Edexcel IGCSE Math A Higher 5 Vectors and Transformation Geometry Questions

Vertices of the transformed shape:
(-9,6), (-9,9), (-3,9), (-6,6)

vertices at (7,3)(10,6)(13,6)(13,3)

Shape in correct
position

1

Transformation:
$$\text{enlargement, scale factor }2,\text{ centre }(-3,3)$$

Final answer:

B1, oe, for example $4(\mathbf b-\mathbf a)$.

Final answer:

M1ft for a correct expression following through their part (a), where $\overrightarrow{AB}$ is of the form $m\mathbf a+n\mathbf b$, $m,n\ne0$.
A1;
allow $\mathbf b+3\mathbf a$.

$$\overrightarrow{BC}=\overrightarrow{BA}+\overrightarrow{AO}+\overrightarrow{OC}$$$$=-(4\mathbf b-\mathbf a)-2\mathbf a+(5\mathbf b-3\mathbf a)$$$$=\mathbf b-4\mathbf a$$

Final answer:
$$\mathbf b-4\mathbf a$$

M1 for a valid unsimplified expression for $\overrightarrow{BC}$. A1 oe.

$$\begin{aligned} (\overrightarrow{O D}=) 2 \mathbf{a}+4 \mathbf{b}-\mathbf{a}+\frac{1}{4}(\text { "b }-4 \mathbf{a} \text { " }) \text { oe }\left(=\frac{17}{4} \mathbf{b} \text { oe }\right) \text { or } (\overrightarrow{O D}=) 5 \mathbf{b}-3 \mathbf{a}-\frac{3}{4}(\text { "b }-4 \mathbf{a} \text { " }) \text { oe } \end{aligned}$$

4
ft their $\overrightarrow{B C}$ provided it is in the form m a+n b for all
method marks

$$\begin{aligned} \operatorname{eg} \overrightarrow{O P}=2 \mathbf{a}+4 \mathbf{b}-\mathbf{a}+x(4 \mathbf{b}-\mathbf{a}) \text { or } \overrightarrow{O P}=2 \mathbf{a}+y(4 \mathbf{b}-\mathbf{a}) \text { or } \overrightarrow{O P}=5 \mathbf{b}-3 \mathbf{a}-(\text { "b }-4 \mathbf{a} \text { " })+\lambda(4 \mathbf{b}-\mathbf{a}) \text { or } \overrightarrow{O P}=5 \mathbf{b}-3 \mathbf{a}-\frac{3}{4}\left(\text { "b }-4 \mathbf{a}^{\prime \prime}\right)+n\left(" \frac{17}{4} \mathbf{b}^{\prime \prime}\right) \text { or } \overrightarrow{O P}=" \frac{17}{4} \mathbf{b}^{\prime \prime}+n \times \frac{17}{4} \mathbf{b}^{\prime \prime} \text { or } \overrightarrow{O P}=n \times{ }^{\prime \prime} \frac{17}{4} \mathbf{b}^{\prime \prime} \text { oe or } \overrightarrow{A P}=x(4 \mathbf{b}-\mathbf{a}) \text { or } \overrightarrow{A P}=-2 \mathbf{a}+n \times " \frac{17}{4} \mathbf{b}^{\prime \prime} \text { oe or } \overrightarrow{B P}=y(4 \mathbf{b}-\mathbf{a}) \text { or } \overrightarrow{B P}=\frac{1}{4}\left(" \mathbf{b}-4 \mathbf{a}^{\prime \prime}\right)+n \times " \frac{17}{4} \mathbf{b}^{\prime \prime} \text { oe } \end{aligned}$$

M1 for a correct expression, including a parameter, for
vector $\overrightarrow{O P}$, must be clearly identified as $\overrightarrow{O P}$ or for a
correct expression, including a parameter, for vector
$\overrightarrow{A P}, \overrightarrow{B P}, \overrightarrow{C P}$ or $\overrightarrow{D P}$ must be clearly identified

eg $\overrightarrow{O P}=2 \mathbf{a}+4 \mathbf{b}-\mathbf{a}+x(4 \mathbf{b}-\mathbf{a})$ and $\overrightarrow{O P}=n \times{ }^{\prime \prime} \frac{17}{4} \mathbf{b}^{\prime \prime}$
or $\overrightarrow{O P}=2 \mathbf{a}+y(4 \mathbf{b}-\mathbf{a})$ and
$$\overrightarrow{O P}=5 \mathbf{b}-3 \mathbf{a}-\frac{3}{4}(\text { "b }-4 \mathbf{a} \text { " })+n\left(\text { " } \frac{17}{4} \mathbf{b} \text { " }\right) \text { or }$$$\overrightarrow{A P}=x(4 \mathbf{b}-\mathbf{a})$ and $\overrightarrow{A P}=-2 \mathbf{a}+n \times{ }^{\prime \prime} \frac{17}{4} \mathbf{b}^{\prime \prime}$ oe or
$\overrightarrow{B P}=y(4 \mathbf{b}-\mathbf{a})$ and $\overrightarrow{B P}=\frac{1}{4}\left({ }^{\prime \prime} \mathbf{b}-4 \mathbf{a}^{\prime \prime}\right)+n \times{ }^{\prime \prime} \frac{17}{4} \mathbf{b}^{\prime \prime}$
for two correct expressions for vector $\overrightarrow{O P}$ or two
correct expressions for vector $\overrightarrow{A P}$, or
two correct expressions for vector $\overrightarrow{B P}$ or
two correct expressions for vector $\overrightarrow{C P}$ or
two correct expressions for vector $\overrightarrow{D P}$
one of which contains $n^{\prime \prime} \frac{17}{4} \mathbf{b}^{\prime \prime}$ and one contains
x(4 b-a)

Dependent on a correct vector method shown

$\frac{32}{17}$
dep on M3
oe allow 1.88(235...)

Total 6 marks