Lemmara logoLemmaraWorked solution

0580/31 Oct/Nov 2024, Question 1: Estimation

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 12 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Answer a set of short number questions: writing a large number in figures, rounding, picking numbers from a list, inserting brackets, estimating, standard form and prime factors.

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

Part (a) · 1 mark

Write six million and thirty in figures.

  1. 1Six million = 6 000 000
  2. 26 000 000 + 30 = 6 000 030

Answer6 000 030

Part (b) · 1 mark

Round 7.896 to 2 decimal places.

  1. 17.896: third decimal digit 6 rounds up
  2. 27.89 → 7.90

Answer7.90

Part (ci) · 1 mark

From the list, choose a multiple of 16.

  1. 116 × 3 = 48
  2. 248

Answer48

Part (cii) · 1 mark

From the list, choose a factor of 24.

  1. 124 ÷ 8 = 3
  2. 28 (or 24)

Answer8 or 24

Part (ciii) · 1 mark

From the list, choose a cube number.

  1. 12³ = 8
  2. 28

Answer8

Part (civ) · 1 mark

From the list, choose a prime number.

  1. 141 has no factors other than 1 and 41
  2. 241

Answer41

Part (d) · 1 mark

Insert one pair of brackets in 10 − 12 ÷ 4 + 2 = 8 to make it true.

  1. 112 ÷ (4 + 2) = 12 ÷ 6 = 2
  2. 210 − 2 = 8
  3. 310 − 12 ÷ (4 + 2) = 8

Answer10 − 12 ÷ (4 + 2) = 8

Part (e) · 2 marks

Round each value to 1 significant figure and estimate (596 × 0.047) ÷ √8.65, showing working.

  1. 1596 ≈ 600, 0.047 ≈ 0.05, 8.65 ≈ 9
  2. 2(600 × 0.05)/√9 = 30/3
  3. 3= 10

Answer10

Part (f) · 2 marks

Calculate (8 × 10⁶) × (3 × 10⁻²) and give the answer in standard form.

  1. 18 × 3 = 24
  2. 210⁶ × 10⁻² = 10⁴
  3. 324 × 10⁴ = 2.4 × 10⁵

Answer2.4 × 10⁵

Part (g) · 1 mark

Given 216 = 2³ × 3³, write 2160 as a product of prime factors.

  1. 12160 = 216 × 10
  2. 2= 2³ × 3³ × 2 × 5
  3. 3= 2⁴ × 3³ × 5

Answer2⁴ × 3³ × 5

Stuck on a step? Read the free lesson: Estimation

Practise more estimation questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on estimation

Also searched as: 0580/31/O/N/24 · 0580_w24_qp_31 · 0580 w24 31 · question 1.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.