(11-16) 2A-Ch.4-Approximation _ Errors - ANS

TB(2A) Ch. 5 Approximation & Errors GHS Past Paper Question Bank – Solutions Page 1 of 6 TB(2A) Ch. 4 Approximation and errors Answers of Multiple Choice Questions 1 B 2 B 3 C 4 C 5 B 6 C 7 B 8 C 9 A 10 B 11 C 12 D 13 C 14 A 15 C 16 C 17 B 18 A 19 B 20 D 21 D 22 B 23 D 24 B 25 B 26 D 27 C 28 C Solutions of Conventional Questions 1. [11-12 Mid-year Exam #7] (a)   2 : 3 : 5 2   x x 2 3 5 2   x x x x 3 10 4   10  x (b)         18 3 5 10 2 10   =       18 3 15 10  = 18 450     m 25  The actual length of his apartment is 25 m (c) 150 100 25       cm 67 . 16  , cor. to the nearest 0.01 cm  The length of his apartment in the scale drawing is 16.67 cm 2. [11-12 Mid-year Exam #10] (a) (i) Maximum absolute error 50 100 5 . 0    Lower limit 28950 50 29000    (ii) Percentage error % 100 29000 50   % 172 . 0  (cor. to 3 sig. fig.) (b) Minimum possible no. of registered voters % 38 28950   11001 

TB(2A) Ch. 5 Approximation & Errors GHS Past Paper Question Bank – Solutions Page 2 of 6 3. [11-12 Mid-year Exam #11] (a) The lower limit ) 05 . 0 50 . 2 )( 05 . 0 0 . 1 ( ) 05 . 0 10 ( 2      6775 . 2 0025 . 99   325 . 96  (cm 2 ) The upper limit ) 05 . 0 50 . 2 )( 05 . 0 0 . 1 ( ) 05 . 0 10 ( 2      3275 . 2 0025 . 101   675 . 98  (cm 2 ) (b) The measured area 5 . 2 0 . 1 10 2    5 . 97  (cm 2 ) Max. area – measured area 5 . 97 675 . 98   175 . 1  (cm 2 ) Measured area – min. area 325 . 96 5 . 97   175 . 1  (cm 2 ) ∴ The accumulated error is 1.175 cm 2 . 4. [11-12 Final Exam #2] (a) The estimated total amount = 26 + 32 +42 + 56 = 156 (dollars) (b) By (a), the actual total amount they have is greater than $155. Thus, they have enough money to buy the gift. 5. [12-13 S6 Mock Exam #9] (a) (i) Simon’ s height is 165.5 cm. Simon’ s weight is 81 kg. (ii) The maximum absolute errors of the measuring tape = 0.25 cm The maximum absolute errors of the bathroom scales = 0.5 kg (b) (i) Maximum BMI of Simon = 2 6525 . 1 5 . 81  29.8 kg/m 2

TB(2A) Ch. 5 Approximation & Errors GHS Past Paper Question Bank – Solutions Page 4 of 6 8. [13-14 S.2 Mid-year Exam #11] (a) (i) Lower limit of her total marks 2 10 230   = 225 (ii) Lower limit of her Maths marks = 225 – 75 – 68 = 82 (b) Absolute error = 85 – 82 = 3 Relative error = 85 3 OR  0.0353 9. [13-14 S.2 Mid-year Exam #14] Min. and max. no. of steel bars = 100 – 2 and 100 + 2 = 98 and 102 Min. and max. lengths of each steel bar = (12.5 – 0.01) m and (12.5 + 0.01) m = 12.49 m and 12.51 m  Min. total length = 98 (12.49) = 1224.02 (m) Max. total length = 102 (12.51) = 1276.02 (m)  1224.02 m  Total true length of the railway track < 1276.02 m . 10. [13-14 S.2 Final Exam #9] (a) Maximum absolute error = 2 2 = 1 (min) (b) % error = % 100 12 1  = 8.33% (cor. to 3 sig. fig.) (c) Lower limit of the actual time = 12 – 1 = 11 (min)  The earliest arrival time is 6:10 p.m.  I agree w. her. 11. [13-14 S.6 Mock Exam #1]

TB(2A) Ch. 5 Approximation & Errors GHS Past Paper Question Bank – Solutions Page 5 of 6 12. [13-14 S.2 Final Exam #4] (a) Relative error 5 . 62 25 . 0  250 1  or 0.004 (b) The upper limit = 62.5 + 0.25 = 62.75 (s) (c) Scale interval = 0.25 × 2 = 0.5 (s) 13. [13-14 S.2 Final Exam #10] (a) Maximum absolute error = 100 ÷ 2 = 50 Percentage error = % 100 46400 50  = 0.108 % (corr. to 3 sig. fig.) (b) 46 350 ≤ Number of Articles < 46 450 And 585 ≤ Number of words in each article < 595 Upper limit of total number of words = 46 450 × 595 = 27 637 750 It is not possible that there are 28 million words. 1 (f.t.) 14. [14-15 S.6 Mock Exam #4] (a) % error of the measured height = 4 . 7 2 . 0 2 1   100%  1.35 % (b) Estimated volume  14  7  8 cm 3 = 784 cm 3 15. [14-15 S.2 Final Exam #3] (a) The max. absolute error = 0.05 m (b) Percentage error % 100 8 . 1 05 . 0    2.78% or % 9 25 