KSS 2021 P1 (MS)

Marking Scheme to 4 NA Prelims Paper 1 No. Workings and Steps 1 2 >10 2x > 7 x > 3.5 x = 5 3a When x = 0, y = 4 point A = (0. 4) b Gradient = -1.5 4 = 1 unit reps $30 12 units rep 12 x $30 = $360 5 6 arc length 4.26 8.53 97.1 49 100 0.6 ´ ´= = 23x+ 345 33 ++ - 4 32 32 4 32 3 35 5 12 6 35 6 12 5 7 2 pr r pp q pr p q pr pq r ÷ =´ = 360 110 21 5360 125 6 p p -=´ ´ =

perimeter = 7a tan angle MAD = b tan angle CMN = CN = cm 8 -3, 3.03, 9a October and November b percentage increase = = 1.80% 10a 125 306 p+ 2310 CN 2 3 10 CN= 210 6.673´= 13,3- 133 1.7 1.67 100%1.67 - ´

bi scale factor = ii y = 4 x 1.8 = 7.2 11a b 12a b OR 13ai 64 aii 2.4 b 14 total distance = km 181.810= 4 10 3 6 4 yx y x yx -- + =- 25 3 25 2(2 5) 6 10 4 25 10 xx xx x -- --= -= 190 156´= (45 15) 3 2 20 -÷ = (45 15) 3 2 20 -÷ ´ = 3920 7.5 20.560´+ =

total time taken = h average speed = km/h 15a angle DCA b AC = 44.8 cm BC = 44.8 – 40 = 4.8 cm 16a 324 = 22 x 34 bi LCM = 23 x 34 x 52 x 7 bii) HCF = 2 x 32 = 18 17a value of handbag = = S$179.21 b watch in A$ = $255 x 1.054 = A$268.77 total cost = A$268.77 x 1.0205 = A$274.28 It is cheaper to buy in Singapore. 18 39 1 23 60 2 20+= 2320.5 17.820÷= 286440 AC CD BF BA AC = =´ 189 1.054657 2 2 82 3 ( 2)( 3) 8 68 14 0 1 1 4(1)( 14) 2 1 57 2 e e ee ee ee e e -= + -+ = +- = +- = -± - -= -±=

e = 3.27 or - 4.27 19a angle ACE = 180º - 80º = 100º Angle ACE = 100º because angle BAC and angle ACE are interior angles, AB // CE OR Angle ACE = 100º because BCE = 47º (alt. s, AB // CE) and ACE is the sum of ACE and BCE b 20 P(late) = 1 – 0.3 – 0.52 = 0.18 21 p = 80% 22 slant height perpendicular height = 21.81742 Volume ÐÐÐÐÐ100 53 47 123 47 76 BCD CBD Ð= ° - ° = ° Ð= ° - ° = ° 22.40100%28p=´ 2226 10 24 =- = 2224 10 476 =- =

23 1 int angle of pentagon = 108º 1 int angle of heptagon = º x = 360º - 108º - x = 117º 24a b c 5x + 3y = 136 ………………….(1) 8x + 9y = 268 ………………….(2) (1) × 3 15x + 9y = 408 …………………(3) (3) – (2) 7x = 140 x = 20 subst x = 20 into (1) 5(20) + 3y = 136 y = 12 x = 20 y = 12 120 20 4763 2910 =´ ´ ´ = (5 2) 180 5 -´ °= (8 2) 180 8 -´ °= 135135°25 15 680 531 3 6 xy xy += += 16 18 536 8 9 268 xy xy += +=

Alternative Method(Substitution) 5x + 3y = 136 ………………….(1) 8x + 9y = 268 ………………….(2) From (1) 3y = 136 – 5x ………..(3) Subst (3) into (2) 8x + 3(136 – 5x) = 268 8x + 408 – 15x = 268 -7x = -140 x = 20 Subst x = 20 into (3) y = 12 x = 20 y = 12 d diff = $20 – $12 = $8

25a b Refer to picture above c Refer to picture above d PA = 5.3 cm

26 Volume of water discharged by the 2 pipes per second