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0580/31 May/Jun 2022, Question 1: Prime Factorization

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 15 marks

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The question, in short

Answer a set of short number questions covering place value, rounding, order of operations, factors, cubes, primes, roots, reciprocals, indices, prime factorisation, LCM and error intervals.

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

Part (a) · 1 mark

Write six and a half million using digits.

  1. 1Six and a half million = 6.5 × 1000000 = 6500000

Answer6500000

Part (b) · 1 mark

Round 6538 to the nearest ten.

  1. 16538 lies between 6530 and 6540; the units digit 8 rounds up
  2. 26540

Answer6540

Part (c) · 1 mark

Evaluate 6 × 5 + 12 ÷ 3.

  1. 16 × 5 + 12 ÷ 3 = 30 + 4
  2. 2= 34

Answer34

Part (di) · 1 mark

From the given list, choose a factor of 48.

  1. 148 ÷ 16 = 3, so 16 is a factor of 48

Answer16

Part (dii) · 1 mark

From the given list, choose a cube number.

  1. 164 = 4 × 4 × 4 = 4³, so 64 is a cube number

Answer64

Part (diii) · 1 mark

From the given list, choose a prime number.

  1. 129 has no factors other than 1 and 29, so 29 is prime

Answer29

Part (e) · 1 mark

Calculate the square root of 0.001225.

  1. 1√0.001225 = 0.035 (since 0.035² = 0.001225)

Answer0.035

Part (f) · 1 mark

State the reciprocal of 8.

  1. 1Reciprocal of 8 = 1/8 = 0.125

Answer1/8 or 0.125

Part (g) · 1 mark

Evaluate 8 to the power 0.

  1. 1Any non-zero number to the power 0 is 1: 8⁰ = 1

Answer1

Part (hi) · 2 marks

Express 180 as a product of prime factors.

  1. 1180 = 2 × 90 = 2 × 2 × 45 = 2 × 2 × 3 × 15
  2. 2180 = 2 × 2 × 3 × 3 × 5

Answer2 × 2 × 3 × 3 × 5

Part (hii) · 2 marks

Find the LCM of 160 and 180.

  1. 1160 = 2 × 2 × 2 × 2 × 2 × 5 = 2⁵ × 5
  2. 2180 = 2² × 3² × 5
  3. 3LCM = 2⁵ × 3² × 5 = 32 × 9 × 5
  4. 4= 1440

Answer1440

Part (i) · 2 marks

Complete the double inequality giving the possible values of m when 473 tonnes is rounded to the nearest tonne.

  1. 1Nearest tonne: half a tonne either side of 473
  2. 2472.5 ≤ m < 473.5

Answer472.5 and 473.5

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Also searched as: 0580/31/M/J/22 · 0580_s22_qp_31 · 0580 s22 31 · question 1.
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