Numeracy Higher June 2024 Unit 2 Q1
1.
A survey was carried out to find the total time people took to read the book ‘Wales is a Celtic Country’.
The results are shown in the frequency polygon below.
Which is the modal group?
Circle your answer. [1]
18 to 24 hours 21 hours 12 to 18 hours 34 hours 30 to 36 hours
How many people took part in the survey?
Circle your answer. [1]
34 30 33 97 108
How many of the people in the survey took 24 hours or more to read this book?
Circle your answer. [1]
13 34 47 24 84
Did any of the people in the survey take less than 6 hours to read this book?
Yes ☐ No ☐ Can’t tell ☐
You must give a reason for your answer. [1]
Four books are placed in a stack.
The thickness of each of the books is as follows:
22 mm 25 mm 29 mm 31 mm
The thickness of each book is measured correct to the nearest mm.
Show that the total height of the stack of these four books cannot be more than 109 mm. [3]
| Scheme | Mark | Comments |
|---|---|---|
| (i) 18 to 24 hours | B1 | |
| (ii) 97 | B1 | |
| (iii) 13 | B1 | |
| (iv) States or unambiguously implies ‘No’ with a reason, e.g. ‘no people in group 0 to 6 hours’ | E1 | Allow ‘No’ with e.g. ‘the point before 6 hours is at zero’ Do not allow ‘Can’t tell’ with e.g. ‘it is grouped data’ Do not accept “No’ with e.g. ‘it is grouped data’ (unless explaining why) ‘there is no point at 6’ ‘6 hours has a frequency of 0’ ‘it does not match a group of people’ ‘the first point is at 0 and the second one is at 20’ ‘the first plot is at 20’ ‘the first plot is at 9 hours’ ‘the first plot above 0 is at 9 hours’ ‘there is no information at 6 hours, it starts at 9 hours’ ‘the shortest time is 9 hours’ |
| Scheme | Mark | Comments |
|---|---|---|
| Sight of 22.5, 25.5, 29.5 and 31.5 (mm) | B1 | Award B1 for sight of 4 × 0.5 in an appropriate calculation Allow 0.4999(….) for 0.5, must clearly be a recurring 9 digit |
| 22.5 + 25.5 + 29.5 + 31.5 or 22+25+29+31 + 4 × 0.5 or equivalent | M1 | If B0, FT provided unambiguously chosen: 22 < ‘their 22.5’ ≤ 23, 25 < ‘their 25.5’ ≤ 26, 29 < ‘their 29.5’ ≤ 30, and 31 < ‘their 31.5’ ≤ 32, |
| 109 (mm) | A1 | CAO. Ignore incorrect units given Ignore any working for least possible thickness also given, e.g. 21.5 + 22.5 + 28.5 + 30.5 = 105 |