2019 A level H1 Math Solutions - students (SAJC)

Appendix 2 1 Solution Template for 2019 A-level Examination Subject: H1 Mathematics ; Paper: 01 Questi on Suggested Solutions 1 Let $A, $B and $C be the price of Style A television, Style B television and Style C television respectively. 22 16 8 96480 (1) 22 16 3120 (2) 2 2 2 13260 (3) Using GC, 1800 2280 2550 The price of a Style B television is $2280. A B C AB A B C A B C + + = − − = − + + = − = = =  2(i) Using GC, when 0, 0.67721 the coordinates of is ( 0.677,0) yx A = =− − 2(ii) 4 3x=−

Appendix 2 2 2(iii) when 0, ln 4 the coordinates of is (0,ln 4) d3 1d 3 4 when 0, d 7 7 , hence gradient of tangent at is .d 4 4 7Equation of tangent at is ln 4 4 xy B y xx x y Bx B y x ==  =+ + = =  = + 3(i) 2 2 2 6 3 (1) 11 9 (2) (1) (2) 2 5 12 0 ( 4)(2 3) 0 34 or 2 substitute 4 to (2) 11(4) 9 53 3substitute to (2)2 3 1511 9 22 3 154, 53 or , 22 y x x yx xx xx x x y x y x y x y = + − → = + → − − − = − + =  = − = = + = =− = − + =−  = = =− =−

Appendix 2 3 3(ii) 2 2 2 6 3 11 9 2 5 12 0 ( 4)(2 3) 0 x x x xx xx + −  + − −  − +  3 42 x−   4(i) 4 4 5 5 1Let (2 3 )(2 3 ) d 4(2 3 ) ( 3)d 12 (2 3 ) yx x y xx x − − = = −− =− − − = −

Appendix 2 4 4(ii) 2 2 3Let 2 94 12 d9 4d 4, 9 yx x yx x y xx pq =−  = − + =−  = =− 4(iii) ( ) 1 22 0 132 0 2 2 2 2 e d e232 1 e 123 2 2 11 e 62 11 1 6 2e x x xx x x − − − − +− = + − − = + + − =+ =+  5(i) Initially, i.e. when t = 0, P = 0, Hence 00 1.5 0.6 0.6 k k =  − =

Appendix 2 5 5(ii) 5(iii) Using GC, when t = 6, P = 6.2344 6.23 5(iv) Using GC, 3 d 0.821d t P t = =

Appendix 2 6 5(v) ( )( ) 32 2 2 2 2 2 2 2 2 10 25 10 d 3 20 25d dAt stationary point on the graph, 0d 3 20 25 0 5 3 5 0 55 or 3 d 6 20d when 5, d 6(5) 20 10 0,d 5 gives a minimum point on the graph . 5when , 3 d d C t t t C ttt C t tt tt t C tt t C t t t C t = − + + = − + = − + = − − = = =− = = − =  = = = 56 20 10 0,3 5 gives a maximum point on the graph .3t  − =−  =

Appendix 2 7 5(vi) 5(vii) 6 32 0 Using GC, ( 10 25 10) d 114 The total cost incurred by Mr Tan over 6 years is $114000 t t t t− + + =   (0, 10) x (5, 10) (6, 16) x , 28.5) C

Appendix 2 8 6(i) Group EI as 1 unit, total permutation of 8 units = 8! Permutate the unit consisting of EI = 2! No. of ways = 8! 2! 80640  = (ii) 9 4 7 4 No. of ways of choosing 4 letters without restriction = No. of ways of choosing 4 letters with no vowel = No. of ways with at least 1 vowel chosen No. of ways of choosing 4 letters without rest C C  97 44 riction No. of ways of choosing 4 letters with no vowel = 91 waysCC − −= 7(i) Let be the number of members in the sal es team that receive bonus out of 8. ~ B(8,0.32) P( 4) 0.15694 0.157 X X X = =  (ii) P( 5) 1 P( 4) 0.074964 0.0750XX = −  =  (iii) ( ) ( ) Mean =E = 8(0.32) = 2.56 Variance = Var =8(0.32)(1 0.32) 1.7408 1.74 X X − = E I _ _ _ _ _ _ _

Appendix 2 9 8(i) ( ) ( ) ( ) ( ) P | 0.1 P 0.1P P 0.1 0.4 0.04 AB AB B AB =  =  =  = 8(ii) It is the probability that event B and (i.e. intersect) the complement of event A will occur at the same time. 8(iii) ( ) ( ) ( ) ( ) ( ) P ' P P 0.6 0.04 0.56 P ' 1 P ' 1 0.56 0.44 A B A A B A B A B  = −  =− =  = −  =− = 9(i) 9(ii) Using GC, 0.92083 0.921r= A B y x 16 30 4.8 2.9 0.112 1.22yx=+

Appendix 2 10 It shows that there is a strong positive linear correlation between x (the marks of the students for the written test) and y (the marks of the students for the practical test). 9(iii) Using GC, 0.11236 1.2183 0.112 1.22, where 0.112 and 1.22 yx yx ab =+ =+ == [For the sketch of the regression line on the scatter diagram, please refer to the scatter diagram in (i)] 9(iv) When 22x= , ( ) ( ) 0.11236 22 1.2183 3.69022 3.7 to 1 decimal place y=+ = = Since 0.921r= is close to 1 and 22x= is within the range of x ( )16 30x given in the table, the estimate is an interpolation, therefore the estimate is reliable. 10(i) 93 24 8 = 1st sock 2nd sock