Numeracy Intermediate November 2019 Unit 1 Q8
8. Sioned and Rhodri are making a kite.
A diagram of the kite they are making is shown below.
\(AC\) and \(DB\) are the diagonals of the kite.
\(AE\) = 22 cm, \(EC\) = 28 cm and \(DE\) = 20 cm.
Diagram not drawn to scale
(a) Rhodri makes a statement about their kite being able to fly in strong wind,
“The length of the long diagonal must be at least 120% of the length of the short diagonal.”
Assuming Rhodri is correct, should their kite be able to fly in strong wind?
You must show all your working. [4]
(b) Sioned says,
“The best length for the tail on a kite depends on the area of the kite.”
Sioned refers to the table below that she has seen on the internet.
| Area of the kite, \(A\) | Best length for the tail |
|---|---|
| \(A \lt 500\,\text{cm}^2\) | 2 m |
| \(500\,\text{cm}^2 \leqslant A \lt 900\,\text{cm}^2\) | 2·4 m |
| \(900\,\text{cm}^2 \leqslant A \lt 1200\,\text{cm}^2\) | 3·1 m |
| \(1200\,\text{cm}^2 \leqslant A\) | 3·5 m |
Work out the best length of tail for Sioned and Rhodri’s kite.
You must show all your working. [4]
| Scheme | Marks | Comments |
|---|---|---|
| Short diagonal 40 (cm) and longer diagonal 50 (cm) | B1 | Check diagram |
| (longer diagonal should be >) 1.20 × 40 or equivalent, OR (shorter diagonal should be <) 50 ÷ 1.2 OR (100 ×) \(\dfrac{50}{40}\) | M1 | FT ‘their 40’ and ‘their 50’ provided
|
| (longer diagonal should be >) 48 (cm), OR (shorter diagonal should be <) 41.6(6.. cm) OR ((100) × \(\dfrac{50}{40}\) =) 1(.)25 | A1 | FT |
| Conclusion, e.g. ‘Yes (certain to fly in strong wind)’ ‘Yes as 48 < longer diagonal’ ‘Yes (125% > 120%)’ ‘Yes (1.25 > 1.2(0)) | E1 | FT provided M1 awarded Do not accept working for area seen in (a) unless used in (b) |
| Scheme | Marks | Comments |
|---|---|---|
(Method to calculate area) e.g.
| M2 | FT ‘their 40’ and ‘their 50’ Allow if working for area seen in (a) and used in (b) M1 for correct method for at least 2 of the 4 possible triangles, e.g. implied from sight of 20 × 22, 440, 20 × 28 or 560 |
| (Area of the kite) 1000 (cm2) | A1 | CAO |
| (Length of tail) 3.1 (m) | B1 | FT provided at least M1 previously awarded for correct length selected from choice of the correct group |