 # SPM Mathematics 2018, Paper 2 (Questions 13 & 14)

Question 13 (12 marks):
(a) Diagram 9.1 shows point P (5, 1) on a Cartesian plane. Diagram 9.1

Transformation T is a translation
Transformation S is an enlargement about the centre (–5, 2) with a scale factor 2.
State the coordinates of the image of point P under the following transformations:
(i) T2,
(ii) TS.

(b) Diagram  9.2 shows geometrical shapes KLMNP, KSRQP and KTUVW drawn on a Cartesian plane. Diagram 9.2

(i)
KTUVW is the image of KLMNP under the combined transformation YZ.
Describe, in full, the transformation:
(a) Z,
(b) Y.

(ii) It is given that KSRQP represents a region of area 30 m2.
Calculate the area, in m2, of the shaded region.

Solution:
(a) (i)
TT = P(–3, 3) → T1 → P’(1, 0) ) → T2 → P’’(5, –3)
(ii) TS =  P (–3, 3) → S → P’(–1, 4) → T → P’’(3, 1)

(b)(i)(a)
Z: Reflection in the line x = 0.

(b)(i)(b)
Y: Enlargement with the centre at (0, 0) and a scale factor of 2.

(b)(ii)
Area of KTUVW = (Scale factor)2 × Area of object
= 22 × 30
= 120 m2

Hence,
= Area KTUVW – Area KSRQP
= 120 – 30
= 90 m2

Question 14 (12 marks):
Diagram 10 shows the marks obtained by a group of 36 students in a Mathematics test. Diagram 10

(a)
Based on the data in Diagram 10, complete Table 3 in the answer space.

(b)
Based on Table 3, calculate the estimated mean mark of a student.

(c)
For this part of the question, use graph paper.
By using the scale of 2 cm to 5 marks on the horizontal axis and 2 cm to 1 student on the vertical axis, draw a frequency polygon for the data.

(d)
Based on the frequency polygon in 14(c), state the number of students who obtained more than 40 marks. Table 3

Solution:
(a) (b)

(c) (d)
Number of students who obtained more than 40 marks
= 10 + 8 + 4
= 22 students