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Date May 2013 Marks available 1 Reference code 13M.1.sl.TZ1.10
Level SL only Paper 1 Time zone TZ1
Command term Write down Question number 10 Adapted from N/A

Question

The straight line, L1, has equation \(2y − 3x =11\). The point A has coordinates (6, 0).

Give a reason why L1 does not pass through A.

[1]
a.

Find the gradient of L1.

[2]
b.

L2 is a line perpendicular to L1. The equation of L2 is \(y = mx + c\).

Write down the value of m.

[1]
c.

L2 does pass through A.

Find the value of c.

[2]
d.

Markscheme

\(2 \times 0 - 3 \times 6 \ne 11\)     (R1)

Note: Stating \(2 \times 0 - 3 \times 6 =  - 18\) without a conclusion is not sufficient.


OR

Clear sketch of L1 and A.

     (R1)

OR

Point A is (6, 0) and \(2y - 3x = 11\) has x-intercept at \(- \frac{11}{3}\) or the line has only one x-intercept which occurs when x is negative.     (R1)     (C1)

a.

\(2y = 3x + 11\) or \(y - \frac{3}{2}x = \frac{{11}}{2}\)     (M1)


Note: Award (M1) for a correct first step in making y the subject of the equation.


\(({\text{gradient equals}}) = \frac{3}{2}(1.5)\)     (A1)     (C2)


Note: Do not accept 1.5x.

b.

\((m = ) - \frac{2}{3}\)     (A1)(ft)     (C1)


Notes: Follow through from their part (b).

c.

\(0 =  - \frac{2}{3}(6) + c\)     (M1)


Note: Award (M1) for correct substitution of their gradient and (6, 0) into any form of the equation.


(c =) 4     (A1)(ft)     (C2)


Note: Follow through from part (c).

d.

Examiners report

There were multiple acceptable reasons why the line did not pass through a given point (including numerically substituting values in the equation; drawing a graph or algebraically finding the x-intercept of the line). This was one of two reasoning marks in the paper.

a.

There were multiple acceptable reasons why the line did not pass through a given point (including numerically substituting values in the equation; drawing a graph or algebraically finding the x-intercept of the line). This was one of two reasoning marks in the paper.

b.

There were multiple acceptable reasons why the line did not pass through a given point (including numerically substituting values in the equation; drawing a graph or algebraically finding the x-intercept of the line). This was one of two reasoning marks in the paper.

c.

There were multiple acceptable reasons why the line did not pass through a given point (including numerically substituting values in the equation; drawing a graph or algebraically finding the x-intercept of the line). This was one of two reasoning marks in the paper.

d.

Syllabus sections

Topic 5 - Geometry and trigonometry » 5.1 » Perpendicular lines, \({m_1} \times {m_2} = - 1\) .
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