2024 Outram Prelim P1 MS

2024 4E5N Prelim Math Paper 1 1 1. Method 1 42.2km = 42200m 4h 45min = 17100s Speed = 42200 17100 =2.47m/s Method 2 342.2 4 8.88424 km/h= 8.8842 1000 3600  =2.47m/s 2. a. 11 12 6 44 6 12 16 44 12 4 3 2 3 256 256 256 4 gf fg f g f g −     =       = = b. 1 2( 1) 4 2( 1) 5 5 9 15 81 5 3 3 5 3 33 2( 1) 5 3.5 k k k k k − − −  =   =   = −= = 3. 55.2 or 124.8 4. a. Divisor 245 = 5 × 72 which is a factor of A. b. k = 2 × 5 = 10 c. A = 27 × 511 × 78 B = 25 × 36 × 73 HCF = 25 × 73 LCM = 27 × 36 × 511 × 78 5. 36 1.6 1242000 1 100   +   = $44063.76 6. a. x2 + 6x + 10 = x2 + 6x + 32 – 32 + 10 = (x + 3)2 + 1

2024 4E5N Prelim Math Paper 1 2 b. (i) x = –3 (ii) The minimum point of the graph is above the x-axis. 7. a. Paul = 125% Mike → Mike = 80% Paul Mike = 75% Oscar 0.8 Paul = 0.75 Oscar Paul : Oscar = 0.75 : 0.8 = 15:16 b. Total cost = 900 × 8 = 7200 Total received = 180 504 900 3 900 7830100 100  +   = Profit = $630 8. a. (i) 420h±2 (ii) 500 – 330 = 170h b. x = 470 9. a. Using 2y + 3x = 2, 3 12yx=− + , y intercept = 1 b. 2(-4) + 3x = 2 D ( 10 3 , - 4 ) 10. 22 22 7 9 7 (3 ) ( 9)( 3) 3 3 ( 3)(3 ) 21 7 12 27 ( 3)(3 ) 9 8 27 8 9 27 or ( 3)(3 ) ( 3)( 3) y y y y y y y y y y y y y y yy y y y y y y y y + − − + +−=+ − + − − − − −= +− − − − += + − + − 11. a. (i) 33x2y + 11xy = 11xy( 3x + 1) (ii) x3 + x2 – 9x – 9 = x2(x + 1) –9(x + 1) = (x + 1)(x2 – 9) = (x + 1) (x +3) (x – 3) b. (x + 3y) (4x – 3y) = 4x2 + 9xy – 9y2

2024 4E5N Prelim Math Paper 1 3 12. Blue: let there be x marbles Green: x + 3 Red: 2x + 3 Total : 4x + 6 ( ) 6 4 6 25 25 6(4 6) 36 P Blue = x x xx x =+ =+ = Green = 39 13. 23(3 10) 2( 10 8) 4x x x x− + + − − 3 2 3 32 32 3 10 2 20 16 4 5 10 20 20 5( 2 4 4) x x x x x x x x x x = − + + − − = − + − = − + − Since expression has a factor of 5 OR is a multiple of 5, it is divisible by 5 for any integer x. 14. Interior angle of polygon C = 140° Exterior angle of polygon C = 40° 360 940 = or ( 2) 180 140, 9n nn − == Polygon C can be a regular polygon with 9 equal sides with each interior angle 140°. 15. The scale on the vertical axis is different and misleading. It can be misinterpreted that the average score for Company C is higher than Company D. 16. a) b) 5 35 33 {2,3, 4,5,6,7,8,9,10,11 } x x  = (i) {4, 8} (ii) A ⊄B

2024 4E5N Prelim Math Paper 1 4 17. 18. 22 22 6 7 5 (3 5 )(2 ) 18 50 2(3 5 )(3 5 ) (2 ) 2(3 5 ) x xy y x y x y x y x y x y xy xy − − − + =− + − += + 19. y k x= When x increased by 300%, 4x 4 2( ) y k x y k x = = y is 2 times, i.e. increased by 1 times, 100%. r = 100% 20. a) P = (6 15 8) b) (3105 3402) c) The total money collected from the ticket sales on Saturday and Sunday respectively. d) ( )111 21. Breadth: let it be x cm. Length: x + 7 cm Perimeter = 2 [(2x + 14) + (2x + 7)] = 138 x = 12