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0580/43 Oct/Nov 2024, Question 6: The Quadratic Formula and Completing the Square

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 9 marks

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The question, in short

Simplify an algebraic fraction product, expand and simplify a product of three binomials, and solve a quadratic equation to 2 decimal places showing working.

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

Part (a) · 2 marks

Simplify the product 24u/(5y) × 10/(3u).

  1. 124u × 10 = 240u and 5y × 3u = 15uy
  2. 2240u/(15uy) = 16/y

Answer16/y

Part (b) · 3 marks

Expand and simplify (x − 1)(x + 2)(x + 3).

  1. 1(x + 2)(x + 3) = x² + 5x + 6
  2. 2(x − 1)(x² + 5x + 6) = x³ + 5x² + 6x − x² − 5x − 6
  3. 3= x³ + 4x² + x − 6

Answerx³ + 4x² + x − 6

Part (c) · 4 marks

Solve 2x² + x − 5 = 0, showing working, giving answers to 2 decimal places.

  1. 1a = 2, b = 1, c = −5
  2. 2x = (−1 ± √(1² − 4 × 2 × (−5)))/(2 × 2) = (−1 ± √41)/4
  3. 3x = (−1 − 6.403)/4 = −1.85
  4. 4x = (−1 + 6.403)/4 = 1.35

Answerx = −1.85 or x = 1.35

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Also searched as: 0580/43/O/N/24 · 0580_w24_qp_43 · 0580 w24 43 · question 6.
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