2024 Outram Prelim P2 MS

2024 4E5N Prelim Math Paper 2 1 1. a) (i) 1000 (ii) 0.573mg × 2 = 1.146mg = 1146μg Yes, he met the daily recommended intake. b) (i) 2.55km (ii) Area scale 1cm2 : 0.09km2 Area on map = 0.36 ÷ 0.09 = 4 cm2 (iii) 0.5625 cm2 : 0.36 km2 1 cm2 : 0.64 km2 1 cm : 0.8 km n = 80000 2. a) 242 3 yzxz z −= (i) 24 ( 1)2(3)( 1) 3( 1) 19 or 4.754 y y −−−= − = (ii) 2 2 22 2 42 3 2 (3 ) 4 64 (6 1) 4 4 61 yzxz z xz z y z xz z y z x y yz x −= =− += += = + b) 7336 2 6 2 7 3 and 7 3 12 1 and 3 5 5 3 xx x x x xx x −−   −  − −   −  −

2024 4E5N Prelim Math Paper 2 2 c) 2 2 25 11 2 5 2(2 5) 5( 1) ( 1)(2 5) 4 10 5 5 2 3 5 2 12 0 2 ( 6) 0 0 or 6 xx x x x x x x x x xx xx x +=+− − + + = + − − + + = − − −= −= = 3. a) ( ) ( ) 22 2 2 0.8 1.5 2.89 1.7 Curved area of cone 0.8 1.7 1.36 (shown) Slant height of cone = hh h h hh h   + = = =   = b) 2 2 2 Total surface area 1.36 2 (0.8 )(1.5 ) 3.76 1504 1504 3.76 20cm h h h h h h   =+ == = = c) Radius = 16 cm, full height = 60 cm 22 7L 6engt 6h of 0r 1od 0 62. 9 = += Length outside funnel = 2.1cm d) 4 a) 2 210107 (2) 2 1 2 a a =+ = b) 21 210(12)2 12 89.5 p p =+ = c) Refer to graph d) (i) 5.9 ±0.2 (ii) 3.2 < x < 9.9 ±0.2 e) (i) refer to graph (ii) x = 5.6 or 10.2 ±0.2

2024 4E5N Prelim Math Paper 2 3 (iii) 6y = 25x + 180 → 25 306yx=+ 21 210 2yx x=+ 2 32 32 1 210 25 30 026 1 25 30 210 026 25 60 420 03 xx x x x x x x x + − − = − − + = − − + = By comparing coefficients with x3 + Ax2 + Bx + C = 0, 25, 60, 4203A B C= =− = 5 a) (i) Angle CBD = CED, angles in the same segment Angle DFE = 90°, OE bisects chord BD Angle FDE = 30°, angle sum in a triangle DFE Angle CDE = 90°, angle in a semi circle Angle BDC = 90 – 30 = 60° Angle CBD = 60°, angle sum in triangle BCD Hence Triangle BCD is an equilateral triangle. OR Angle CBD = CED, angles in the same segment Angle BED = 2×60 = 120° (OE bisects chord BD, Triangle DEF and BEF are congruent) Angle CBD = 60°, angle sum in triangle BCD Hence Triangle BCD is an equilateral triangle. (ii) Angle BOC = 120°, angle at centre = 2x angle at circumference Angle BAC = 360 – 90 – 90 – 120 = 60° b) (i) T7=36 (ii) Tn = 1 ( 1)( 2)2 nn++

2024 4E5N Prelim Math Paper 2 4 (iii) 2 2 ( 1)( 2) 351 3 2 702 3 700 0 28(reject) or 25 nn nn nn n + + = + + = + − = =− n = 25

2024 4E5N Prelim Math Paper 2 5

2024 4E5N Prelim Math Paper 2 6 6 a) (i) 22 2 2 23 4 5 4 5 ( 4) 13units 25 8 16 169 8 128 0 8 or 16 (rejected) 8 PQ OQ OP m m PQ m mm mm m m =− −   =−       = − = + − = + − + = − − = =− =− (ii) 2QP PR= 5 12 2 51 122 2.5 3 64 5.5 10 ( 5.5,10) QP QP PR OR OP OR OR R −= = − =− −−   +=       −= − b) (i) 2 3 11When x = 5, y = 7, 3 2 11 33 y x C C yx =+ = =+ (ii) Let y = 1, x = – 4 21area 9 9 40.5units2=   = (iii) PQ and BC are parallel Angle PAQ = Angle BAQ (commo