Lemmara logoLemmaraWorked solution

4024/21 Oct/Nov 2024, Question 2: Histograms (Unequal Class Intervals)

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 7 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Traffic survey: complete a frequency/angle table and pie chart for 160 morning vehicles, then use a speed histogram to question a range claim and complete a frequency table.

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

Part (ai) · 2 marks

Using 160 vehicles and the given frequencies, find the missing pie chart angles, including the 90° sector for 3 or more.

  1. 11 person: 72/160 × 360 = 162°
  2. 22 people: 48/160 × 360 = 108°

Answer| 1 | 72 | 162° | | 2 | 48 | 108° |

Part (aii) · 1 mark

Draw the remaining sectors on the pie chart using the angles found, with 3 or more already shown as 90°.

  1. 1Draw sectors of 162° (1 person) and 108° (2 people) next to the 90° sector and label them

AnswerCorrect pie chart

Part (bi) · 1 mark

Explain why the histogram does not show the speed range as 50 km/h, referring to the grouped classes.

  1. 1The data is grouped, so the individual speeds (the slowest and fastest) are not known; the range need not be 70 − 20 = 50

AnswerData grouped so individual speeds not known

Part (bii) · 3 marks

Use frequency density and class width from the histogram to find the missing frequencies, given 24 for 20 < s ≤ 30.

  1. 1Frequency = frequency density × class width
  2. 230 < s ≤ 40: 4.6 × 10 = 46; 40 < s ≤ 45: 8.8 × 5 = 44
  3. 345 < s ≤ 50: 7.6 × 5 = 38; 50 < s ≤ 70: 1.4 × 20 = 28

Answer| 30 < s ≤ 40 | 40 < s ≤ 45 | 45 < s ≤ 50 | 50 < s ≤ 70 | | 46 | 44 | 38 | 28 |

Stuck on a step? Read the free lesson: Histograms (Unequal Class Intervals)

Practise more histograms (unequal class intervals) questions

Real 4024 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on histograms (unequal class intervals)

Also searched as: 4024/21/O/N/24 · 4024_w24_qp_21 · 4024 w24 21 · question 2.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.