**SPM Mathematics (Model Test Paper)**

*Section***B**

[48 marks]

Answer any

**four**questions from this section.**13**. (

*a*) Diagram 8.1 shows point

*K*( 3, 2 ) marked on a Cartesian plane.

Diagram 8.1

The transformation

*T**is a translation $\left(\begin{array}{l}-2\\ \text{}3\end{array}\right).$*

The transformation

**is a reflection in the line***R**y*= 3.State the coordinates of the image of point K under each of the following transformations.

(i)

*T*(ii)

*TR*[3 marks](b) Diagram 8.2 shows three trapeziums,

*ABCD, PQRS*and*PTUV*drawn on a Cartesian plane.

Diagram 8.2

(i) Trapezium

*PTUV*is the image of trapezium

*ABCD*under the combined transformation

**.**

*VW*Describe in full, the transformation

**and the transformation***W**V*.*[ 6 marks]* (ii) Given that the area of trapezium

[3 marks]

*ABCD*is 14 cm^{2}, calculate the area, in cm^{2}, of the shaded region.[3 marks]

*Answer and solution:*

**(a)(i)**(3, 2) →

**T**→ (1, 5)

**(3, 2) →**

(a)(ii)

(a)(ii)

**R**→ (3, 4) →

**T**→ (1, 7)

(b)(i)

(b)(i)

** W** : Rotation, 90 clockwise at centre (0 , −1)

**: Enlargement, scale factor of 2, centre of enlargement at point**

*V**P*(2 , 1)

(ii)

(ii)

Area of

*PTUV*= (scale factor)^{2}× Area of object= 2

^{2 }× 14= 56 cm

^{2}**Area of shaded region = 56 – 14 = 42 cm**

^{2}