HIHS Sec 2 Math 2021 EOY P2 (Ans key)

Marking Scheme Secondary 2 Express 2021 EOY Paper 2 1 a 5 cm : 1 km 1 cm : 0.2 km 1 cm : 20000 cm 1 : 20000 1 b 1 cm : 0.04 km2 Area = 2542 0.04 21.68km= 2 a 292 7.340 = 2 b 8 2 c 7 2 d Mode, as it was the size which the most shoes were sold. Alt Median, as it gives the middle shoe size that the shopkeeper can order. 3 a 33 °C 3 b 28 °C 3 c 29 °C 3 d Singapore, as the median temperature was higher. Alt Singapore, as the mean temperature was higher. Singapore as the noon temperature peaks/clusters at 30 °C, which is higher than Bangkok’s peak at 27 °C. 3 e 8 360 102.928 =  4 a 46 2 232 x x− =− 4 b 2 2 2 2 (23 ) 264 2 46 264 2 46 264 0 23 132 0 xx xx x xx −= − + = − + − = − + =

4 c 2 23 132 0 ( 11)( 12) 0 11 or 12 22 or 24 xx xx xx BC − + = − − = == = 5 a cos 60 20 20cos 60 10 cm x x x = = = 5 b 75 ,10 cm 5 ci 170 100% 85%200= 5 cii Loading at 85% 60 , 10 cm cos 60 10 10cos 60 5 cm d x x x  =  = = = = 75 , 15 cm cos 75 15 15cos 75 3.88 cm d x x x  =  = = = = Largest value of x is 5 cm. 6 ai False 6 aii False 6 aiii False 6 bi 180 90 35 55− − = 

6 bii 25 78 8( 2) 5( 7) 8 16 5 35 3 19 16 3 116 7 13 cm33 x x xx xx x x DF + =+ + = + + = + = = = + = 7 a 2 22 22 2 (3 1) 2(2 3)(2 3) 9 6 1 2(4 9) 9 6 1 8 18 6 19 x x x x x x x x x xx − − − + = − + − − = − + − + = − + 7 b 2 3 23 3 3 2 2 3 2 2 34 8 2 28 16 1 16 b a b ab a ba ab a b ab ab b  = = = 7 c 2 2 1 5 63 2 1 5 ( 3)( 2) 3 2 1 5( 2) ( 3)( 2) 39 ( 3)( 2) x x x x x x x x xx xx x xx − −+ − + −=− + − + − − −= +− −+= +− 8 a 36

8 b Draw axes and all points plotted correctly Draw smooth curve through all points 8 ci $69 8 cii 6 8 di See above 8 dii 3, 4, 5, 6, 7, 8, 9 9 a 3 1(15)(10)(8) (10)(8)(6)3 1360 m + = 9 b By pythagoras’ theorem Slant height triangle VBC = 61 m Slant height triangle VAB = 52 m Area of triangles ( ) ( ) 112 (10) 52 2 (8) 6122 134.59    =+       = Area of rectangular surfaces (10 10 8 8)(15) 540= + + + = Total Area = 134.59 + 540 = 674.59 = 675 m2

9 c 674.59 35 23610.76 23600$$ = =