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0580/42 Oct/Nov 2021, Question 6: Solving Linear Equations

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 17 marks

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The question, in short

Work through algebra tasks: solve an equation and an inequality, change the subject of a formula, prove a divisibility claim, complete the square, locate a maximum, and handle a proportional change.

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

Part (ai) · 3 marks

Find the value of x that satisfies 4(2x − 3) = 24.

  1. 18x − 12 = 24
  2. 28x = 36
  3. 3x = 4.5

Answer4.5, 4 1/2 or 9/2

Part (aii) · 2 marks

Find the range of x values satisfying 6x + 14 > 6.

  1. 16x > 6 − 14
  2. 26x > −8
  3. 3x > −4/3

Answerx > −4/3 or x > −1 1/3

Part (b) · 3 marks

Rewrite V = 2x³ − 3y³ so that y is expressed in terms of V and x.

  1. 13y³ = 2x³ − V
  2. 2y³ = (2x³ − V)/3
  3. 3y = ∛((2x³ − V)/3)

Answer∛((2x³ − V)/3)

Part (c) · 3 marks

Prove that (2n − 5)² − 13 always divides by 4 when n is an integer.

  1. 1(2n − 5)² = 4n² − 10n − 10n + 25 = 4n² − 20n + 25
  2. 2(2n − 5)² − 13 = 4n² − 20n + 12
  3. 3= 4(n² − 5n + 3), which is a multiple of 4 for all integers n

Answer4(n² − 5n + 3) or correct explanation linked to expression

Part (di) · 3 marks

Express 5 + 12x − 2x² as q − 2(x + p)² and state p and q.

  1. 1q − 2(x + p)² = q − 2x² − 4px − 2p²
  2. 2Compare x terms: −4p = 12, so p = −3
  3. 3Constant: q − 2 × 9 = 5, so q = 23
  4. 45 + 12x − 2x² = 23 − 2(x − 3)², p = −3 and q = 23

Answerp = −3 and q = 23

Part (dii) · 1 mark

Give the coordinates of the highest point on y = 5 + 12x − 2x².

  1. 1Maximum when x − 3 = 0: maximum point (3, 23)

Answer(3, 23)

Part (e) · 2 marks

Energy varies with the square of speed; find the percent increase in energy when speed rises by 30%.

  1. 1E = kv², new speed = 1.3v
  2. 2New energy = k(1.3v)² = 1.69kv²
  3. 3Percentage increase = 69%

Answer69

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Also searched as: 0580/42/O/N/21 · 0580_w21_qp_42 · 0580 w21 42 · question 6.
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