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Date None Specimen Marks available 3 Reference code SPNone.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, \(\boldsymbol{u} = \overrightarrow {{\rm{AB}}} \) and \(\boldsymbol{v} = \overrightarrow {{\rm{BD}}} \) .

 


The midpoint of \(\overrightarrow {{\rm{AD}}} \) is E and \(\frac{{{\rm{BD}}}}{{{\rm{DC}}}} = \frac{1}{3}\) .

Express each of the following vectors in terms of \(\boldsymbol{u}\) and \(\boldsymbol{v}\) .

\(\overrightarrow {{\rm{AE}}} \)

[3]
a.

\(\overrightarrow {{\rm{EC}}} \)

[4]
b.

Markscheme

\(\overrightarrow {{\rm{AE}}}  = \frac{1}{2}\overrightarrow {{\rm{AD}}} \)     A1

attempt to find \(\overrightarrow {{\rm{AD}}} \)     M1

e.g. \(\overrightarrow {{\rm{AB}}}  + \overrightarrow {{\rm{BD}}} \) , \({\boldsymbol{u}} + {\boldsymbol{v}}\)

\(\overrightarrow {{\rm{AE}}}  = \frac{1}{2}(u + v)\) \(\left( { = \frac{1}{2}{\boldsymbol{u}} + \frac{1}{2}{\boldsymbol{v}}} \right)\)     A1     N2

[3 marks]

a.

\(\overrightarrow {{\rm{EC}}}  = \overrightarrow {{\rm{AE}}}  = \frac{1}{2}({\boldsymbol{u}} + {\boldsymbol{v}})\)     A1

\(\overrightarrow {{\rm{DC}}}  = 3{\boldsymbol{v}}\)     A1

attempt to find \(\overrightarrow {{\rm{EC}}} \)     M1

e.g. \(\overrightarrow {{\rm{ED}}}  + \overrightarrow {{\rm{DC}}} \) , \(\frac{1}{2}({\boldsymbol{u}} + {\boldsymbol{v}}) + 3{\boldsymbol{v}}\)

\(\overrightarrow {{\rm{EC}}}  = \frac{1}{2}{\boldsymbol{u}} + \frac{7}{2}{\boldsymbol{v}}\) \(\left( { = \frac{1}{2}({\boldsymbol{u}} + 7{\boldsymbol{v}})} \right)\)     A1     N2

[4 marks]

b.

Examiners report

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

Syllabus sections

Topic 4 - Vectors » 4.1 » Algebraic and geometric approaches to the sum and difference of two vectors; the zero vector, the vector \( - v\).

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