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0580/31 Oct/Nov 2021, Question 3: Tally Charts and Frequency Tables

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 17 marks

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The question, in short

Fill in missing entries in a 360-person trips table across four destinations, then work out probabilities, coach numbers and seats, cost expressions, a distance, a rounded-length range, and money fractions.

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

Part (a) · 3 marks

Use the row and column totals to fill every blank cell in the table.

  1. 1Girls, Adventure park: 144 − 65 − 15 = 64
  2. 2Girls, Red castle: 163 − 64 − 9 − 62 = 28
  3. 3Staff, Red castle: 71 − 36 − 28 = 7
  4. 4Staff, Wildlife centre: 37 − 15 − 3 − 7 = 12
  5. 5Boys, Wildlife centre: 121 − 62 − 12 = 47
  6. 6Boys total: 65 + 12 + 47 + 36 = 160

AnswerBoys: Wildlife centre 47, Total 160; Girls: Adventure park 64, Red castle 28; Staff: Wildlife centre 12, Red castle 7

Part (bi) · 1 mark

Work out the chance that a randomly chosen girl went to the Wildlife centre.

  1. 1Girls = 163, girls at Wildlife centre = 62
  2. 2P = 62/163

Answer62/163

Part (bii) · 1 mark

Work out the chance that someone chosen from the Botanic gardens group is a girl.

  1. 1Botanic gardens total = 24, girls = 9
  2. 2P = 9/24 = 3/8

Answer3/8

Part (biii) · 1 mark

Work out the chance that a randomly chosen person went to the Adventure park or the Botanic gardens.

  1. 1Adventure park or Botanic gardens = 144 + 24 = 168
  2. 2P = 168/360 = 7/15

Answer7/15

Part (c) · 2 marks

With 52 passenger seats per coach, give the smallest number of coaches for the Adventure park group and the resulting empty seats.

  1. 1144 ÷ 52 = 2.76…
  2. 2So 3 coaches are needed
  3. 33 × 52 = 156 seats
  4. 4156 − 144 = 12 empty seats

Answer3, 12

Part (di) · 1 mark

Write an expression, in dollars, for Rapid coaches' total cost over x kilometres.

  1. 1Fixed cost $550 plus $1.12 for each of x km
  2. 2550 + 1.12x

Answer550 + 1.12x

Part (dii) · 3 marks

Form an equation from the two companies' equal charges and solve it for the distance travelled.

  1. 1600 + 0.72x = 550 + 1.12x
  2. 2600 − 550 = 1.12x − 0.72x
  3. 350 = 0.4x
  4. 4x = 125 km

Answer125

Part (e) · 2 marks

Given 53 km rounded to the nearest kilometre, give the lower and upper bounds for l.

  1. 1Nearest km: half a unit either side
  2. 2Lower bound 53 − 0.5 = 52.5
  3. 3Upper bound 53 + 0.5 = 53.5

Answer52.5 ≤ l < 53.5

Part (fi) · 1 mark

Work out two sevenths of $31.50, the amount spent on food.

  1. 12/7 × 31.50
  2. 2= $9

Answer9

Part (fii) · 2 marks

From $31.50 taken and $4.50 left, find the fraction spent, in simplest form.

  1. 1Spent = 31.50 − 4.50 = 27
  2. 227/31.50 = 270/315
  3. 3= 6/7

Answer6/7

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