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0580/41 Oct/Nov 2024, Question 1: Solving Linear Equations

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 19 marks

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The question, in short

Answer a set of number and algebra questions: prime factorisation, HCF and LCM, simplifying expressions, solving two equations, and evaluating and rearranging a formula.

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

Part (ai) · 2 marks

Express 70 as a product of prime factors.

  1. 170 = 2 × 35
  2. 235 = 5 × 7
  3. 3So 70 = 2 × 5 × 7

Answer2 × 5 × 7

Part (aii) · 2 marks

Find the HCF of 70 and 112.

  1. 170 = 2 × 5 × 7
  2. 2112 = 2⁴ × 7
  3. 3HCF = 2 × 7 = 14

Answer14

Part (aiii) · 2 marks

Find the LCM of 70x⁴y² and 112x³y⁵.

  1. 170 = 2 × 5 × 7 and 112 = 2⁴ × 7
  2. 2LCM of 70 and 112 = 2⁴ × 5 × 7 = 560
  3. 3Highest powers: x⁴ and y⁵
  4. 4LCM = 560x⁴y⁵

Answer560x⁴y⁵

Part (bi) · 1 mark

Simplify a¹² ÷ a⁴.

  1. 1a¹² ÷ a⁴ = a¹²⁻⁴ = a⁸

Answera⁸

Part (bii) · 2 marks

Simplify 5/(2b) × (bc)/20.

  1. 1Multiply the tops and the bottoms: 5bc/(40b)
  2. 2Cancel b: 5c/40
  3. 3Divide top and bottom by 5: c/8

Answerc/8

Part (c) · 2 marks

Solve 4 + 2x = 15 for x.

  1. 12x = 15 − 4 = 11
  2. 2x = 11/2 = 5.5

Answer5.5 or 11/2 or 5 1/2

Part (d) · 3 marks

Solve (34 + 2x)/5 = 4 − x for x.

  1. 134 + 2x = 5(4 − x)
  2. 234 + 2x = 20 − 5x
  3. 37x = −14
  4. 4x = −2

Answer−2

Part (ei) · 2 marks

Given P = d + ∛(m²), find P when d = 7 and m = −8.

  1. 1P = 7 + ∛((−8)²) = 7 + ∛64
  2. 2P = 7 + 4 = 11

Answer11

Part (eii) · 3 marks

Rearrange P = d + ∛(m²) to make m the subject.

  1. 1P − d = ∛(m²)
  2. 2(P − d)³ = m²
  3. 3m = ±√((P − d)³)

Answer±√((P − d)³)

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Also searched as: 0580/41/O/N/24 · 0580_w24_qp_41 · 0580 w24 41 · question 1.
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