CAIE IGCSE Mathematics Extended E7.4.3 Use the Sum and Difference of Two or More Vectors to Express Given Questions

Practise Extended CAIE IGCSE Mathematics by following directed vector routes, converting midpoint or ratio data into fractional combinations and collecting base-vector coefficients accurately.

Exam points

Choose a valid route between named points and add each directed vector with the correct sign.
Convert midpoint or section-ratio information into a fractional multiple of a known vector.
Collect coefficients of the base vectors and present each requested vector in simplest form.

[Maximum number: 3]

NOT TO SCALE

ABCD is a parallelogram.
$\overrightarrow{A B}=\mathbf{m}$ and $\overrightarrow{A D}=\mathbf{p}$ .
F is a point on BC and B F=4 F C.
E is a point on AD and A E: E D=1: 2.

Find $\overrightarrow{EF}$ , in terms of $\mathbf{m}$ and $\mathbf{p}$ , in its simplest form.

$\mathbf{m}+\frac{7}{15} \mathbf{p}$

M2 for correct unsimplified expression in terms of $\mathbf{m}$ and $\mathbf{p}$

or M1 for a correct route

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CAIE IGCSE Mathematics Extended E7.4.3 Use the Sum and Difference of Two or More Vectors to Express Given Questions question 1