| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2020 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Estimate percentages or proportions from graphs |
| Difficulty | Easy -1.2 This is a straightforward histogram reading question requiring students to find frequency density values, calculate frequencies for given intervals, use the given total to find a scaling factor, then compute a percentage. It involves only basic arithmetic and understanding of histogram interpretation—standard AS-level data representation with no problem-solving insight required. |
| Spec | 2.02b Histogram: area represents frequency |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| 1 square is \(\frac{78}{12\times3+3\times4+2\times2} = \frac{78}{52} = 1.5\) and \((8\times1+1\times8)\times\)"1.5" | M1 | Use of frequency density to establish fd scale, then use area to find frequency of <11 minutes. Allow max 3 errors in heights or widths in total if working shown. Allow for finding total number of squares (88), max 4 errors in heights/widths, and number <11 minutes (16) with max 1 error |
| 24 students took less than 11 minutes | A1 | Allow 88 and 16 |
| Percentage of students \(= \frac{\text{"24"}}{78+\text{"24"}+1\times8\times\text{"1.5"}+3\times4\times\text{"1.5"}}\times100\) | M1 | For realising need to find total number and calculating percentage with "their 24" as numerator. Allow \((8\times1+2\times8)\times\)"1.5" instead of "24"\(+1\times8\times\)"1.5". Max 2 errors in heights/widths in total calculation |
| \(= 18.18\ldots\) awrt 18% | A1 | awrt 18 |
| (4) | Total 4 |
## Question 1:
| Answer/Working | Mark | Guidance |
|---|---|---|
| 1 square is $\frac{78}{12\times3+3\times4+2\times2} = \frac{78}{52} = 1.5$ **and** $(8\times1+1\times8)\times$"1.5" | M1 | Use of frequency density to establish fd scale, then use area to find frequency of <11 minutes. Allow max 3 errors in heights or widths in total if working shown. Allow for finding total number of squares (88), max 4 errors in heights/widths, and number <11 minutes (16) with max 1 error |
| **24** students took less than 11 minutes | A1 | Allow 88 and 16 |
| Percentage of students $= \frac{\text{"24"}}{78+\text{"24"}+1\times8\times\text{"1.5"}+3\times4\times\text{"1.5"}}\times100$ | M1 | For realising need to find total number and calculating percentage with "their 24" as numerator. Allow $(8\times1+2\times8)\times$"1.5" instead of "24"$+1\times8\times$"1.5". Max 2 errors in heights/widths in total calculation |
| $= 18.18\ldots$ awrt 18% | A1 | awrt 18 |
| | (4) | **Total 4** |
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\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{d62e5a00-cd23-417f-b244-8b3e24da4aa2-02_849_1271_246_303}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
The histogram in Figure 1 shows the times taken to complete a crossword by a random sample of students.
The number of students who completed the crossword in more than 15 minutes is 78\\
Estimate the percentage of students who took less than 11 minutes to complete the crossword.
\hfill \mbox{\textit{Edexcel AS Paper 2 2020 Q1 [4]}}