SPM 2021 Add Maths Trial Paper (Selangor) – Paper 2 (Question 6)


Question 6:
Diagram 5 shows two curves x= y  and x= y 2 8 are intersecting at point A. The straight line AB is parallel to the x-axis.


Find
(a) the equation of the straight line AB, [2 marks]

(b) area, in unit2, of the shaded region, [3 marks]

(c) the volume generated, in term of π, when the region P, which bounded by the curve x= y 2 8 , the straight line AB and the y-axis, is revolved 360 about the y-axis. [3 marks]


Solution:
(a)

x= y  ….. ( 1 ) x= y 2 8  ….. ( 2 ) Substitute (1) into (2), y = y 2 8 ( y 1 2 ) 2 = ( y 2 8 ) 2 y= y 4 64 64= y 4 y y 3 =64 y=4 From (1), x= 4 =2 Point A=( 2, 4 ) Equation of the straight line AB is y=4.


(b)

x= y y= x 2 x= y 2 8 y= 8x Area of the shaded region = 0 2 ( y 1 y 2 )dx = 0 2 ( 8 x 1 2 x 2 )dx = [ 8 x 3 2 3 2 x 3 3 ] 0 2 = [ 2×2 ( 2 ) 1 2 x 3 2 3 x 3 3 ] 0 2 = 4 ( 2 ) 1 2 ( 2 ) 3 2 3 ( 2 ) 3 3 0 = 16 3 8 3 = 8 3  unit 2


(c)

x= y 2 8 x 2 = y 4 64 V=π a b x 2 dy = π 64 0 4 y 4 dy = π 64 [ y 5 5 ] 0 4 = π 64 [ 4 5 5 0 ] = π 64 [ 1024 5 ] = 16π 5  unit 3

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