Integrated Exercise B
Integrated Exercise B
Part A
1. (a) 8134.235 = 8100 (cor. to 2 sig. fig.)
(b) –0.007 961 = – 0.0080 (cor. to 2 sig. fig.)
2. Absolute error
3. (a) Scale interval of the measuring tool
(b) Lower limit of the actual volume
Upper limit of the actual volume
∴ The actual volume of the bottle of soft drink ranges between 247.5 mL and 252.5 mL.
4. (a) Maximum absolute error
(b) Relative error
(c) Percentage error
5. (base Ðs, isos. r)
(int. Ðs, AB // DE)
6. In rBEF,
(ext. Ð of r)
(corr. Ðs, BA // DC)
In rCGH,
(ext. Ð of r)
7. (vert. opp. Ðs)
(vert. opp. Ðs)
(vert. opp. Ðs)
(vert. opp. Ðs)
(vert. opp. Ðs)
(vert. opp. Ðs)
∴ (Ð sum of polygon)
8. (a) / Height (cm) / Frequency146 – 150 / 6
151 – 155 / 14
156 – 160 / 22
161 – 165 / 38
166 – 170 / 16
171 – 175 / 4
(b) Number of people shorter than 160.5 cm
9. / pH value / Class mark / Frequency6.2 – 6.4 / 6.3 / 3
6.5 – 6.7 / 6.6 / 11
6.8 – 7.0 / 6.9 / 24
7.1 – 7.3 / 7.2 / 16
7.4 – 7.6 / 7.5 / 6
pH values of 60 bottles of mineral water
Part B
10. (a) The number 24.50 has 4 significant figures.
The number 0.0109 has 3 significant figures.
The number has 3 significant figures.
(b) For 24.50,
percentage error
For 0.0109,
percentage error
For ,
percentage error
11. (a) Maximum absolute error
(b) Lower limit of the actual speed
Upper limit of the actual speed
∴ The actual speed of the tennis ball ranges between 122.5 km/h and 127.5 km/h.
(c) Relative error
12. (a) (i) Lower limit of the actual length of the longer side
Upper limit of the actual length of the longer side
(ii) Lower limit of the actual length of the shorter side
Upper limit of the actual length of the shorter side
(b) Maximum area of the rectangle
Minimum area of the rectangle
13. ∵ BD = BE
∴ △BDE is an isosceles triangle.
(ext. Ð of △)
∵ ÐBAC = ÐABC = 72°
∴ BC = AC (sides opp. equal Ðs)
∴ △ABC is an isosceles triangle.
ÐCFG = ÐBAC = 72° (alt. Ðs, FG // EA)
ÐCGF = ÐABC = 72° (alt. Ðs, FG // EA)
∴ ÐCFG = ÐCGF = 72°
∴ CG = CF (sides opp. equal Ðs)
∴ △CFG is an isosceles triangle.
14. (a)
(b) ∵ ÐBCG + (3x – 7°) = 180° (adj. Ðs on st. line)
∴
15. (a) / Marks less than / Cumulative frequency20.5 / 0
30.5 / 3
40.5 / 8
50.5 / 15
60.5 / 29
70.5 / 53
80.5 / 65
90.5 / 73
100.5 / 80
(b)
Results of 80 S2 students in a Mathematics test
(c) From the graph, the number of students passing the test
16.
(a) The cumulative frequency that corresponds to the lower quartile
From the graph, the weight that corresponds to a cumulative frequency of 15 is 53 kg.
∴ Lower quartile
(b) The cumulative frequency that corresponds to the median
From the graph, the weight that corresponds to a cumulative frequency of 30 is 58 kg.
∴ Median
(c) The cumulative frequency that corresponds to the upper quartile
From the graph, the weight that corresponds to a cumulative frequency of 45 is 62.5 kg.
∴ Upper quartile
(d) The cumulative frequency that corresponds to the 80th percentile
From the graph, the weight that corresponds to a cumulative frequency of 48 is 63.5 kg.
∴ The 80th percentile
Multiple Choice Questions
1. Answer: C
For 2.058, 0 is the second sig. fig.
2. Answer: B
25.4648 = 25.46 (cor. to 4 sig. fig.)
3. Answer: B
4. Answer: C
5. Answer: B
6. Answer: C
7. Answer: B
Lower limit of the actual length of the eraser
Upper limit of the actual length of the eraser
8. Answer: C
Lower limit of the actual weight of the box
Upper limit of the actual weight of the box
The actual weight of the box ranges between 1.045 kg and 1.055 kg.
∴ Only 1.0501 kg lies within this range.
The answer is C.
9. Answer: C
∠ACD = y (alt. Ðs, DC // AB)
∵ CE = CD
∴ ∠CED = 2y (base Ðs, isos. △)
Consider △CED.
(Ð sum of △)
10. Answer: D
(Ð sum of polygon)
∴
11. Answer: B
Consider △ACF and △AEB.
ÐA = ÐA (common angle)
AF = AB (given)
AC = AE (given)
∴ △ACF △AEB (SAS)
∴
12. Answer: A
∵ AB = BC = CA
∴ △ABC is an equilateral triangle
and ÐBAC = ÐABC = ÐACB = 60 °.
In △ACD,
ÐADC = ÐCAD = 50° (base Ðs, isos. △)
and (Ð sum of △)
In △BCD,
∵ ÐCBD = ÐCDB (base Ðs, isos. △)
∴
13. Answer: D
14. Answer: D
For choice A, the cumulative frequency that corresponds to the median
From the graph, the marks that corresponds to a cumulative frequency of 20 is 44.
∴ The median is 44 marks.
∴ Choice A is correct.
For choice B, the number of students who pass the examination
∴ Choice B is correct.
For choice C, the cumulative frequency that corresponds to the upper quartile
From the graph, the marks that corresponds to a cumulative frequency of 30 is 54.
∴ The upper quartile is 54 marks.
∴ Choice C is correct.
For choice D, the cumulative frequency corresponds to the lower quartile
From the graph, the marks that corresponds to a cumulative frequency of 10 is 24.
∴ The lower quartile is 24 marks.
∴ Choice D is wrong.
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