DHS 2009 Sec 4 (SAP) Preliminary Examination Mathematics Paper 1 Page 1 DHS 2009 Sec 4 SAP Preliminary Exam Mathematics Paper 1 1 The diameter of a H1N1 flu virus in a form of a circle is measured by a team of health officers from WHO as 0.000 131 01 mm. Find the area of the H1N1 flu virus, giving your answer in square metres and express this answer in standard form correct to 3 significant figures. Answer: 1 8 0.000 131 01 10 100 Radius 2 6.5 10 m − ÷ ÷ = = × ( ) 2 8 14 14 area of H1N1 flu virus is π 6.5 10 1.348 10 1.35 10 m (to 3sf) − − − ∴ × × ≈ × = × M1 A1 Correct conversion of mm to m cao 2 (i) Simplify ( )( ) 2 a a b a b − − + . (ii) Hence evaluate 2 31.01 28.01 34.01 − × . Answer: 2(ai) ( )( ) ( ) 2 2 2 2 2 2 2 2 a a b a b a a b a a b b − − + = − − = − + = B1 (aii) ( ) ( ) 2 2 2 Hence, 31.01 28.01 34.01 31.01 31.01 3 31.01 3 3 9 − × = − − × + = = B1 Award this mark only if result from (ai) is used
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Dunman High School 2009 Maths D Paper 1 Answer Key
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DHS 2009 Sec 4 SAP Preliminary Exam Mathematics Paper 1 1 The diameter of a H1N1 flu virus in a form of a circle is measured by a team of health
officers from WHO as 0.000 131 01 mm. Find the area of the H1N1 flu virus, giving your answer in square metres and express this answer in standard form correct to 3 significant figures.
Answer:
1
8
0.000 131 01 10 100Radius2
6.5 10 m−
÷ ÷=
= ×
( )28 14
14
area of H1N1 flu virus is π 6.5 10 1.348 10
1.35 10 m (to 3sf)
− −
−
∴ × × ≈ ×
= ×
M1 A1
Correct conversion of mm to m cao
2 (i) Simplify ( )( )2a a b a b− − + .
(ii) Hence evaluate 231.01 28.01 34.01− × . Answer:
9 A map of the downtown district of Singapore is drawn to a scale of 1 : 2000.
The diagram below shows a section of the Marina’s Floating Platform.
(i) Measure the radius of the audience seating area on the map with a ruler and write down the actual radius in metres.
(ii) The organizer wanted to light up a section of the audience seating area denoted by arc BC and the perimeter of the whole floating stage EFGH in the upcoming 44th National Day Parade.
By using a protractor and a ruler, measure and calculate the actual length, in metres, of wire required.
(iii) If the holding area for all the participants of the 44th National Day Parade contingents (not shown in this section of map) covers an area of 1.5 square kilometers. Find, in square centimeters, the area representing the holding area on the same map.
Answer:
(i) Actual map measurement of radius = 4.9 cm Actual radius = 4.9 2000 9 800× = cm = 98 m
(ii) Arc length BC of the audience area (sector) = 2π360
rθ× ×
°
= 75 2π 98360
× ×
= 540 π 1286
≈ m
(to 3 s.f.) Actual length of the stage = 3.9 × 2000 cm = 7800 cm = 78 m Actual width of the stage = 5.9 × 2000 cm = 11 800 cm = 118 m
Required length = ( )540 π 2 78 1186
+ +
= 520 m (to 3 s.f.)
M1 B1 B1
Accept if using equivalent angle in radian to calculate ( )1± ° s.o.i., and 0.1± cm or 2± m, both must be correct at the same time to get this mark. cao, accept correct answers derived from those within acceptable range
(iii) Ratio of length = 1 : 2000 Therefore, Ratio of areas = 1: 4 000 000
11 For the 44th National Day Parade (NDP) held at the Marina Floating Platform (MFP), it is estimated that a total of 50 000 people gathered at the MFP, Marina and Collyer Quay area to view and bask in the atmosphere of the Parade and its celebrations.
(a) Given that the holding capacity of the MFP for audience is 42.7 10× pax, calculate the percentage of people gathered at the Marina and Collyer Quay area who celebrated the National Day outside the MFP.
(b) If in addition to the 50 000 present at the MFP, Marina and Collyer Quay area, an estimated TV and internet viewership of 3.2 million was also recorded all around the world. Moreover, 89% of these two groups of people took the National pledge at 20 22 at the same time, calculate the number of people who watched the parade and took the pledge that night.
Answer:
(a) Number of people celebrated outside the platform = 450 000 2.7 10− × = 23 000 Percentage of people celebrated outside the platform
= 23 000 100%50 000
× = 46%
M1 A1
Indication of subtraction cao
(b) Total who watched the NDP = 50 000 3 200 000+ = 3 250 000 Number of people who took the pledge that night
= 89 3 250 000100
× = 2 892 500
B1 B1
cao o.e. in standard form etc cao o.e. in standard form etc
12 Yvonne started her journey from home for the ‘Danzage’ performance at 18 24. Due to a massive traffic jam, she did not manage to reach Dunman High’s Performing Arts Centre (PAC) until 20 02.
(i) Calculate, expressing your answer in exact form and in hours, the time taken by her to reach her destination.
(ii) Find the distance, in kilometers, between her home and the PAC if her taxi travelled at an average speed of 19.92 km/h.
Answer:
(i) Time taken by her = 20 02 – 18 24 = 1 hours and 38 mins
= 19130
hours
B1
cao, no mark if not in fraction in lowest term
(ii) Distance = 1919.92 130
×
= 32.536 km
M1 A1
ft with c’s result from (i) ft with c’s result from (i) ; if 32.536 is rounded off, this mark is lost.
13 In a bid to encourage Singaporeans to go Green for the environment, Singapore Power Grid Pte Ltd conducted a survey to find out the extent of Singaporeans’ readiness in this drive.
Out of a total of 200 Singaporeans surveyed, 130 claimed that they used energy-efficient electrical appliances while 80 claimed that they had replaced using air-conditioners with electric fans. The survey also revealed that 30 neither used energy-efficient electrical appliances nor replaced air-conditioners with electric fans.
If ξ, E and A represent the sets of Singaporeans surveyed, and those who used energy-efficient electrical appliances and those who replaced using air-conditioners with electric fans respectively,
(i) draw a Venn diagram to illustrate the above information.
(ii) Find the number of Singaporeans who used energy-efficient electrical appliances and had replaced using air-conditioners with electric fans.
(iii) Find the number of Singaporeans who had started using energy-efficient electrical appliances but still had not replaced air-conditioners with electric fans.
Answer:
(i)
B2
Deduct 1 mark for any missing relevant information
(ii) 130 80 30 200x+ − + = 40x =
M1 A1
ft c’s Venn diagram cao
(iii) Number of Singaporeans who had started using energy-efficient electrical appliances but still had not replaced air-conditioners with electric fans = 130 – x = 90
(bi) See answer on grid B1 cao (bii) XY = 2 26 3 45 6.71+ = = units (to 3 s.f.) B1 ft c’s answer for
(bi) (ci) See answer on grid B1 ft c’s answer for
(bi) – i.e. use c’s point Y to draw the vector correctly.
(cii) X, Z and Y are collinear points or XZ is parallel to ZY or equivalent or mentioning about the correct ratio of lengths of line segments formed by these 3 points
Which segment of the 2009 Miss World Pageant was more competitive amongst the 11 semi-finalists? Explain your answer.
Answer:
(i) x = 7.9
y = 8.4
z = 9.5
B2
Deduct 1 mark for any mistake
(ii) Since the range of scores of the middle 50% of the semi-finalists is much smaller in the Interview Segment as indicated by its smaller inter-quartile range, it shows that the Interview Segment was more competitive.
B2 1 mark – key word smaller interquartile range 1 mark – key word Interview segment more competitive
22 Hafiz left home at 17 00 and took a bus to the National Stadium to witness the opening ceremony of the Asian Youth Games. He reached the National Stadium at 18 30. The speed-time graph below shows the bus journey that Hafiz took.