Higher November 2024 Paper 1 Q13
13
(a) By rounding each number to one significant figure,
estimate the value of \(\quad \dfrac{\sqrt{401} + 1.9^3}{\cos 58.7^\circ}\)
You must show your working. [3 marks]
(b) Here is a triangle.
Not drawn accurately
Sam attempts to find the value of \(\cos x\) using the cosine rule.
Here is his working.
| \(5^2 = 3^2 + 7^2 + 2 \times 3 \times 7 \times \cos x\) \(5^2 = 10^2 + 42 \times \cos x\) \(25 = 142 \cos x\) Therefore \(\quad \cos x = \dfrac{25}{142}\) |
Identify two errors Sam has made. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\sqrt{400}\) or 20 or \(2^3\) or 8 or \(\cos 60^\circ\) or 0.5 | M1 | oe |
| 20 and 8 and 0.5 | M1 | |
| 56 with correct values | A1 |
Additional guidance
| 56 seen then rounded to 60 | M1M1A1 |
| 28 rounded to 30 then \(\dfrac{30}{0.5}\) leading to 60 as final answer | M1M1A0 |
| Answer | Mark | Comments |
|---|---|---|
| Any two of It should be \(-2 \times 3 \times 7 \times \cos x\) \(3^2 + 7^2\) is not \(10^2\) \(10^2 + 42 \cos x\) is not \(142 \cos x\) | B2 | oe B1 any one error identified SC1 answer should be \(\cos x = \dfrac{33}{42}\) oe or answer should be \(\cos x = -\dfrac{33}{42}\) oe |
Additional guidance
| All three errors identified | B2 |
| Three errors identified with one or two correct | B1 |
| The second + should be \(-\) | B1 |
| You have to rearrange (to make \(\cos x\) the subject) | B0 |