SPM Mathematics 2018, Paper 2 (Questions 11 & 12)


Question 11 (6 marks):
Diagram 8 shows sectors OABC and ODE with the common centre respectively.

Diagram 8

Calculate
(a) the perimeter, in cm, of the whole diagram,
(b) the area, in cm2, of the shaded region.



Solution:
(a)

Perimeter of the whole diagram =OP+PE+Arc DE+DC +Arc CBA+AO =10+5+( 50 o 360 o ×2× 22 7 ×15 )+5 +( 230 o 360 o ×2× 22 7 ×10 )+10 =30+ 275 21 + 2530 63 = 5245 63 =83.254 cm


(b)
Area of the shaded region =( 230 o 360 o × 22 7 × 10 2 ) +[ ( 50 o 360 o × 22 7 × 15 2 )( 50 o 360 o × 22 7 × 10 2 ) ] = 12650 63 +( 1375 14 2750 63 ) = 3575 14 =255.36  cm 2



Question 12 (12 marks):
(a) Complete Table 2 in the answer space, for the equation y= 30 x  by writing down the values of y when x = 2 and x = 5.

(b)
 For this part of the question, use the graph paper. You may use a flexible curve ruler.
Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of  y= 30 x  for 0x7.  

(c)
 From the graph in 12(b), find
(i) the value of y when x = 2.6,
(ii) the value of x when y = 17.5.

(d)
 Draw a suitable straight line on the graph in 12(b) to find the values of x which satisfy the equation  30 x =5x+30 for 0x7.
State the values of x.

Answer:
Table 2


Solution:
(a)



(b)



(c) From the graph

(i) When x = 2.6; y = 11.5
(ii) When y = 17.5; x = 1.7

(d)
Given, 30 x =5x+30   y=5x+30 From the graph; x=1.25 and 4.75



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