Numeracy Intermediate November 2023 Unit 1 Q11
11. An old postage stamp has a width of 2 cm and a height of 2·4 cm.
Frank makes a poster that is mathematically similar to the postage stamp, as shown below.
Diagrams not drawn to scale
He places a thin tape along the four edges of the poster.
Calculate the total length of this tape, correct to 1 significant figure.
You must show all your working. [4]
| Scheme | Marks | Comments |
|---|---|---|
| (Width of poster) 2 × \(\frac{26.4}{2.4}\) or 2 × 11 or equivalent | M1 | |
| 22 (cm) | A1 | Mark final answer for the width of the poster |
| (Perimeter of poster 2 × (22 + 26.4) =) 96.8 (cm) | A1 | FT ‘their 22’ provided M1 previously awarded |
| 100 (cm) | B1 | FT provided 95 < ‘their 96.8’ <100, as 100 correct to 1 significant figure Accept working in mm or m, units must then be given in the final answer Do not accept an unsupported answer of 100 (cm) |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| (Perimeter of stamp) 8.8 (cm) AND sight of \(\frac{26.4}{2.4}\) (= 11) or \(\frac{2.4}{26.4}\) (= \(\frac{1}{11}\)) | B1 | |
| (Perimeter of poster) (2 + 2.4 + 2 + 2.4) × \(\frac{26.4}{2.4}\) or 8.8 × \(\frac{26.4}{2.4}\) or 8.8 × 11 or equivalent | M1 | FT ‘their 2 + 2.4 + 2 + 2.4’ |
| 96.8 (cm) | A1 | |
| 100 (cm) | B1 | FT provided 95 < ‘their 96.8’ <100, as 100 correct to 1 significant figure Accept working in mm or m, units must then be given in the final answer Do not accept an unsupported answer of 100 (cm) |
The alternative method is printed in italics in the original.