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4024/21 May/Jun 2023, Question 6: Constructing Equations

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 11 marks

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The question, in short

Four separate algebra tasks: combine like terms, use a purchase and change scenario to set up and solve for m, use direct proportion with a cube to find a new y, and combine two algebraic fractions into one.

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

Part (a) · 2 marks

Collect the u terms and the w terms to reduce the expression to its simplest form.

  1. 1u terms: 3u − 5u = −2u
  2. 2w terms: −6w + 9w = 3w
  3. 33w − 2u

Answer3w − 2u

Part (b) · 4 marks

Using 40 cents per pencil and 85 cents per pen, with $20 paid and $2.20 change, build an equation in m, solve it, and state how many pencils are bought.

  1. 1Amount spent = 2000 − 220 = 1780 cents
  2. 240m + 12 × 85 = 1780
  3. 340m + 1020 = 1780
  4. 440m = 760
  5. 5m = 19

Answer19

Part (c) · 2 marks

Given y varies directly with the cube of (x − 2) and y = 12 when x = 4, work out y at x = 5.

  1. 1y = k(x − 2)³
  2. 212 = k × 2³, so k = 12/8 = 3/2
  3. 3x = 5: y = 3/2 × 3³
  4. 4y = 81/2 = 40.5

Answer81/2 or 40 1/2 or 40.5

Part (d) · 3 marks

Combine 3/(x − 1) and 4/(2x + 1) by subtraction into one fraction, fully simplified.

  1. 1Common denominator (x − 1)(2x + 1)
  2. 2= (3(2x + 1) − 4(x − 1))/((x − 1)(2x + 1))
  3. 3= (6x + 3 − 4x + 4)/((x − 1)(2x + 1))
  4. 4= (2x + 7)/((x − 1)(2x + 1))

Answer(2x + 7)/((x − 1)(2x + 1)) or (2x + 7)/(2x² − x − 1)

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

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