Date | May 2011 | Marks available | 2 | Reference code | 11M.1.sl.TZ2.5 |
Level | SL only | Paper | 1 | Time zone | TZ2 |
Command term | Find | Question number | 5 | Adapted from | N/A |
Question
The straight line \(L\) passes through the points \({\text{A}}( - 1{\text{, 4}})\) and \({\text{B}}(5{\text{, }}8)\) .
Calculate the gradient of \(L\) .
Find the equation of \(L\) .
The line \(L\) also passes through the point \({\text{P}}(8{\text{, }}y)\) . Find the value of \(y\) .
Markscheme
\(\frac{{8 - 4}}{{5 - ( - 1)}}\) (M1)
Note: Award (M1) for correct substitution into the gradient formula.
\(\frac{2}{3}{\text{ }}\left( {\frac{4}{6}{\text{, }}0.667} \right)\) (A1) (C2)
[2 marks]
\(y = \frac{2}{3}x + c\) (A1)(ft)
Note: Award (A1)(ft) for their gradient substituted in their equation.
\(y = \frac{2}{3}x + \frac{{14}}{3}\) (A1)(ft) (C2)
Notes: Award (A1)(ft) for their correct equation. Accept any equivalent form. Accept decimal equivalents for coefficients to 3 sf.
OR
\(y - {y_1} = \frac{2}{3}(x - {x_1})\) (A1)(ft)
Note: Award (A1)(ft) for their gradient substituted in the equation.
\(y - 4 = \frac{2}{3}(x + 1)\) OR \(y - 8 = \frac{2}{3}(x - 5)\) (A1)(ft) (C2)
Note: Award (A1)(ft) for correct equation.
[2 marks]
\(y = \frac{2}{3} \times 8 + \frac{{14}}{3}\) OR \(y - 4 = \frac{2}{3}(8 + 1)\) OR \(y - 8 = \frac{2}{3}(8 - 5)\) (M1)
Note: Award (M1) for substitution of \(x = 8\) into their equation.
\(y = 10\) (\(10.0\)) (A1)(ft) (C2)
Note: Follow through from their answer to part (b).
[2 marks]
Examiners report
Generally, a well answered question with many candidates achieving full marks. Indeed, marks which tended to be lost were as a result of premature rounding rather than method. On a number of scripts, part (a) produced a rather curious wrong answer of \(8.2\) following a correct gradient expression. It would seem that this was as a result of typing into the calculator \(8 - 4 ÷ 5 + 1\).
Generally, a well answered question with many candidates achieving full marks. Indeed, marks which tended to be lost were as a result of premature rounding rather than method.
Generally, a well answered question with many candidates achieving full marks. Indeed, marks which tended to be lost were as a result of premature rounding rather than method.