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4024/22 May/Jun 2023, Question 2: Mean, Median, Mode and Range

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 13 marks

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The question, in short

Solve five algebra items: form and solve a cost equation for p, factorise an expression, simplify a product of algebraic fractions, rearrange a formula for x, and use mean changes to find k.

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

Part (a) · 3 marks

Using p cents per bar and 75 cents per sweets packet, with $9.10 spent on 5 bars and 8 packets, write an equation and solve for p, showing working.

  1. 1$9.10 = 910 cents
  2. 25p + 8 × 75 = 910
  3. 35p + 600 = 910
  4. 45p = 310
  5. 5p = 62

Answer62

Part (b) · 2 marks

Factorise the expression 6ac − 27c fully.

  1. 1HCF of 6ac and 27c is 3c
  2. 26ac − 27c = 3c(2a − 9)

Answer3c(2a − 9) or −3c(9 − 2a)

Part (c) · 2 marks

Combine (3m²n)/10 × 5n/(9m) into one fraction and reduce it to simplest form.

  1. 1(3m²n × 5n)/(10 × 9m)
  2. 2= 15m²n²/(90m)
  3. 3= mn²/6

Answermn²/6

Part (d) · 2 marks

Make x the subject of y = 3x²/5.

  1. 15y = 3x²
  2. 2x² = 5y/3
  3. 3x = ±√(5y/3)

Answer±√(5y/3) or √(5y/3)

Part (e) · 4 marks

A set of k values averages 56.8; adding 52 lowers the average to 56.5. Determine k.

  1. 1Total of k numbers = 56.8k
  2. 2(56.8k + 52)/(k + 1) = 56.5
  3. 356.8k + 52 = 56.5k + 56.5
  4. 40.3k = 4.5
  5. 5k = 15

Answer15

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Also searched as: 4024/22/M/J/23 · 4024_s23_qp_22 · 4024 s23 22 · question 2.
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