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4024/11 May/Jun 2021, Question 23: Standard Form

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 8 marks

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The question, in short

Use a = (b² + c)/d with b = 4 × 10², c = 6 × 10³, d = 2 × 10²; rearrange for b; then use m × 10⁴ + m × 10² = 36 360 to find m × 10⁴ − m × 10².

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Part (ai) · 3 marks

Substitute b = 4 × 10², c = 6 × 10³ and d = 2 × 10² into a = (b² + c)/d and give a in standard form.

  1. 1b² = (4 × 10²)² = 16 × 10⁴ = 160 000
  2. 2a = (160 000 + 6000)/(2 × 10²) = 166 000/200
  3. 3= 830 = 8.3 × 10²

Answer8.3 × 10²

Part (aii) · 3 marks

Rearrange a = (b² + c)/d to make b the subject.

  1. 1ad = b² + c
  2. 2b² = ad − c
  3. 3b = ±√(ad − c)

Answer±√(ad − c)

Part (b) · 2 marks

Given m × 10⁴ + m × 10² = 36 360, work out the value of m × 10⁴ − m × 10².

  1. 1m × 10 000 + m × 100 = 10 100m = 36 360
  2. 2m = 36 360 ÷ 10 100 = 3.6
  3. 33.6 × 10⁴ − 3.6 × 10² = 36 000 − 360 = 35 640

Answer35640

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Also searched as: 4024/11/M/J/21 · 4024_s21_qp_11 · 4024 s21 11 · question 23.
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