300 is not a square number, so √300 is irrational
  3. 3√300 ≈ 17.32, an irrational number between 15 and 20

AnswerAny irrational number between 15 and 20

Part (f) · 2 marks

Round 423.8, 78.4 and 23.5 to 1 significant figure, then estimate (423.8 − 78.4) ÷ 23.5, showing working.

  1. 1423.8 ≈ 400, 78.4 ≈ 80, 23.5 ≈ 20
  2. 2(400 − 80)/20 = 320/20
  3. 3= 16

Answer16

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