Easy -1.2 This is a straightforward histogram question requiring only the understanding that total area represents total frequency. Students need to find frequency density (20/1.5 = 13.33), recognize that area = frequency (12×1.5 corresponds to frequency 20), then calculate total frequency from total area (94.5/1.5 = 63). It's a standard S1 exercise with clear steps and no conceptual challenges beyond basic histogram interpretation.
2. The time taken to complete a puzzle, in minutes, is recorded for each person in a club. The times are summarised in a grouped frequency distribution and represented by a histogram.
One of the class intervals has a frequency of 20 and is shown by a bar of width 1.5 cm and height 12 cm on the histogram. The total area under the histogram is \(94.5 \mathrm {~cm} ^ { 2 }\)
Find the number of people in the club.
(3)
VILM SIMI NI JIIIM I ON OC
VILV SIHI NI JAHM ION OC
VJ4V SIHI NI JIIYM ION OC
20 people represented by 18 (cm²) or 1 person is represented by 0.9 (cm²)
M1
2nd M1 for correct expression/equation for total frequency e.g. \(\frac{20}{18} = \frac{94.5}{x}\)
\(x = \frac{20 \times 94.5}{18}\) oe
M1
\(= 105\) (people)
A1cao
A1 for 105cao
Total: 3 marks
| Part | Answer/Working | Marks | Guidance |
|------|---|---|---|
| | $1.5 \times 12 = 18$ | M1 | 1st M1 for attempt to relate area to frequency |
| | 20 people represented by 18 (cm²) or 1 person is represented by 0.9 (cm²) | M1 | 2nd M1 for correct expression/equation for total frequency e.g. $\frac{20}{18} = \frac{94.5}{x}$ |
| | $x = \frac{20 \times 94.5}{18}$ oe | M1 | |
| | $= 105$ (people) | A1cao | A1 for 105cao |
**Total: 3 marks**
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2. The time taken to complete a puzzle, in minutes, is recorded for each person in a club. The times are summarised in a grouped frequency distribution and represented by a histogram.
One of the class intervals has a frequency of 20 and is shown by a bar of width 1.5 cm and height 12 cm on the histogram. The total area under the histogram is $94.5 \mathrm {~cm} ^ { 2 }$
Find the number of people in the club.\\
(3)\\
VILM SIMI NI JIIIM I ON OC\\
VILV SIHI NI JAHM ION OC\\
VJ4V SIHI NI JIIYM ION OC\\
\hfill \mbox{\textit{Edexcel S1 2016 Q2 [3]}}