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Date November 2013 Marks available 2 Reference code 13N.1.sl.TZ0.1
Level SL only Paper 1 Time zone TZ0
Command term Express Question number 1 Adapted from N/A

Question

In the following diagram, \(\overrightarrow {{\text{OP}}} \) = p, \(\overrightarrow {{\text{OQ}}} \) = q and \(\overrightarrow {{\text{PT}}}  = \frac{1}{2}\overrightarrow {{\text{PQ}}} \).

Express each of the following vectors in terms of p and q,

\(\overrightarrow {{\text{QP}}} \);

[2]
a.

\(\overrightarrow {{\text{OT}}} \).

[3]
b.

Markscheme

appropriate approach     (M1)

eg     \(\overrightarrow {{\text{QP}}}  = \overrightarrow {{\text{QO}}}  + \overrightarrow {{\text{OP}}} ,{\text{ P}} - {\text{Q}}\)

\(\overrightarrow {{\text{QP}}} \) = pq     A1     N2

[2 marks]

a.

recognizing correct vector for \(\overrightarrow {{\text{QT}}} \) or \(\overrightarrow {{\text{PT}}} \)     (A1)

eg     \(\overrightarrow {{\text{QT}}}  = \frac{1}{2}\)(pq), \(\overrightarrow {{\text{PT}}}  = \frac{1}{2}\)(qp)

appropriate approach     (M1)

eg     \(\overrightarrow {{\text{OT}}}  = \overrightarrow {{\text{OP}}}  + \overrightarrow {{\text{PT}}} ,{\text{ }}\overrightarrow {{\text{OQ}}}  + \overrightarrow {{\text{QT}}} ,{\text{ }}\overrightarrow {{\text{OP}}}  + \frac{1}{2}\overrightarrow {{\text{PQ}}} \)

\(\overrightarrow {{\text{OT}}}  = \frac{1}{2}\)(p + q)   \(\left( {{\text{accept }}\frac{{p + q}}{2}} \right)\)     A1     N2

[3 marks]

b.

Examiners report

[N/A]
a.
[N/A]
b.

Syllabus sections

Topic 4 - Vectors » 4.1 » Algebraic and geometric approaches to unit vectors; base vectors; \(i\), \(j\) and \(k\).

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