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0580/41 May/Jun 2024, Question 3: Algebraic Fractions

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 13 marks

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The question, in short

Answer four algebra items: evaluate a formula, combine and simplify algebraic fractions, expand a product with a squared bracket, and simplify a negative fractional power.

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

Part (ai) · 2 marks

Substitute x = 5 and y = 8 into C = 1/4 xy² and calculate C.

  1. 1C = 1/4 × 5 × 8²
  2. 2= 1/4 × 5 × 64 = 80

Answer80

Part (aii) · 2 marks

Given C = 15 and x = 2.4, solve for the positive y in C = 1/4 xy².

  1. 115 = 1/4 × 2.4 × y²
  2. 2y² = 15 × 4 ÷ 2.4 = 25
  3. 3y = 5

Answer5

Part (b) · 3 marks

Combine 4/(x − 1) − 3/(2x + 5) into one fraction in simplest form.

  1. 1Common denominator (x − 1)(2x + 5)
  2. 2[4(2x + 5) − 3(x − 1)] / ((x − 1)(2x + 5))
  3. 3= (8x + 20 − 3x + 3) / ((x − 1)(2x + 5))
  4. 4= (5x + 23)/((x − 1)(2x + 5))

Answer(5x + 23)/((x − 1)(2x + 5)) or (5x + 23)/(2x² + 3x − 5)

Part (c) · 3 marks

Expand and simplify (2x + 3)(4 − x)².

  1. 1(4 − x)² = 16 − 8x + x²
  2. 2(2x + 3)(x² − 8x + 16) = 2x³ − 16x² + 32x + 3x² − 24x + 48
  3. 3= 2x³ − 13x² + 8x + 48

Answer2x³ − 13x² + 8x + 48

Part (d) · 3 marks

Simplify (y⁸/(16x¹⁶))^(−3/4), giving a simplified expression.

  1. 1(y⁸/(16x¹⁶))^(−3/4) = (16x¹⁶/y⁸)^(3/4)
  2. 2Fourth root: 2x⁴/y²
  3. 3Cube: (2x⁴/y²)³ = 8x¹²/y⁶

Answer8x¹²/y⁶ or 8x¹²y⁻⁶

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Also searched as: 0580/41/M/J/24 · 0580_s24_qp_41 · 0580 s24 41 · question 3.
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