SPM 2021 Add Maths Trial Paper (Selangor) – Paper 1 (Question 10)


Question 10:
(a) Given the gradient of the tangent to the curve y = x2 (3 + px) is -3 when x = -1.
Find the value of p. [2 marks]

(b) Volume, V cm3, of a solid is given by V=8π r 2 + 2 3 π r 3 , r is the radius. Find the approximate change in V, in terms of π, if r increases from 3 cm to 3.005 cm. [3 marks]


Solution:
(a)

Given  dy dx =3, x=1 y= x 2 ( 3+px ) dy dx = x 2 ( p )+( 3+px )( 2x ) 3=p x 2 +6x+2p x 2 3=p ( 1 ) 2 +6( 1 )+2p ( 1 ) 2 3=p6+2p 3=3p6 3p=3 p=1


(b)

Given δr=3.0053=0.005 V=8π r 2 + 2 3 π r 3 δV δr = dV dr δV= dV dr ×δr δV=[ 2( 8 )πr+3( 2 3 )π r 2 ]×0.005  =( 16πr+2π r 2 )×0.005  =[ 16π( 3 )+2π ( 3 ) 2 ]×0.005  =66π×0.005  =0.33π


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