2020_H2_Prelim_P1_Marker_s_Report

1 2020 ACJC H2 Math Prelim P1 Marker’s Report Marking Annotations used in scripts: K:Knowledge Gap; C:Carelessness; R:Read/Interpret question wrongly; P:Presentation issue Qn Solutions Comments 1(i) Given u = 2x – 1. Then 1 ( 1)2xu and d1 d2 x u  .       2 1 2 2 22 1 21 2 1 2 2 1 1 2 12 12 d 1 (2 1) ( 1) 1 d21 11 dd4 11 11 2 1 d sin42 111 sin42 1 sin 14 11sin (2 1) 1 (2 1)44 where is an arbitrar x x x u u u u uu uu u u u u C u uC u u C x x C C                                              y constant. The common mistakes are  Changing ‘dx’ to ‘2du’  When applying of the formula 1 f ( )[f ( )] d [f ( )] ,1 n n u u u u Cn      for the 1st integral, the negative sign or ½ in the denominator is left out.  The result of the 1st integral 2 d 1 u u u becomes 2 3/ 2(1 ) 3/ 2 u or 2ln 1 u Some students are able to integrate correctly but do not substitute u as 2x – 1 and add the arbitrary constant C in the final answer. 1(ii) 1sin (2 1) dxx  1 2 dsin (2 1) 1 d d2 d 1 (2 1) vux x u vxx x      1 1 2 sin (2 1) d 2sin (2 1) d 1 (2 1) xx xx x x x          The part is badly done. Not many students are able to see this is a question on ‘Integration by Parts’. Some students are able to choose ‘u’ as sin-1(2x – 1), but fail to differentiate it correctly.

2 1 1 2 12 11sin (2 1) sin (2 1) 1 (2 1)22 11 sin (2 1) 1 (2 1)22 where is an arbitrary constant. x x x x C x x x C C                   2(i) Note: Do indicate coordinates of points when question requires it. Many students do not indicate the coordinates of the x- intercepts and the equation of the three asymptotes as required in the question. The common mistakes are  The asymptote y = 3 still remains in the graph  The maximum turning point at x = 2.5.  The asymptote y = 1 is missing 2(ii) Note: Do indicate coordinates of points when question requires it. Generally well done. However, the parts of the curve when x  are not properly drawn. The curve should get closer and closer to the asymptote y = 1/3 or the asymptote y = 0 when x . The common mistake is that the curve is either too short, turns away from asymptote or seems going to cut the asymptote. For example, Another common mistake can be seen when x . The curve cuts the negative x-axis and approaches to the asymptote y = 1/3 instead of y = 0. 3(i)   3f e sec2 xxx    33f ' 3e sec2 2e sec2 tan 2xxx x x x Some students do not differentiate sec 2x directly. x (2, 0) (-1, 0) y y =1 y =0 x =0 y x O (2,-2) (-1,-0.5) y =1/3 Asymptotes A short curve

3 3 2 tan 2y y x   3 2tan 2yx They differentiate 1 cos 2x by quotient rule which required more working steps. 3(ii)  