2013 CCHY 4E5N Prelim II EMaths P1 solutionS/NSolution

1a

+ 0029 x 10= 3027368679

1b(i)300

b(ii)30274

b(iii)3027 x 10

2a28 m 01 m = 27 m

2b(i)239 m

2b(ii)0207 m

3a(i)12 = 1 x 12 = 2 x 6 = 3 x 4

F= { 1,2,3,4,6, 12}

or the elements of Fare 1,2,3,4,6,12

a(ii)Possible values of k are 11, 13, 17, 19

3b(i)B onlyor B A

b(ii)P U S

4a

Y X =

=

4bDifference in price in cents per 100 g of cereals between the two monthsIncrease in price in cents per 100g of cereals from May to JuneChange in price in cents per 100 g of cereals in May and June

4cM =

5awhen x = 0, y = k k = 3

5bAt (1,6), 6 = 3a a = 2

6a9 correct answers

6bx 360 = 288

6c6,7,7,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,11,11,12,12,12,12,12

Q is at = 65th data, Q = = 85

Qis at = 13th data, Q= 9

Qis at x (25+1) = 195th data, Q= 11Hence, the required answers are6, 85, 9, 11, 12

7aTermvaluepattern

13939 (1-1) x 2

23739 (2-1) x 2

33539 (3-1) x 2

43339 (4-1) x 2

n39 (n-1) x 2= 41 2n

Formula : 39 2(n-1) or 41 2n

7b20th term = 41 2(20) = 1

8a(i)c =

= = 2

a(ii)c =

8 = h 1 hh -9 - 9h

h -9 - 8h

8h = h 9

h 8h 9 = 0( h + 1)(h 9) = 0 h = 1 or h = 9

8b

h k = ch

k = h(h c)

k =

8ch c or c h for k to be defined when h > 0

9a18 or 180625

9b9

9c

9d

7 or or

10aFrequency of A = 2 x 256 Hz = 512 Hz

10b

2 x 067 x 10m = 2 x 067 x 10x 10m

= 134 x 10m = 134 picometre

11aAverage speed = = = m/s

11bCost price 12 eggs ------ p cents

1 egg -------- cents

n eggs -------- centsselling price1 egg -------- s centsn eggs ------- ns cents

profit = (ns ) cents

or n( s )

or n

12ab = 1

12b(i)n = 1

b(ii)n = 3

b(iii)n = 2

13a 3y + 6 = 7y 10 4y = 16 y = 4

13b3x( x + 2 ) = 0x = 0 or x = 2

13c( 2a 3 )= 162a 3 = 4 or 2a 3 = 4a = 35 a = 05or a = 3, p =

14aPRQ TRS

14bQR = RS ( R is the mid-pt of QS)PR = RT ( R is the mid-pt of PT)PRQ = TRS (vertically opp s) PRQ TRS (SAS)

15a(i)Arc length PQ = r

= 17 x cm = 10625 cm or 10 cm

a(ii)

Area of sector POA = x 17x cm

= 903125 cm

or 90 cm

15b(i)OM is the perpendicular bisector of PQ

OPM17

In OMP,

sin=

PM = 17sin

PQ = 2 x 17sin cm = 2826996682 cm ~ 28 cm

b(ii)Area of shaded segment

= 903125 (17)sincm

= 1502244941 cm

~ 150 cm

16aAcceleration = m/s

= 15 m/s

or 1 m/s

16bDistance travelled in k sec :x 20 x 30 + 30(k 20) = 750 k 20 = = 15 k = 35

17aTotal cost for trip = $70 x 35 = $2450Cost per person = = $8750

17bNumber of people = = 49

18a

Let the volume of the smaller and bigger bottle be V and V respectively.

=

=

V = 478 x = 5975

Hence, volume of smaller bottle = 5975 cm(exact)

18b

Let the mass of the smaller and bigger bottle be m and m respectively.

=

=

= 65 x 8 = 520 Hence, mass of larger bottle = 520g

18cMethod 1Larger bottle :520g -------- $795

100g -------- = $1528846154

Smaller bottle :65g ------- $095

100 g ----- = $1461538462

Hence, the smaller bottle is a better value for money

Method 2Larger bottle :520g -------- $795

65g -------- = $099375

Smaller bottle : 65g ------ $095

Hence, the smaller bottle is a better value for money

Method 3Larger bottle :$795 -------- 520 g

$1 -------- g = 6540880503 g

Smaller bottle :$095 ------- 65 g

$1 ------- g = 6842105263 gHence, the smaller bottle is a better value for money

Method 4Larger bottle :$795 -------- 520 g

$0.95 -------- x 095 g = 6213836478 gHence, the smaller bottle is a better value for money

Method 5

= = 8

= 8368421053Thus, the bigger bottle is more expensive. Thus, the smaller bottle is a better value for money

19a2ps 4s + 3p 6 = 2s(p 2) + 3(p 2) = (p 2)(2s + 3)

19b

12m 3n= 3[(2m) ] = 3(2m + n)(2m n)

20a

= x

=

20b

+ =

=

=

or

21P(cycles to school) = P(oversleeps & cycle) + P(didnt oversleep & cycle)= 04(07) + 06(01)= 034 or

22aOCD = (OCD is isos) = 69

22bAED = 180 ACD (s in the opp segment) = 180 69 = 111

22cCBD = (42) ( at centre = 2 at circumference) = 21

22dABC = 90 ( in a semi-circle)ABD = 90 CBD = 90 21 = 69ORABD = ACD (s in the same segment) = OCD (common ) = 69

2013 CCHY 4E5N Prelim II P1 Marking SchemePage 8 of 8