 # Exam-Style Questions.

## Problems adapted from questions set for previous Mathematics exams.

### 1.

IGCSE Extended

OABC is a parallelogram with O as origin. The position vector of A is $$a$$ and the position vector of C is $$c$$. F is the mid-point of AB and the point E divides the line OC such that OE:EC = 2:1.

The point E also divides the line AD such that AE:ED = 3:2.

Find the following in terms of $$a$$ and $$c$$.

(a) $$\overrightarrow{OB}$$

(b) $$\overrightarrow{AC}$$

(c) $$\overrightarrow{AE}$$

(d) the position vector of F.

(e) $$\overrightarrow{AD}$$

(f) $$\overrightarrow{BD}$$

### 2.

GCSE Higher

(a) Shape $$A$$ is translated to shape $$B$$ using the vector $$\begin{pmatrix}m\\n\\ \end{pmatrix}$$. What are the values of $$m$$ and $$n$$? (b) Vectors $$a, b, c, d$$ and $$e$$ are drawn on an isometric grid. Write each of the vectors $$c, d$$ and $$e$$ in terms of $$a$$ and/or $$b$$. ### 3.

GCSE Higher

ABCD is a quadrilateral. The points E, F, G and H are the midpoints of the sides of this quadrilateral. $$\vec{CH} = a, \vec{DG} = b \text{ and } \vec{DF} = c$$

Show that HG is parallel to EF.

### 4.

GCSE Higher

In the parallelogram OABC two of the sides can be represented by vectors $$a$$ and $$c$$.

$$\overrightarrow{OA} = a$$ and $$\overrightarrow{OC} = c$$ $$X$$ is the midpoint of the line $$AC$$.

$$OCD$$ is a straight line such that $$OC:CD = k:1$$

Given that $$\overrightarrow{XD} = 3c - \frac12 a$$ find the value of $$k$$.

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