Intermediate November 2024 Unit 2 Q14
14.
(a) Calculate the length of AC. [3]
Diagram not drawn to scale
(b) Calculate the value of \(x\). [3]
Diagram not drawn to scale
| Scheme | Marks | Comments |
|---|---|---|
| (\(AC^2\) =) \(13{\cdot}5^2 + 10{\cdot}8^2\) or equivalent | M1 | Check diagram for answers. (\(AC^2\) =) 182·25 + 116·64 = 298·89. |
| (\(AC\) =) \(\sqrt{13{\cdot}5^2 + 10{\cdot}8^2}\) or equivalent | m1 | (\(AC\) =) √298·89. Sight of √‘their 298·89’ or √‘their 298·89’ evaluated is awarded m1 provided M1 previously gained. |
| (\(AC\) =) 17·3 or 17·2(88…) or 17·29 or \(\dfrac{27\sqrt{41}}{10}\) (cm) | A1 | CAO. Mark final answer. Allow 17 provided from correct workings. Final answer of \(AC\) = 298·89 is M1m0A0. Accept a rounded or truncated answer. An unsupported correct answer is awarded M1m1A1. |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| Correct use of a two-step trigonometric method | M2 | A partial trigonometric method is awarded M0. |
| (\(AC\) =) 17·3 or 17·2(88…) or 17.29 or \(\dfrac{27\sqrt{41}}{10}\) (cm) | A1 | CAO. Mark final answer. Allow 17 provided from correct workings. Accept a rounded or truncated answer. |
| Scheme | Marks | Comments | ||||||
|---|---|---|---|---|---|---|---|---|
| (\(x\) =) \(\tan^{-1} \dfrac{19{\cdot}8}{8{\cdot}7}\) | M2 | Check diagram for answers. Award M1 for \(\tan x = \dfrac{19{\cdot}8}{8{\cdot}7}\) (= 2·275(8..) | ||||||
| An answer in the range 66·2 to 66·32 | A1 | Mark final answer. Allow 66 provided from correct workings. Accept a rounded or truncated answer. Allow correct angles given in radians or gradians.
|
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| Correct use of a two-step trigonometric method | M2 | A partial trigonometric method is awarded M0. |
| An answer in the range 66·2 to 66·32 | A1 | Mark final answer. Allow 66 provided from correct workings. Accept a rounded or truncated answer. Allow correct angles given in radians or gradians. |