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4024/12 Oct/Nov 2020, Question 11: Standard Form

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

Work with numbers in standard form: convert 340 000, divide 4 × 10⁷ by 8 × 10²¹, and find k in 7 × 10ᵃ − 3 × 10ᵃ⁻¹ = k × 10ᵃ.

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Part (a) · 1 mark

Write 340 000 in standard form.

  1. 1340 000 = 3.4 × 100 000 = 3.4 × 10⁵

Answer3.4 × 10⁵

Part (b) · 2 marks

Evaluate (4 × 10⁷)/(8 × 10²¹), giving the answer in standard form.

  1. 1(4 × 10⁷)/(8 × 10²¹) = (4/8) × 10⁷⁻²¹ = 0.5 × 10⁻¹⁴
  2. 2= 5 × 10⁻¹⁵

Answer5 × 10⁻¹⁵

Part (c) · 1 mark

Given 7 × 10ᵃ − 3 × 10ᵃ⁻¹ = k × 10ᵃ, find the value of k.

  1. 13 × 10ᵃ⁻¹ = 0.3 × 10ᵃ
  2. 27 × 10ᵃ − 0.3 × 10ᵃ = 6.7 × 10ᵃ
  3. 3k = 6.7

Answer6.7

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