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4024/22 Oct/Nov 2020, Question 5: Constructing Equations

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 8 marks

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The question, in short

Solve three algebra tasks: form and solve an equation about stamps to find Sanjay's count, simplify a division of algebraic fractions in t and v, and simplify a rational expression in x.

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

Part (a) · 3 marks

Using n for Gita's stamps, write an equation from the given relationships totalling 108, solve for n, then find Sanjay's stamps.

  1. 1n + 2n + (2n − 7) = 108
  2. 25n − 7 = 108
  3. 35n = 115, n = 23
  4. 4Sanjay has 2 × 23 − 7 = 39 stamps

Answer39

Part (b) · 2 marks

Simplify the quotient of 6t²v³ over 5 by 3t² over v².

  1. 1(6t²v³)/5 × v²/(3t²)
  2. 2= 6t²v⁵/(15t²)
  3. 3= 2v⁵/5

Answer2v⁵/5

Part (c) · 3 marks

Simplify the fraction with numerator x² − 16 and denominator 3x² + 10x − 8.

  1. 1x² − 16 = (x + 4)(x − 4)
  2. 23x² + 10x − 8 = (3x − 2)(x + 4)
  3. 3Cancel (x + 4): (x − 4)/(3x − 2)

Answer(x − 4)/(3x − 2)

Stuck on a step? Read the free lesson: Constructing Equations

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Also searched as: 4024/22/O/N/20 · 4024_w20_qp_22 · 4024 w20 22 · question 5.
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