Integrated Exercise 2 (Chapter 5 - Chapter 7)
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1 Integrated Exercise 2 (Chapter 5 - Chapter 7) Level 1 1 Each of the following pairs of triangles are either congruent or similar Write down the pair of congruent or similar triangles with reasons (a) (b) 2 In the figure, ABC ~ AED Find y 3 In the figure, AEC is a straight line ABE ADE Prove that ABC ADC 4 It is given that 168 lies between two consecutive numbers x and y Without using a calculator, determine which of the following surds lie between x and y 130, 140, 150, 160, In the figure, find the length of AB (Give your answer correct to 3 significant figures) 6 In the figure, ABCD is a rectangle, where AB : BC 4 : 5 If the length of the diagonal is 164 cm, find the area of rectangle ABCD 1
2 7 The frequency polygon shows the amount spent by a group of students on lunch yesterday It is given that the first class interval is $23 - $25 (a) Which class interval has the highest frequency? (b) How many students are there in that group? (c) What percentage of students who spent $345 or above on lunch yesterday? 8 The cumulative frequency curve shows the pay rise of 36 employees in a company Find the ratio of the number of employees with a pay rise less than 395% to those with a pay rise not less than 395% 9 The cumulative frequency polygon shows the estimated volumes of a bottle of water given by 60 people (a) Find P 30 (b) Find the median of the data (c) How many people gave the estimations between cm and 480 cm for the volume of the bottle of water? 2
3 Level 2 10 In the figure, BCD is a straight line, BAC BDA (a) Prove that CBA ~ ABD (b) If AB 12 and BC 8, find the length of CD 11 In the figure, ABC is an isosceles triangle, where AB AC APQB and MACN are squares PXZC, MYZB, AXB and AYC are straight lines (a) Prove that ABM ACP (b) Prove that ZBC ZCB 12 In the figure, APB and AQC are straight lines (a) Prove that APQ ~ ACB (b) Find the length of PB (c) Prove that PBC PQC 13 In the figure, BCD is a straight line If AC 16 cm, AE 8 cm, AB 20 cm and DE 30 cm, find BC : CD 14 The following figures show a square box and a rectangular box Which box can allow a cardboard with dimensions 15 cm 20 cm to be put inside? Explain briefly 3
4 15 The table shows the frequency distribution of entrance fee income from an exhibition each day (a) Construct a cumulative frequency table (b) Draw a cumulative frequency polygon [ Horizontal scale: 10 squares $10 000; vertical scale: 5 squares 10 days ] 16 In a talent show, participants competed for performing longer in front of the judges The cumulative frequency curve shows the distribution of the performance time of the participants (a) How many participants were there? (b) For the performance time, find (i) the lower quartile (ii) the median (iii) the upper quartile (c) How many participants performed less than 32 s? (d) Any participants performed 45 s or more would receive cash awards How many participants would receive the cash awards? MC Question 17 In the figure, ABC ~ DEF Find x 18 In the figure, A D and B E What additional information is required for ensuring the congruence of ABC and DEF? A 75 B 15 C 30 D 36 A C F B AC DE C BC DF D AB DE 4
5 19 In the figure, AC and BD intersect at E, AE CE and BE DE 22 Find the length of PS in the figure correct to 3 significant figures Which of the following must be correct? I AD // BC II AEB CED III ADE ABE A I and II only B I and III only C II and III only D I, II and III 20 In the figure, AC and BD intersect at E Find x A 25 B 40 C 50 D If a 0, which of the following must be correct? I a is a surd II The square roots of a are a and a III The negative square root of a is A II only B III only C I and II only a D I and III only A 242 cm B 336 cm C 470 cm D 483 cm 23 Simplify A 8 B 64 C D Which of the following is / are rational number(s)? I 5 II 007 III 256 A I only B II only C I and II only D II and III only 5
6 25 In a Mathematics test, most of the students in S2A obtained very good results Which of the following cumulative frequency curves can best describe the above situation? 26 The following frequency polygon shows the weights of some watermelons A Which of the following is the corresponding cumulative frequency polygon? A B B C C D D 6
7 27 The following cumulative frequency polygon shows the time taken by 60 people to finish a sudoku game Find the difference between the upper quartile and lower quartile of the time taken A 14 min B 18 min C 21 min D 50 min 28 The following cumulative frequency curve shows the ages of audience of a tennis match What percentage of audience are smaller than 20 years old? A 8% B 16% C 42% D 84% 7
8 Answers 1 (a) ABC ~ DFE (equiangular) 2 5 (b) ABC FED (RHS) 4 150, cm 25 C 26 D 27 A 28 B 6 80 cm 2 7 (a) $26 - $28 (b) 100 (c) 11% 8 4 : 5 9 (a) 460 cm 3 (b) 470 cm 3 (c) (b) (b) 3 cm 13 2 : 3 14 Square box 15 (a) 16 (a) C 18 D 19 A 20 D 21 B 22 B 23 D 24 D (b) (i) 345 s (ii) 37 s (iii) 40 s (c) 4 (d) 3 8
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