Higher November 2021 Unit 2 Q4
4. Show that the triangle below is not a right-angled triangle. [5]
Diagram not drawn to scale
| Scheme | Marks | Comments |
|---|---|---|
| \(5x - 17 + 2x + 9 + x + 20 = 180\) | M1 | |
| \(8x = 168\) | A1 | |
| \(x = 21\) | A1 | F.T. from \(ax = b\). Allow all 3 marks for \(x = 21\). |
| Substituting \(x = 21\) into at least one expression. | M1 | If \(x \ne 21\) FT ‘their derived value of \(x\)’. F.T. for this A1 if \(x \geqslant 4\). |
| \((5x - 17 =)\ 88(^\circ)\) \((2x + 9 =)\ 51(^\circ)\) \((x + 20 =)\ 41(^\circ)\) (So not a right-angled triangle) | A1 | Any two of these expressions correctly evaluated with no incorrect evaluation, provided the sum of the two found is > 90. (statement not required). Note If further work indicates that the values found are not treated as angles (e.g. showing \(51^2 + 41^2 \ne 88^2\)) then award final M0A0. |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| \(5x - 17 = 90\) OR \(2x + 9 = 90\) OR \(x + 20 = 90\) | M1 | |
| \(x = 21{\cdot}4\) AND \(x = 40{\cdot}5\) AND \(x = 70\) | A2 | Award A1 for any one of these: \(x = 21{\cdot}4\) OR \(x = 40{\cdot}5\) OR \(x = 70\) |
| Then verifying: If \(x = 21{\cdot}4\): \(5x - 17 + 2x + 9 + x + 20 = 183.2\) AND If \(x = 40{\cdot}5\): \(5x - 17 + 2x + 9 + x + 20 = 336\) AND If \(x = 70\): \(5x - 17 + 2x + 9 + x + 20 = 572\) (So not a right-angled triangle) | A2 | Award A1 for any one of these: If \(x = 21{\cdot}4\): \(5x - 17 + 2x + 9 + x + 20 = 183.2\) OR If \(x = 40{\cdot}5\): \(5x - 17 + 2x + 9 + x + 20 = 336\) OR If \(x = 70\): \(5x - 17 + 2x + 9 + x + 20 = 572\) |