North Vista 4E 2024 Prelim Paper 2 Solutions

1 North Vista Secondary Secondary 4 Express Mathematics (4052) 2024 Paper 2 Marking Scheme Qn Solutions Mark AO Total 1(a) 5 3 2 13 3 3 15 15 x x x −  −  −   −   3 3 and 3 15 1 and 5 15 xx xx x −   −   −   M1 A1 AO1 2 1(b) 1 5 --- (1)2 2 3 13 --- (2) xy xy += −= (1) 4 2 4 20 --- (3)xy  += (2) – (3) 77 1 y y − =− = When 1y= , ( )2 3 1 13 8 x x −= = 8, 1xy = = M1 A1 A1 AO1 3 1(c)(i) When 7r = and 15q=− , AO1 1

2 Qn Solutions Mark AO Total 3 3 41 7 15 4(7) 1 2 3 rqp r += − −= − =− B1 1(c)(ii) ( ) ( ) 3 3 3 33 33 33 3 3 41 41 41 4 4 41 41 rqp r rqp r p r r q p r p r q p r r p q r p p q pqr p += − += − − = + − = + − = + − = + += − M1 M1 A1 AO1 3 1(d) ( ) 2 15 321 2 1 ( 3) 15 2 5 18 0 (2 9)( 2) 0 1422 xx xx xx xx x or x =+− − + = + − = + − = =− = M1 M1 A1 AO1 3 2(a)(i) Total Food Waste Output AO1 1

3 Qn Solutions Mark AO Total 6 565 000 605 000  640 000 1.81 10 tonnes = + + = B1 2(a)(ii) Percentage increase (2009-2010) 99000 75000 10075000 32% −= = Food Waste Recycled in 2011 132 99000100 130680 tonnes = = M1 A1 AO1 2 2(a)(iii) Per capital food waste 565000 1000 4.84 1000000 365 0.319823 0.320 kg/day =  = = Per capital food waste 565000 1000 4.84 1000000 0.318949 kg y 366 0 d.3 /a19 =  = = M1 A1 AO1 2 2(a)(iv) Food Waste Output 509000 100100 8.6 556892.779 557000 tonnes = − = = M1 A1 AO1 2 2(b)(i) Perimeter of the lake on map A 1700 9612 25 cm = = M1 A1 AO1 2 2(b)(ii) Actual area of lake ( ) 2 2 36 68 166464 m = = M1 AO2 2

4 Qn Solutions Mark AO Total Area of lake on Map B 2 2 166464 51 64 cm = = A1 3(a) 2 = 120 4 120 4 2 2(60 2 ) 2 60 2 (shown) rx xr x x     − −= −= −= M1 A1 AO2 2

5 Qn Solutions Mark AO Total 3(b) ( ) 2 2 2 2 22 2 60 2 60 2 3600 240 4 (4 ) 240 3600 0 (shown) xx xx x x x xx      −=  −= =−+ − − + = M1 A1 AO2 2 3(c) ( ) ( ) ( )( ) 2 240 240 4 4 3600 2(4 ) 240 45238.93421 2(4 ) 263.68 or 15.90 x    − −  − − −= − = − = M1 M1 A1, A1 AO1 4 3(d) Reject 263.68x= because - the perimeter of the square (4x) must be less than the length of the wire - the radius of the circle cannot be negative B1 AO3 1 4(a)(i) Mean = 166 cm B1 AO1 1 4(a)(ii) Standard deviation ( ) 2331532 16612 8.47 cm =− = B1 AO1 1

6 Qn Solutions Mark AO Total 4(a)(iii) 1. Since the mean height of Group B (168 cm) is greater mean height of Group A (166 cm), the students in Group B are generally taller on average. 2. Since standard deviation of heights of Group B (9.5 cm) is greater standard deviation of heights of Group A (8.47 cm), the heights of students in Group B have a wider spread / less consistent. B1 B1 AO3 2 4(b)(i) 1