DHS ans

DHS 2019 Year 6 H2 Math Prelim P1 Mark Scheme 2019 Year 6 H2 Math Prelim P1 Mark Scheme Qn Suggested Solution 1 Number sold before 7 pm Number left after 7 pm Banana 10 10 Chocolate 45 5 Durian 20 10 Let the selling price of banana cake, chocolate cake, durian cake before discount be $b, $c, $d respectively.

29.50 1 10 45 20 730 2 9 4 146 2 0.6 10 5 10 880 730 10 5 10 250 2 2 50 3 abc bcd bcd bc d bc d bc d " " " Solving (1), (2), (3) using GC, a = 8.50, b = 9, c = 12 The selling price of banana cake, chocolate cake and durian cake is $8.50, $9 and $12 respectively. Qn Suggested Solution 2(a) 2 2 2 2 2 0 3 0 01 1 30 11 2( 21 1 1 2 (2 3 9 )( 4) (3 ) ( 29 9) 0 9 3) x x xx x xx x xx xx d

d

d

d 3 23o r 3 4xx? d d 4 3 –3 ++ – – + x 00000000000000000000000 4))4))4))4)4)4))))4)4)4 3)33))))))))))))33))

ddd ++ ++ – – www.KiasuExamPaper.com 218

2 DHS 2019 Year 6 H2 Math Prelim P1 Mark Scheme (b) 3 3 2 2 2 n (3) e 0 30 e 0 3 3 si ce for all or 3 ax bx ax bx ab x ab x a b aa bb x x xx

! ! ! Qn Suggested Solution 3(i) Since A, B and C are collinear and AB ba JJJG 5P? 55 65 OC OB BC

=b b a ba JJJ G JJJ G JJJ G (ii)

1 65 ( 1)2 731 2 OE k OE ON OAOO O O OO §· ¨¸©¹ b b a a b a JJJ G JJJ G JJJG JJJ G 72 610 27 7 kOO Ÿ Ÿ 6 7OE P? bb JJJ G Qn Suggested Solution A C B O N E B B E E 6 7777777777777 b bbbbbbb 6 www.KiasuExamPaper.com 219

3 DHS 2019 Year 6 H2 Math Prelim P1 Mark Scheme 4 (i) Since the shape of the curve is For f to be 1-1, the largest b can take is the x-coordinate of the turning point. 2 2 1f' ( ) 1 () 110 () 1 x xa xa xa r x-coordinate of turning point is a+1, since ba! For graph to be 1-1, 1bad , (ii) Let f( )yx 2 2 2 2 2 2 2 1 1 (1 ) (1 ) 1 1 (1 ) 1 0 (1 ) (1 ) 1024 (1 ) ( 1) 124 (1 ) ( 1) 124 yx x xy x x xy y x x xy x y yyxy yyx yyx §· ¨¸©¹ §· ¨¸ ©¹ r Since 37,22 §· ¨¸©¹ is a point on the curve of f( )yx , 2(1 ) ( 1) 124 yyx 2 1 (1 ) ( 1)f( ) 1 24 xxx The domain of 1f is the range of f = [3, )f . x = a y x 2222 ( 111111111111) 111 4444444 yyy ( ((((((( ( 22222222222 1 )))) (((( 1111)))) 11 )) (( ) ( )) ((

www.KiasuExamPaper.com 220

4 DHS 2019 Year 6 H2 Math Prelim P1 Mark Scheme Qn Suggested Solution 5(a) Series of transformations: 2 2 2 22 ln 1 1ln ln 1 21 21ln ln(2 ) 4 xy x xxy xx xxy xx p p (b) (i) (ii) Qn Suggested Solution 6 >@ >@ iarg( ) 1 ( 1) 2aarg ( ii rg 1 arg 1 1)nwn n n 1. Reflect in the x-axis (replace y with y) 2. Scale by factor 1 2 parallel to the x-axis (replace x with 2x) y x O y x O www.KiasuExamPaper.com 221

5 DHS 2019 Year 6 H2 Math Prelim P1 Mark Scheme (i) (ii) >@ >@

>@ >@ >@ >@ 12 12 1 2 1 1 a i arg( ) arg iiarg i arg i i i arg(1) 2arg(1 i) arg(1 2i) a 2 rg(1 i) 2 arg(1 2i) arg(1 3i) arg(1 rg arg( ) arg( ) arg( ) 1 ( 1) 1 ( 1) 1 1( 1 ) a r g 1 2 arg 1 ( 1) n n n n k k n k n k z ww ww kk k kk k w w w } } §

· ¨¸¨¸©¹

¬

ªº ¼ ¦ ¦ ¦ > >@ > @ 1 4