2023 BCSE Mathematics Past Paper PDF

BHUTAN CERTIFICATE OF SECONDARY EDUCATION DECEMBER 2023 MODEL ANSWER & MARKING SCHEME – MATHEMATICS GENERAL INSTRUCTIONS 1) The Marking Scheme provides general guidelines to reduce subjectivity in the marking. The answer...

BHUTAN CERTIFICATE OF SECONDARY EDUCATION DECEMBER 2023 MODEL ANSWER & MARKING SCHEME – MATHEMATICS GENERAL INSTRUCTIONS 1) The Marking Scheme provides general guidelines to reduce subjectivity in the marking. The answers given in the marking scheme are suggested answers. The content is thus indicative. If a student has given any other answer, which is different from the one given in the Marking Scheme, but conveys the meaning, such answers should be given full weighting. 2) Evaluation is to be done as per instructions provided in the marking scheme. It should not be done according to one’s own interpretation or any other consideration. The Marking Scheme should be strictly adhered to and strictly followed once the answers are thoroughly standardized. 3) If a question has parts, please award marks in the right-hand side for each part. Marks awarded for different parts of the question should then be totaled up and written in the left-hand margin. If a question does not have any parts, marks must be awarded in the left-hand margin. 4) If a candidate has attempted an extra question, it will be cancelled. The extra question attempted will be the last questions in the sequence of the question paper. 5) Some examinees may attempt the questions giving equally correct answers in a different way. If the examiners are convinced that the response given by an examinee is genuinely correct, full weighting should be given. 6) If there are questions on distinction between two concepts, in such questions, sometimes some students give one aspect of the difference correctly and the other is either wrong or not given at all, no marks should be awarded. 7) There may be some questions requiring the examinees to give new ideas of their own or pass their own judgments and give valid justifications. In such cases, marks should be awarded for their efforts though there may be several possible answers. 8) If the questions ask for two features/characteristics/points but the examinee writes more than two features/characteristics/points, say, five of which the first is correct, second is incorrect, the best two should be assessed and the remaining should be ignored. 9) It is expected that the Marking Scheme be followed objectively for reliable marking. For instance, if an examinee scores 35 (BCSE) / 35 (BHSEC) marks, his/her marks should not be inflated to 40 (BCSE) / 40 (BHSEC) simply to pass him/her. Similarly, whenever an examinee has answered the question effectively, his/her marks should not be deducted unnecessarily. Do not hesitate to award full marks if the answer deserves it. 10) Marks should be awarded keeping in view the total marks of that particular question and not the total marks of the question paper. For example, if 1 mark is given to a question carrying 3 marks, even if nothing is correct, then that 1 mark constitutes 33% of the total marks ear-marked for this answer. This must be avoided. If a candidate fails in the subject by 1 to 3 marks, the marking may be reviewed. BCSE/15/2023 MA&MS Page 1 of 23 Copyright Reserved  SECTION A [40 MARKS] ANSWER ALL QUESTIONS Question 1 Direction: For each question, there are four alternatives: A, B, C and D. Choose the correct alternative and circle it. DO NOT circle more than ONE alternative. If there are more than ONE choice circled, NO score will be awarded. i) The digraph shows the number of bus services in three stations. Thimphu Phuntsholing Paro How many bus services are there between Paro to Phuntsholing? A 2 B 3 C 4 D 5 ii) What is the simplified form of 3 40 ? A 10 3 2 B 2 3 10 C 53 2 D 23 5 Solution : 3 40 = 3 2´ 2´ 2´5 = 3 23 ´ 3 5 = 2´ 3 5 iii) Yuden wants to invest Nu 5,000 in one of her accounts for one year. Account A: 6.0% p.a. simple interest Account B: 5.0% p.a. compounded annually Account C: 3.0% p.a. compounded semiannually Account D: 2.9% p.a. compounded quarterly In which account will she earn more money? A Account A B Account B C Account C D Account D BCSE/15/2023 MA&MS Page 2 of 23 Copyright Reserved  Solution : Account A : Nu 5000 ´ 0.06 ´1 = Nu 300 Amount = Nu 5000 + Nu 300 = Nu 5300 Comparing accounts B, C and D, account Bis the best as it has highest rate of interest 1´1 æ 0.05 ö Account B : Nu 5000 ç1 + ÷ = Nu 5250 è 1 ø Therefore, account A will earn her more money iv) In a game of dart, Roshan is awarded the following points as shown. Mode of scoring Points Hit target 15 Miss target -5 After 20 throws, he scored 60 points. How many times did Roshan hit the target? A 4 B 8 C 12 D 16 Solution : x + y = 20 ® (i ) 15 x - 5 y = 60 3 x - y = 12 ® (ii ) x + y = 20 3 x - y = 12 4x = 32 32 x= =8 4 Roshan hit the target 8 times v) For the function f ( x) = ( 2 x + 3)( 4 x - 2 ) , the values of ‘p’ and ‘q’ are 3 1 A p = and q = -. 2 2 3 1 B p = - and q =. 2 2 C p = 3 and q = -2. D p = -3 and q = 2. Solution : f ( x) = ( 2 x + 3)( 4 x - 2 ) 2x + 3 = 0 -3 x= 2 4x - 2 = 0 2 1 x= = 4 2 BCSE/15/2023 MA&MS Page 3 of 23 Copyright Reserved vi) Which pattern best represents the relationship between x and f(x) in the table? x f(x) 0 5 1 10 2 15 3 20 A f ( x) = 10 x + 5 B f ( x) = 10 x - 5 C f ( x) = 5 x + 5 D f ( x) = 5 x - 5 Solution : Difference = 5 f ( x) = 5 x ± ? x = 0 f ( x) = 5 5 = 5 ´ 0 + ?(5) 5=5 Therefore, pattern is f ( x ) = 5 x + 5 vii) Which of the following represents a function? A Input Output 1 a 2 b 3 4 c Input Output B 1 a 2 b 3 4 c Input Output C 1 a 2 b 3 4 c BCSE/15/2023 MA&MS Page 4 of 23 Copyright Reserved  D Input Output 1 a 2 b 3 4 c viii) The longer leg of a right angled triangle is 4 cm more than the shorter leg. If the hypotenuse is 20 cm, find the length of the shorter leg. A 12 cm B 16 cm C 20 cm D 24 cm Solution : let the length of shorter leg be ' x ' length of longer length = x + 4 a 2 + b2 = c2 ( x + 4) 2 + x 2 = 20 2 x 2 + 8 x + 16 + x 2 = 400 2 x 2 + 8 x - 384 = 0 x 2 + 4 x - 192 = 0 x 2 + 16 x - 12 x - 192 = 0 x ( x + 16) - 12( x + 16) = 0 ( x - 12)( x + 16) = 0 x - 12 = 0 x = 12cm ix) Khamsum made a wooden jewelry box in the shape of a rectangular prism. The jewelry box had the dimensions as given. If the surface area of the box was 684 cm2 , determine the height of the box. A 3.0 cm B 3.8 cm C 6.0 cm D 7.6 cm BCSE/15/2023 MA&MS Page 5 of 23 Copyright Reserved  Solution : l = 15cm w = 12cm h=? SA = 684cm 2 SA = 2 A + hp 684cm 2 = 2 ´ (12cm ´ 15cm ) + h ´ 54 684cm 2 - 360cm 2 = h ´ 54cm 324cm 2 h= = 6cm 54cm x) A pentagon based prism with the following dimensions was filled with water to a height of 3 cm. When a stone is immersed, the water level increased to a height of 5 cm. What is the volume of the stone? A 60 cm3 B 120 cm3 C 180 cm3 D 360 cm3 Solution : 8 cm Change in height = 5cm - 3cm = 2cm = h 3 cm æ 5 ´ 8cm ´ 3cm ö V = Ah = ç ÷ ´ 2cm è 2 ø V = 120cm 3 xi) Four square based prisms have a capacity of 360 mL each. Which prism with the following base is the most efficient? A 7 cm ´ 7 cm B 6 cm ´ 6 cm C 5 cm ´ 5 cm D 4 cm ´ 4 cm Solution : V = Ah V h= A Prism A Prism B Prism C Prism D 360 360 360 360 h= h= h= h= 49 36 25 16 h = 7.4cm h = 10cm h = 14.4cm h = 22.5cm Therefore, Prism A is most efficient because the height of prism A is closest to the length of the sides of the base. BCSE/15/2023 MA&MS Page 6 of 23 Copyright Reserved xii) Which conversion is correct? p A 30° = rad 3 p B 40° = rad 4 p C 60° = rad 6 p D 90° = rad 2 Solution : p 180° rad = = 90° 2 2 3 1 xiii) If sin q = and q lies in the first quardant, the value of tan q + is 5 cos q A –3. B –2. C 2. D 3. Solution : O 4 tan q = = A 3 A 3 cos q = = H 5 1 4 1 tan q + = + cos q 3 3 5 4 5 9 = + = =3 3 3 3 xiv) An online delivery company delivers a football packed in a cubical box. If the ball exactly fits in the box, what is the radius of the ball? A 3.0 cm B 3.5 cm C 4.0 cm Vcube = 343 cm3 D 4.5 cm BCSE/15/2023 MA&MS Page 7 of 23 Copyright Reserved  Solution : Vcube = e3 = 343cm3 e = 3 343cm3 e = 7cm = diameter of theball 7cm r= = 3.5cm 2 xv) Jigme could tighten this nut in three complete rotations. The order of turn symmetry is A 6. B 12. C 18. D 24. Solution : Order of turn symmetry for the prism hexagon based = 6 ® for single rotation For 3 rotations = 3 ´ 6 = 18 xvi) Which of the following statement is true? A The circumcentre of a right triangle will be on the midpoint of the hypotenuse. B The point of intersection of the medians is called the orthocentre. C The circumcentre of an obtuse triangle will be inside the triangle. D The point of intersection of the altitudes is called the centroid. xvii) The table shows the weekly expenditure of 200 families. Expenditure (Nu) Frequency 0 – 1000 28 1000 – 2000 46 2000 – 3000 54 3000 – 4000 42 4000 – 5000 30 What is the median of the weekly expenditure? A Nu 1478.26 B Nu 2481.48 C Nu 2500.00 D Nu 3523.81 BCSE/15/2023 MA&MS Page 8 of 23 Copyright Reserved  Solution: Expenditure (Nu) Frequency CF 0 – 1000 28 28 1000 – 2000 46 74 2000 – 3000 54 128 3000 – 4000 42 170 4000 – 5000 30 200 i æn ö Q2 = L + ç - c ÷ f è2 ø 1000 æ 200 ö Q2 = 2000 + ç - 74 ÷ = Nu 2481.48 54 è 2 ø xviii) Which of the following pair of variables are negatively correlated? A The outside temperature and the cold drink sales. B The amount of time spent in studying and the exam grades. C The amount of money you save and your financial security. D The time elapsed and the distance left to be covered in a marathon. xix) Anjuli is taking part in two races. The probability of winning the first race is 0.2. The probability of winning the second race, if she has already won the first race is 0.6. Calculate the probability of Anjuli winning both the races. A 0.12 B 0.40 C 0.80 D 3.00 Solution : P( A) = 0.2 P( B / A) = 0.6 P( A and B ) = P ( B / A) ´ P ( A) = 0.6 ´ 0.2 = 0.12 xx) Which of the following pair of events are independent? A Event A: Rolling a die and getting a 3 Event B: Getting a total of 4 or more for both rolls B Event A: Rolling an odd number in the first roll of a die Event B: Rolling a second time and getting a difference of 1 for both rolls C Event A: Rolling a 3 or 4 on the first roll of a die Event B: Rolling a number less than 5 on the second roll D Event A: Rolling an even number in the first roll of a die Event B: Rolling a number such that the product of the first and second rolls are greater than 4 BCSE/15/2023 MA&MS Page 9 of 23 Copyright Reserved  SECTION B [60 MARKS] ATTEMPT ANY SIX QUESTIONS [ Under this section, there are 8 questions (Question 2 – 9)] Question 2 a) Given K = 29 ´ 36 ´ 5 y. What values of ‘y’ if any, would make ‘K’ a perfect cube? Explain. Solution : Any non-negative multiples of 3 - - - - - - In order to become a perfect cube, the exponents should be divisible by 3 - - - - - - b) Palden bought some pens and pencils for a total sum of Nu 600. A pen costs Nu 75 and a pencil costs Nu 15. i. Write an equation to model the situation. ii. Write a function to calculate the number of pens if you know the number of pencils he bought. iii. Use the function to calculate the number of pens if Palden bought 10 pencils. Solution : let the number of pens be ' x ' let the number of pencils be ' y ' i. 75 x + 15 y = Nu 600 ------ ii. 75 x + 15 y = Nu 600 75 x = Nu 600 - 15 y ------[0.5] Nu 600 - 15 y Nu 600 - 15 y x= OR f ( y ) = ------[0.5] 75 75 iii. y = 10 Nu 600 - 15(10) f (10) = ------[0.5] 75 f (10) = 6 pens ------[0.5] c) This cylindrical tube has 20 rounds of wrapping paper. 5 cm 21 cm BCSE/15/2023 MA&MS Page 10 of 23 Copyright Reserved  Kuenga can wrap 8 cubical boxes of the same dimension using all the wrapping 22 papers. What could be the dimension of the cubical box? (Use p = ) 7 Solution : 22 A curved lateral surface = 2p rh = 2 ´ ´ 5 cm ´ 21 cm = 660 cm 2 (Area of one round) ------[0.5] 7 Totalsurface area of 20 rounds = 20 ´ 660 cm 2 = 13, 200 cm 2 ------[0.5] 13, 200 cm 2 Amount of paper required for a box = =1650 cm 2 ------[0.5] 8 SA cube = 1650 cm 2 6l 2 = 1650 cm 2 ------[0.5] 1650 cm 2 l2 = = 275 cm 2 ------[0.5] 6 l = 275 = 16.58 cm ------[0.5] d) Describe the turn symmetry of the 3D shape. Solution : One axis of rotation from centre of one base to the centre of the opposite base with a turn order of 4. ------ Four axes of rotation from the midpoint of one edge to the midpoint of the opposite edge in the lateral faces with a turn order of 2. ------ Question 3 a) In a high school, the boys and girls basketball teams had their heights measured. The following data was recorded for their heights (in cm). Girls Boys 165 155 170 154 177 165 170 172 164 155 145 160 180 162 165 172 157 171 162 168 167 160 179 176 i. Construct a double stem and leaf plot for the data. ii. Make a conclusion based on the graph. BCSE/15/2023 MA&MS Page 11 of 23 Copyright Reserved  Solution: i. Arrange data in ascending order. ------[0.5] Girls Boys 145 154 155 155 160 162 165 165 157 160 162 164 167 170 172 172 165 168 170 171 176 177 179 180 Girls Stem Boys 5 14 7 5 5 4 15 8 5 4 2 0 16 0 2 5 5 7 1 0 17 0 2 2 6 7 9 18 0 Correct data placement ------ Selection of appropriate stem ------[0.5] ii. Most of the heights of the students measured fall between 160 cm to 170 cm. OR The shortest height measured was 154 cm OR The tallest height measured was 180 cm OR Generally, boys were taller than girls OR Students can make conclusion based on mean, median and mode Any one of the above ------ b) The perimeter of a rectangular swimming pool is 160 m. Its length is 2 m more than twice its width. What are the length and width? Solution : width = w length = l l = 2w + 2 ® (i )------[0.5] Prectangle = 2 ( l + w ) = 160 m 2l + 2 w = 160 m l + w = 80 m ® (ii ) ------[0.5] Put (i ) in (ii ) 2w + 2 + w = 80 m ------[0.5] 3w = 80 - 2 ------[0.5] 78 w= = 26 m ------[0.5] 3 l = 2w + 2 = ( 2 ´ 26 ) + 2 = 54 m ------[0.5] c) Draw ΔXYZ : XY = 6.9 cm, YZ = 8.3 cm and ÐY = 65° and locate the centroid of the triangle. BCSE/15/2023 MA&MS Page 12 of 23 Copyright Reserved  Solution: Triangle construction ------ Side bisectors ------ Median construction ------ Location of centriod ------ Question 4 a) The length of a rectangular garden is 4 m more than its width. The area of the garden is 60 m2. Determine the dimensions of the rectangle. Solution : Width = w Length = w + 4 Arectangle = l ´ w = 60 cm 2 ------ ( w + 4 ) ´ w = 60 cm 2 w2 + 4 w - 60 = 0 ------ w2 + 10 w - 6 w - 60 = 0 w( w + 10) - 6( w + 10) = 0 ( w - 6)( w + 10) = 0 ------ w-6 = 0 w = 6 cm l = w + 4 = 6 cm + 4 cm = 10 cm ------ b) The table shows the data of three teams in 2021 season of BoB Bhutan Premier League. A win is worth 3 points, a draw is worth 1 point and a loss means no points. Team Win Draw Loss Paro FC 14 3 1 Druk Lhayul FC 10 3 5 Gelephu FC 2 1 15 i. Create a matrix for the above situation. ii. Use matrix multiplication to calculate the points secured by each team. BCSE/15/2023 MA&MS Page 13 of 23 Copyright Reserved  Solution : é14 3 1 ù i. êê10 3 5 úú ------ êë 2 1 15úû é14 3 1 ù é 3ù ii. êê10 3 5 úú ´ êê1 úú ------ êë 2 1 15úû êë0 úû é 45ù ê 33ú ------[0.5] ê ú êë 7 úû \ Paro FC secured 45 points, Druk Lhayul FC secured 33 points and Gelephu FC secured 7 points. ------[0.5] c) Prove that tan A + cot A = 1. sin A cos A Solution : 1 tan A + cot A = sin A cos A sin A cos A + ------ cos A sin A sin A ´ sin A + cos A ´ cos A ------ sin A cos A sin 2 A + cos 2 A ------[0.5] sin A cos A 1 ------[0.5] sin A cos A Question 5 a) Sonam purchased 300 shares with a face value of Nu 200 each from the market at Nu 225 per share. A dividend rate of 24% is declared at the end of the year. Calculate: i. rate of premium ii. dividend amount iii. yield percentage Solution : i. Change in FV = Nu 225 - Nu 200 = Nu 25 ------[0.5] 25 Premium% = ´100 200 = 12.5% ------[0.5] ii. DA = r ´ FV ´ n = 0.24 ´ Nu 200 ´ 300 ------[0.5] = Nu 14, 400 ------[0.5] iii. Original investment = 300 ´ Nu 225 = Nu 67,500 ------ yield yield % = ´ 100% Original investment 14, 400 = ´ 100% ------[0.5] 67500 = 21.33% ------[0.5] BCSE/15/2023 MA&MS Page 14 of 23 Copyright Reserved b) A cylindrical container is fitted with a heating element. The dimensions of the container and heating element are as given. 1m 60 cm 12 cm 12 cm How much water can the container hold? Solution : Vcylinder = p r 2 h = p ´ (30 cm) 2 ´100 cm = 282, 743.34 cm3 ------ Vrectangular prism = l ´ w ´ h = 12 cm ´12 cm ´100 cm = 14, 400 cm3 ------ Vwater = 282, 743.34 cm3 - 14, 400 cm3 = 268,343.34 cm3 The container can hold 268,343.34 cm3 of water.------ c) In a class, 17 students play cricket, 12 students play football, 5 students play both the games and 2 students play neither. A student is randomly selected. What is the probability that the student plays i. only cricket? Cricket Football ii. only football? iii. cricket and football? 12 5 7 Solution : 2 12 1 i. P (only cricket ) = OR ------ 36 3 7 ii. P (only football ) = ------ 36 34 17 iii. P (cricket and football ) = OR ------ 36 18 BCSE/15/2023 MA&MS Page 15 of 23 Copyright Reserved Question 6 a) A pastry bag is a tool used to decorate cakes and cupcakes. It takes the form of a truncated cone. What is the volume of this pastry bag? 4 cm 8 cm Solution: 8 cm Missing height 8 8+ x = 4 x x 2x = 8 + x x = 8 cm Height of full cone = 8 cm + 8 cm = 16 cm ------ p r 2h 4 cm Vfull cone = 3 p ´ ( 8 cm ) ´16 cm 2 8 cm = 3 = 1072.33 cm3 ------ Vmissing cone = p r 2h 8 cm 3 p ´ ( 4 cm ) ´ 8 cm 2 = 3 = 134.04 cm3 ------ Vtruncated cone = 1072.33 cm3 - 134.04 cm3 = 938.29 cm3 ------ b) Determine the point of intersection of the lines 3 x - 2 y = 3 and 1 x - 1 y = 3. 4 3 2 2 Solution : æ3 2 ö ç x - y = 3 ÷ ´ 12 è 4 3 ø æ1 1 ö ç x - y = 3 ÷ ´ 2 ------[0.5] è2 2 ø 9 x - 8 y = 36 ® (i ) x - y = 6 ® (ii ) ------[0.5] Eliminate y 9 x - 8 y = 36 -8 x + 8 y = -48 x = -12 ------ x- y =6 -12 - y = 6 - y = 18 y = -18 ------ BCSE/15/2023 MA&MS Page 16 of 23 Copyright Reserved  c) This table shows the age of a sample of people and how many hours each person engages in physical activity each week. Age Hours of Activity 20 15 22 11 30 6 30 7 34 6 26 14 26 8 18 16 36 3 40 3 i. Create a scatter plot of the data. ii. Identify the type of correlation. Solution: Hours of Activity 20 15 10 5 0 0 10 20 30 40 50 i. Scatter plot Appropriate scale and axis ------[0.5] Plotting the points correctly ------[1.5] ii. Negative correlation. ------ Question 7 5 x3 ´ 9 x 4 a) Simplify. 80 x Solution : 5 x3 ´ 9 x 4 80 x 5 x3 ´ 9 x 4 ------ 80 x 9 x6 16 3x3 ------ 4 BCSE/15/2023 MA&MS Page 17 of 23 Copyright Reserved b) Write the mapping notation for the following functions. i. f ( x) = 2 x 2 - 0.5 ii. f ( x) = -3( x + 1)2 - 4 iii. f ( x) = ( x - 3)2 + 6 Solution : i. f ( x) = 2 x 2 - 0.5 ( x, y ) ® ( x, 2 y - 0.5) ------ ii. f ( x) = -3( x + 1) 2 - 4 ( x, y ) ® ( x - 1, - 3 y - 4) ------ iii. f ( x) = ( x - 3) 2 + 6 ( x, y ) ® ( x + 3, y + 6) ------ c) The data represents points scored by Bikram in ten basketball matches. 17, 11, 9, 11, 14, 22, 20, 18, 20, 19 Calculate 5 number summary of the data. Solution : Arrange data in ascending order 9, 11, 11, 14, 17, 18, 19, 20, 20, 22 min imum value = 9 max imum value = 22 ------[0.5] Q1 = 11 ------[0.5] 17 + 18 Q2 = = 17.5 ------[0.5] 2 Q3 = 20 ------[0.5] 13 d) If cot A = , calculate five other t-ratios. 5 Solution : 13 cot A = 5 13 Adj = 132 - 52 5 = 169 - 25 = 144 A = 12 ------[0.5] 5 \ tan A = or 0.42 ------[0.5] 12 5 sin A = or 0.38------[0.5] 13 12 cos A = or 0.92 ------[0.5] 13 13 sec A = or 1.08 ------[0.5] 12 13 csc A = or 2.6 ------[0.5] 5 BCSE/15/2023 MA&MS Page 18 of 23 Copyright Reserved Question 8 a) Sangla invested Nu 25,000 in an account. After three years, the amount of money has grown by Nu 4,450. What was the rate of interest compounded monthly? Solution : P = Nu 25, 000 A = Nu 29, 450 t = 3 years n = 12 n´t æ rö A = P ç1 + ÷ è nø 12´3 æ r ö Nu 29, 450 = Nu 25, 000 ç1 + ÷ è 12 ø 1 1 36´ æ Nu 29, 450 ö 36 æ r ö 36 ç ÷ = ç1 + ÷ ------[0.5] è Nu 25, 000 ø è 12 ø r 1.0046 = 1 + ------[0.5] 12 r 1.0046 - 1 = 12 r = 0.0046 ´ 12 ------[0.5] r = 0.0552 ´ 100% r = 5.52% ------[0.5] b) Sketch the graph of the function f ( x) = -2( x + 1)( x - 2). Solution : f ( x) = -2( x + 1)( x - 2) x - intercepts x +1 = 0 x-2=0 x = -1 x=2 (-1, 0) (2, 0) ------[0.5] Coordinates of vertex -1 + 2 x= = 0.5 2 y = -2(0.5 + 1)(0.5 - 2) = 4.5 (0.5, 4.5) ------[0.5] y - intercept f (0) = -2(0 + 1)(0 - 2) = 4 (0, - 4) ------[0.5] Graphing: Appropriate axis and scale ------[0.5] Plotting the points correctly ------ BCSE/15/2023 MA&MS Page 19 of 23 Copyright Reserved c) Tashi is asked to paint the exterior walls of a structure with the following dimensions. 5.3 m 12.4 m 8m If he is offered Nu 55 per m2, determine the amount he will get by painting the walls. Solution : l = 12.4 m w = 8m h = 5.3 m Awalls = 2 ( lh + wh ) = 2 (12.4 m ´ 5.3 m + 8 m ´ 5.3 m ) ------ = 2 ´ ( 65.72 m 2 + 42.4 m 2 ) = 216.24 m 2 ------ Amount 1 m 2 ® Nu 55 216.24 m 2 ® 216.24 m 2 ´ Nu 55 ------[0.5] Nu 11,893.2 ------[0.5] d) The graph shows the relation between wind speed and the mechanical power in a power station. Mechanical Power (W) Wind Speed (m/s) BCSE/15/2023 MA&MS Page 20 of 23 Copyright Reserved  i. Identify the independent and dependent variables. ii. What kind of relationship is it? Solution: i. Independent: Wind speed ------[0.5] Dependent: Mechanical power ------[0.5] ii. Exponential relationship ------ Question 9 a) Find the values of ‘a’ and ‘b’. é a 2ù é -4 3 ù é 2 1ù é -5 4ù ê -3 4ú + ê 2 -1ú - ê 4 3ú = ê b 0 ú ë û ë û ë û ë û Solution : é a 2 ù é -4 3 ù é 2 1ù é -5 4 ù ê -3 4 ú + ê 2 -1ú - ê 4 3ú = ê b 0 ú ë û ë û ë û ë û a - 4 - 2 = -5 ------[0.5] a - 6 = -5 a = 1 ------[0.5] -3 + 2 - 4 = b ------[0.5] b = -5 ------[0.5] b) Two regular based 3D shapes have a volume of 400 cm3 each. 13 cm 4 cm 12.5 cm 10 cm 8 cm i. Calculate the surface area of each shape. ii. Which 3D shape is more efficient? Why? BCSE/15/2023 MA&MS Page 21 of 23 Copyright Reserved  Solution : i. SApyramid = Abase + Alateral faces æ æ 10 cm ´13 cm ö ö = (10 cm ´10 cm ) + ç 4 ´ ç ÷ ÷ ------[0.5] è è 2 øø = 100 cm + 260 cm ------[0.5] 2 2 = 360 cm 2 ------[0.5] SArectangular prism = 2 A + hp = 2 ´ ( 8 cm ´12.5 cm ) + 4 cm ´ 41cm ------[0.5] = 200 cm 2 + 164 cm 2 ------[0.5] = 364 cm 2 ------[0.5] ii. The pyramid is more efficient ------[0.5] Because it has lesser surface area ------[0.5] c) Shade six triangles to make a pattern with order of turn symmetry 6. Solution: OR Correctly shaded ------ BCSE/15/2023 MA&MS Page 22 of 23 Copyright Reserved d) From a bag of counters, a counter is drawn but not replaced, then a second counter is drawn. What is the probability of drawing a black counter, then a white counter? Solution : P( Black ) ´ P(White / Black ) = P( Black and White) ------[0.5] 6 9 ´ ------[0.5] 15 14 54 9 = OR ------ 210 35 BCSE/15/2023 MA&MS Page 23 of 23 Copyright Reserved