SPM 2016 Mathematics (Forecast Paper)



SPM 2016 Mathematics (Forecast 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 ( 2  3 ).  
The transformation R is a reflection in the line 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 W and the transformation V.                     [ 6 marks]
     
  (ii)  Given that the area of trapezium ABCD is 14 cm2, calculate the area, in cm2, of the shaded region.                                                                                                                     [3 marks]

Answer and solution:

(a)(i) (3, 2) → T → (1, 5)
(a)(ii) (3, 2) → R → (3, 4) → T → (1, 7)

(b)(i)

W : Rotation, 90  clockwise at centre (0 , −1)
V: Enlargement, scale factor of 2, centre of enlargement at point P (2 , 1)

(ii)
Area of PTUV = (scale factor)2 × Area of object
=  22  × 14
= 56 cm2
Area of shaded region = 56 – 14 = 42 cm2