SHSS 2022 MA S4E5N Prelim soln P1

1 2022/Prelim/4Exp5NA/Mathematics/4048/01 Mathematics Paper 1 Solution 1 (a) [1] (b) [1] 2 22 69 33 96 6 4 pr rp r p −     =       = [2] 3 (a) [1] (b) 'AB or ( ')'AB [1] 4 2 22 2 22 :117 3 13 : 2 3 13 2 3 13 234 3 13 1521 HCF LCM m n =  =   = =  = [2] 5 1 33 2 1 1.35 27 3.2 64 3 4 3 274 20.25 cm h h h == = = = [2] 2 ay x= , where 0a 3 2y ax=− , where 0a

2 2022/Prelim/4Exp5NA/Mathematics/4048/01 6 n n ky x k yx = = Let ,.x a y b== Then 12 , . 16x a y b== ( ) ( ) 4 1 216 1 216 2 16 22 4 nn n n n n n ba b a aa n = = = = = [3] 7 (a) 41 – 8n [1] (b) 41 8 101 8 142 17.75 n n n − =− = = Since n is not an integer, −101 is not a term in the sequence. [2] 8 (a) 1200000 6 200000 n= = [1] (b Length scale 6 cm :12 km 1 cm : 2 km= Area scale 221 cm : 4 km Actual area of park 4 0.05= 20.2 km= [2] 9 (a) (i) 145 155(3) 165(5) 175(14) 185(2)Mean 25 170.2 + + + += = [1] (ii) SD = 9.43 [1] (b) 9P(<170 cm) 25= or 0.36 [1] 10 36 72 9 9 EF DF DE=− −   =−   −    −= 22( 9) 9 12.7 EF = − +  [3] or   2 26 ( 3) ( 2 7) 12.7 EF = − − + − − 

3 2022/Prelim/4Exp5NA/Mathematics/4048/01 11 (a) 3(2 ) 5( 2 ) 6 3 5 10 13 b d b d b d b d bd + − − = + − + =+ [1] (b) 2 2 2 2 41 (5 3 ) 5 3 4 (5 3 ) (5 3 ) 453 (5 3 ) 31 (5 3 ) xx x x x x x x −−− −−= − −+= − −= − [2] 12 (a) ( ) ( ) 2 2 2 67 3 9 7 32 xx x x −+ = − − + = − − [2] (b) Min point = (3, −2) [1] 13 (a) 30 32Median 2 31 += = [1] (b) 1 1 45 22 23 3 Q Q p −= = = [2] 14 X Y W Z

4 2022/Prelim/4Exp5NA/Mathematics/4048/01 15 (a) 3 6 639 10 100%3.99 10 16.015% 216.0% or 16 %133   =  [2] (b) 63 66 6 3.99 10 639 10 3.99 10 0.639 10 3.351 10  −  =  −  = [2] 16 (a) 2( 3) 25 ( 3 5)( 3 5) ( 2)( 8) x x x xx − − = − + − − = + − [2] (b) 2 2 ( 3) 25 9191 ( 3) 9216 3 96 99 x x x x − − = −= −= = The 2 factors are 101 and 91. [2] 17 (a) 5000 1.255000 5200 100 62.5 200 3.2 4 n n n n +   = or 5000 1.255000 5200 100 62.5 200 3.2 4 n n n n += = =  [2] (b) 3200 1.08 1000 2962962.9 2963000  =  [2] 18 (a) The median is a better measure as it is not affected by the extreme value of 20; OR the mean is affected by the extreme value of 20. [1] (b) (i) 2 2 11x+ and 13 11x− [1] (ii) 2 2 11 2 9 4.5 x x x +   and 13 11 2 2 x x x −   2 4.5x 3, 4x= [2]

5 2022/Prelim/4Exp5NA/Mathematics/4048/01 19 (a) F 0.37 0.90 1.15  = [1] (b) O 0.3730 25 8 0.9042 35 4 1.15  =   42.80 51.64 = [2] (c) or Company A spends a total of $42.80 on postage and Company B spends a total of $51.64 on postage. The amount of money that Company A and B spend on postage is $42.80 and $51.64 respectively. [1] 20 (a) P (both caramel) 10 9 18 17 =  5 17= [1] (b) P (NN, CN) 8 7 10 8 18 17 18 17    =+        4 9= [2] (c) P (NC, CN) 8 10 10 8 8 10 or 218 17 18 17 18 17      = +            80 153= [2] 21 (a) 22 20Retardation 15 41 m/s or 1 m/s33 = = [1] (b) 11(20)(10 30) (30 5)22 800 25 32 v v v + = − = = [2] (c) 2 32Acceleration of Car 15 10 3.2 m /s 20Time taken 3.2 6.25 s Time met 5 6.25 11.25 s N = − = = = =+ = [3]

6 2022/Prelim/4Exp5NA/Mathematics/4048/01 End of Paper 22 (a) 120 2 12 20 AB = = y-coordinate of A = 20 – 5 = 15 A (0,15) [2] (b) 15q= , 15 12 1 1.25 or 1 4 p=− =− − [2] (c) 225 12 13 BC =+ = Let d be the shortest distance. 1 13 1202 240 13 618 or 18.513 d d   = = = [3] 23 (a) (i) 24cos 25PRQ= [1] (ii) 2225 24 7 cm sin sin 7 25 PQ PRS PRQ =− =  =  = [2] (b) 1 7sin 25 16.26 180 16.26 163.7 PRQ PRS − =  =  = −   [2]