Numeracy Higher November 2017 Unit 1 Q11
11. A company is building a new headquarters.
The diagram below shows the ground plan of the new headquarters.
Diagram not drawn to scale
The plan consists of a square and a sector of a circle.
(a)
Using the information given in the diagram, calculate the radius of the sector of the circle.
Give your answer in the form \(a\sqrt{b}\), where a is an integer and b is a prime number. [5]
(b)
The square is to be covered in concrete.
Calculate the area of the square.
Expand any brackets, and simplify your answer. [3]
| Scheme | Marks | Comments |
|---|---|---|
| \(200\pi = \dfrac{40}{360} \times \pi \times \text{radius}^2\) | M1 | |
| \(\text{radius}^2 = \dfrac{200\pi \times 360}{40\pi}\) or equivalent | A1 | |
| (radius =) √1800 | A1 | CAO |
| Writing 1800 or as a product of 2 or more factors | M1 | e.g. √1800 = √18 × √100, or √1800 = √3 × √6 × √100, or 1800 = 900 × 2 FT ‘their 1800’ provided previous M1 awarded |
| 30√2 (m) | A1 | Needs to be in the form a√b where b is a prime number |
| Scheme | Marks | Comments |
|---|---|---|
| (10 + 30√2)2 | M1 | FT for all marks ‘their 30√2’ provided of equivalent difficulty i.e a√b, where b does not need to be a prime number |
| 100 + 300√2 + 300√2 + 1800 | A1 | Allow A1 for any 3 correct terms |
| = 1900 + 600√2 (m2) | A1 | Accept e.g. 100(19 + 6√2) (m2) Mark final answer |