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0580/32 Oct/Nov 2022, Question 1: Compound Interest

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 15 marks

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The question, in short

From a given list pick numbers meeting five properties, round 0.003857 two ways, compute compound interest on $16000 at 3.8% for 5 years, factorise 48, find LCM of 48 and 126, and give bounds for m = 28.5 tonnes.

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

Part (ai) · 1 mark

From the list, identify a number divisible by 8.

  1. 180 = 8 × 10
  2. 280 is a multiple of 8

Answer80

Part (aii) · 1 mark

From the list, identify a number that divides 46 exactly.

  1. 146 = 2 × 23
  2. 22 is a factor of 46

Answer2

Part (aiii) · 1 mark

From the list, identify a number that is a square.

  1. 149 = 7²
  2. 249 is a square number

Answer49

Part (aiv) · 1 mark

From the list, identify a number that is a cube.

  1. 127 = 3³
  2. 227 is a cube number

Answer27

Part (av) · 1 mark

From the list, identify a prime number.

  1. 12 has exactly two factors, 1 and 2
  2. 22 is prime (29 is also prime)

Answer2 or 29

Part (bi) · 1 mark

Write 0.003857 rounded to 3 decimal places.

  1. 10.003 857: third decimal place is 3, next digit 8 ≥ 5
  2. 2Round up: 0.004

Answer0.004

Part (bii) · 1 mark

Write 0.003857 rounded to 3 significant figures.

  1. 1First significant figure is 3: 0.003 857
  2. 23 s.f.: 0.00385|7 → round up
  3. 3= 0.00386

Answer0.00386

Part (c) · 2 marks

Calculate the value of $16000 invested at 3.8% per year compound interest after 5 years.

  1. 1Value = 16 000 × 1.038⁵
  2. 2= 19 279.98...
  3. 3≈ $19 280

Answer19 300 or 19 280 or 19 279.98 to 19 279.99

Part (di) · 2 marks

Express 48 as a product of its prime factors.

  1. 148 = 2 × 24 = 2 × 2 × 12
  2. 2= 2 × 2 × 2 × 6 = 2 × 2 × 2 × 2 × 3
  3. 348 = 2⁴ × 3

Answer2 × 2 × 2 × 2 × 3 or 2⁴ × 3

Part (dii) · 2 marks

Find the lowest common multiple of 48 and 126.

  1. 148 = 2⁴ × 3
  2. 2126 = 2 × 3² × 7
  3. 3LCM = 2⁴ × 3² × 7
  4. 4= 1008

Answer1008

Part (e) · 2 marks

Complete the inequality giving the lower and upper bounds of m, where m = 28.5 tonnes to 1 decimal place.

  1. 1Accuracy is 0.1 tonnes, so half of 0.1 = 0.05
  2. 2Lower bound = 28.5 − 0.05 = 28.45
  3. 3Upper bound = 28.5 + 0.05 = 28.55

Answer28.45 ≤ m < 28.55

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Also searched as: 0580/32/O/N/22 · 0580_w22_qp_32 · 0580 w22 32 · question 1.
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