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 (common) Angle APQ = Angle ABC (corresponding angle) Triangle APQ and ABC are similar 7 a) (i)

2024 4E5N Prelim Math Paper 2 7 (ii) 260 (iii) Students in class A has a higher score for the science test than class B. The median marks for class A is higher than B. Students in class A has a less consistent score than class B. The interquartile range for class A is higher than class B. b) (i) mean = 51 Standard deviation = 9.165≈9.17 (ii) a) 18 17 153 80 79 3160= or 0.0484 b) 6 32 32 6 24 80 79 80 79 395 +  = 8 a) Vol of pyramid = 3 11 8 8 sin 60 2032 184.75cm      = b) 1 2 1 3 2 2 1 2 39.96 27 185 125 27 3 125 5 39 5 25 V V l l A A == ==  == c) Method 1 2 3 8 4.85 1area of triangle FGH 4.8 4.8sin(60)2 9.98cm HF =  = =   = Method 2 2 91area of triangle FGH 6 6sin(60)25 2 9.98cm =    =

2024 4E5N Prelim Math Paper 2 8 9 a) Compare unit cost 1 Egg Type Cost Sets Pasar 10 0.27 60 trays Pasar 30 0.23 20 trays Dasun 15 0.3033 40 trays 1 Bread Garden14 0.1928 22 loaves Sunny12 0.2083 25 loaves 1 Sausages Chicken F 10 0.525 30 packs Chef S 6 0.504 50 packs 1 Ham FP 10 0.435 30 packs SC 10 0.33 30 packs 1 coffee Nes35 6.15 9 packs Ind 25 3.95 12 packs Compare cost for 300 sets 600 eggs Type Cost Sets Pasar 10 162 60 trays Pasar 30 138 20 trays Dasun 15 182 40 trays 600 Breads Garden14 116.10 43loaves Sunny12 125 50loaves 300 Sausages Chicken F 10 157.50 30 packs Chef S 6 160 151.25 (0.35disc) 50 packs 300 Ham FP 10 130.50 104.40 (20%disc) 30 packs SC 10 99 30 packs 300 coffee Nes35 55.35 49.20 (disc1) 9 packs Ind 25 47.40 12 packs Lowest possible cost 138 + 116.10 + 151.25 + 99 + 47.40 = $551.75

2024 4E5N Prelim Math Paper 2 9 b) Possible solution 1 Let the selling price be $x. Total sales = $300x To meet cover expenses criteria 40% of sales = 551.75 100% of sales = 551.75 ÷ 40% = 1379.375 60% of sales = 1379.375 × 60% = 827.625 Meets the donation criteria T3 Selling price of each set = 1379.375 ÷ 300 = $2.75875 ≈ $4.60 Alternative solution 1379.375 – 200 = 1179.375 1179.375 ÷ 300 = 3.93 ~ $4 Possible assumption: 1) All 300 breakfast sets can be made without any loss of ingredient. 2) All 300 breakfast sets are sold at the minimum selling price during the carnival. 3) Did not include funding, as it is uncertain if it can be achieved.