NJC_9758_2022_Promo_Solutions

National Junior College Mathematics Department 2022 / SH1 H2 Maths / Promos / Suggested Solutions Page 1 of 20 Qn Suggested Solutions 1 Let $A, $B and $C be the selling price of 1 kg of salmon, 1 kg of tuna and 1 kg of swordfish respectively before discount. 2 3 246 (1) 18 18 (2) 0.85 0.9 0.95 123.3 (3) A B C A C B ABC A B C              By G.C., 48, 60, 30A B C   The selling price of 1 kg of salmon, tuna and swordfish before discount is $48, $60 and $30 respectively. Qn Suggested Solutions 2(a) (b)  hyx   1 h y x    1 h y xp     1 h y xp     1 h yq xp   2y 0.5y 0.5y 0.5y 0.5 1 1.5 yq q      1,0 1x 1xp  1xp 12 3 xp p     x y O

National Junior College Mathematics Department 2022 / SH1 H2 Maths / Promos / Suggested Solutions Page 2 of 20 Qn Suggested Solutions 3(i) (ii) Solve for intersection between the curves: 1xb xbxa           11 or 1 1 1 1 0 or 0 x b x b x b x bx a x a x b x b x a x a                     11 or x b x a xa    or 11 or x b x a xa    Therefore, we have or or x b x a x a   From graph in part (i), xa or 0x x y for (ii)

National Junior College Mathematics Department 2022 / SH1 H2 Maths / Promos / Suggested Solutions Page 3 of 20 Qn Suggested Solutions 4(a)     2 22 22 2 21 1 d .43 1 d d4 3 4 3 1 6 1 3 d d6 4 3 3 23 1 1 3ln 4 3 tan62 23 x xx x xxxx x xxx x xxA                    (b)   2 1 1 1 or 1 yx yx y x y x            2211 00 Volume required π 1 d π 1 d 8.3776 (4 d.p.) by GC x x x x       Alternatively (Shell Method) – For Teacher’s Ref only   2 2 0 Volume required 2 π 1 1 d 8.3776 (4 d.p.) by GC y y y     

National Junior College Mathematics Department 2022 / SH1 H2 Maths / Promos / Suggested Solutions Page 4 of 20 Qn Suggested Solutions 5(i) By Ratio Theorem,  1 22 2 2 BA BCBR               a b c b a b c  : 2 , 2 BRl BR          r b b a b c (ii) Given that  : 2 ,AQl      r a a b c To show that lines BR and AQ meet, we let         222 1 1 222                       b a b c a a b c a b c a b c Since the points O, A, B and C do not lie on the same plane, we can compare the coefficients of a, b and c to obtain 1 2 (1)2 1 (2) (3)2         Sub (3) into (2), we obtain 21 23     . Hence    11 33OG         b a 2b c a b c (iii) Length of projection of OS   onto OA   OAOS OA       

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