Index No: 0 1 0 1 4 Alternative No. Supervising Examiner s/ Invigilator s initial: Mathematics READ THE FOLLOWING DIRECTIONS CAREFULLY: Writing Time: 3 hours Total Marks : 100 1. Do not write for the first fifteen minutes. This time is to be spent on reading the questions. After having read over the questions, you will be given Three hours to answer all questions. 2. Write your index number in the space provided on the top right hand corner of this cover page only. 3. In this paper, there are three sections: Section A, Section B and Section C. You must answer ALL the questions in Section A and Section B. Under Section C, there are 8 questions (question numbers 14-21). Each question has two parts, I and II. Attempt either I or II from each question. The intended marks for a question or its parts are stated in the brackets. 4. Read the directions to each question carefully and write all your answers in the space provided in the question booklet itself. 5. Remember to write quickly but neatly. 6. You are not allowed to remove any page from this booklet. 7. Do not leave the examination hall before you have made sure that you have answered all the required number of questions. 8. The use of calculator (fx-82/fx-100) without memory is allowed. For Chief Marker s and Markers Use Only Section A B C Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Award Marker s initial BCSE/Math/2014 Page 1 of 36 This booklet contains 36 pages
BCSE/Math/2014 Page 2 of 36
SECTION A Answer all questions. Question 1 [2 10 = 20] A B C D i. In the matrix E F G H, the address of the element G is I J K L A ( 3, 2 ) B ( 2, 3 ) C ( 2, 2 ) D ( 3, 3 ) Answer. ii. A lunch in a restaurant costs Nu 120. A special rate of Nu 90 is being offered for a lunch during a Tshechu. What is the discount? A 25% B 30% C 50% D 75% Answer. iii. Which one of the following is a linear function? A f(x) = 2(x + 1) (x-2) B f(x) = 4x 2 + x 1 C f(x) = 5 (x + 3) D f(x) = 3( x +4) 2 Answer. BCSE/Math/2014 Page 3 of 36
iv. Which one of these given shapes with the same area would have the shortest perimeter A B C D Answer. v. The factors of 2 9x 49are A (3x-7)(3x + 7) B (9x 7) (9x +7) C (9x + 49) (9x 49) D (3x-7)(3x-7) Answer. vi. Find the coordinates of the vertex for the function f(x) = -2(x + 1) 2-1. A (-2,-1) B (-1,-1) C ( 1,-1) D (-1, 1 ) Answer. BCSE/Math/2014 Page 4 of 36
vii. The following data shows the weight of eight students in kilogram 35 37 32 40 37 42 28 30 What is the median of the above data? A 35 B 36 C 37 D 38.5 Answer. viii. Find the value of x in the figure given below: A A 3.6cm 6cm B 60cm C 6cm B 10cm C 6cm D 10cm D x E Answer. ix. The acute angle for secx= 2is A 30 0 B 49 0 C 60 0 D 87 0 Answer. x. What is the number of planes of symmetry in a regular pentagon based prism? A 4 B 5 C 6 D 7 Answer. BCSE/Math/2014 Page 5 of 36
SECTION B (32 marks) Answer all questions Question 2 Matrix A shows four students scores on class work and an examination and matrix B shows the percentage of each marks [3] Class work Exams Dechen 69 78 A= Karma Tenzin Pema 72 75 53 60 55 48 a) Multiply Matrix A and Matrix B. B= 0.4 0.6 b) What does the product Matrix tell you? BCSE/Math/2014 Page 6 of 36
Question 3 [4] a) Simplify: 9 + 9 3 4 5 b) Find the value of p in 15p p = 27 5 Question 4 Calculate the values of x and y which satisfy both the equations y = 4x 1 and 2x + 3y = 11 [3] BCSE/Math/2014 Page 7 of 36
Question 5 [2] a) Transform the linear equation 6x + 8y= 40 to slope and y-intercept form. b) Sketch the graph of the resulting linear function. BCSE/Math/2014 Page 8 of 36
Question 6 Write down the number of significant figures in each number given below: [3] i. 25.0 ii. 138 10-6 iii. 3.008 iv. 4600 v. 0.0320 vi. -3 10 11 Question 7 Factorize and solve for x. x 2-6x- 16 [2] BCSE/Math/2014 Page 9 of 36
Question 8 Determine the equation of the parabola that would result from applying each composite transformation to the graph of y = x 2 [3] a) ( x, y) (x - 3, -2y ) b) ( x, y) (x, y - 5) BCSE/Math/2014 Page 10 of 36
Question 9 The data set below shows the weekly saving of 65 people. [3] Weekly saving Saving (Nu) Number of people 0-200 16 200 400 12 400 600 8 600-800 12 800-1000 10 1000-1200 7 Construct the Box and Whisker plot for the above data. BCSE/Math/2014 Page 11 of 36
Question 10 [3] Dorji randomly chooses an integer from 1 to 50 EVENT A: The integer is Even EVENT B :The integer is a multiple of 4 a) What is the probability of Event A and Event B both happening? b) Are Event A and Event B dependent or independent? Show your work. BCSE/Math/2014 Page 12 of 36
Question 11 Determine the Cosine and Tangent for angle A in the given figure. [2] 17 15 x Question12 A flag pole is 6 metre tall. It casts a shadow that is 12 metre long. At what angle do the rays from the sun meet the top of the flag pole? [2] BCSE/Math/2014 Page 13 of 36
Question 13 [2] a) Sketch a 2-D shape with turn symmetry of order 4 that is not a square. b) Sketch a 2-D shape that has no rotational symmetry. BCSE/Math/2014 Page 14 of 36
BCSE/Math/2014 Page 15 of 36 SECTION C [48 marks] Under this section, there are 8 questions (question numbers 14 21). Each question has two parts, I and II. Attempt either I or II from each question. Question 14 ( I ) [3] a) The given Matrix is D C B A D C B A 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 0 i. Create a digraph for the matrix given above. ii. How many one-stopover trips are there from vertex A to B?
b) Describe the situation for each: [3] i. When you might multiply a matrix by a scalar ii. When you might multiply two matrices Question 14 (II) OR a) The given diagram is a digraph [3] A B C i. Create an adjacency matrix. BCSE/Math/2014 Page 16 of 36
ii. How many two stop-over trips are there from vertex A to A? b) Sonam added Matrices A and B. The sum Matrix is [3] 4 6 0 C = 10 3 2 What could Matrices A and B have been? Find one possible matrices A and B. BCSE/Math/2014 Page 17 of 36
Question 15 ( I ) a) Nima borrowed Nu 30,000 from the Bank of Bhutan Ltd. He repaid the loan at the end of 3 years with a single repayment of Nu 40,680. What interest rate was charged, if the compounding was semi-annual? [3] b) Druk Panjab National Bank declares a 20% dividend rate on its stock. Lhamo owns 250 shares each with a face value of Nu 150. [3] i. What dividend amount will Lhamo receive? BCSE/Math/2014 Page 18 of 36
ii. Lhamo bought the shares originally at a premium of 30%. What is the yield percentage? OR Question 15 ( II ) a) Khandu bought 300 shares that had a face value of Nu 100 for Nu 85 each. He sold the shares for Nu 200 each. What was his profit percent? [3] BCSE/Math/2014 Page 19 of 36
b) A car is sold for Nu 450,000. The cost price of the car was Nu 310,000. The salesperson is offered the following options: [3] Option 1: A commission amount of Nu 12,500 Option 2 : an 8% commission rate based on the dealer s profit. Option 3: 3% commission rate based on the selling price. Which option is the best for the salesperson? BCSE/Math/2014 Page 20 of 36
Question 16 ( I ) a) Sketch the relation 4y 8 > 3x [3] BCSE/Math/2014 Page 21 of 36
b) Karma withdrew Nu 5,000 in 50 and 100 denominations from the Bank of Bhutan. [3] i. Write an equation to model the above situation. ii. Write a function that tells the number of 50 denomination notes, if Karma knows the number of 100 denomination notes. BCSE/Math/2014 Page 22 of 36
Question 16 (II) OR a) Write the inequality for the given graph [3] BCSE/Math/2014 Page 23 of 36
b) Find the values of x and y in the given diagram. [3] x y y 3y Question 17 (I) a) Calculate the total volume of the given figure. [3] 4cm 10cm 5cm 8cm 5cm BCSE/Math/2014 Page 24 of 36
b) Kinley is buying materials to fence his new apple orchard. He buys three strands of barbed wire and a metal post for every 4 metre of fence. Each metal post costs Nu 150 and barbed wire costs Nu 30 per metre. What would be the shape of Kinley s orchard enclosing the largest possible area, if he spends Nu 3,100 for the materials? [3] Question 17 (II) a) Calculate the total surface area of the given Cone. [3] OR 3m 8m BCSE/Math/2014 Page 25 of 36
b) Karchung is making a rectangular table with an area of 20,736 cm 2. He wants to put wood trim around the four edges. [3] i. What is the shortest length of trim he could use? ii. How much less trim would he need if the table was round and the trim was flexible? BCSE/Math/2014 Page 26 of 36
Question 18 (I) a) Sketch the graph of the function, if f(x) = (2x 6) ( 3x + 3) [3] BCSE/Math/2014 Page 27 of 36
b) Bidha had a rectangular piece of cloth measuring 20cm wide and 23cm long. When she decreased the width and length by the same amount, the area decreased by 120cm 2. Determine the dimensions of the new rectangle? [3] Question 18 (II) OR a) Determine the equation of the parabola. [3] BCSE/Math/2014 Page 28 of 36
b) A rectangular play area is twice as long as its width. If you increase the length by 4 metre and decrease the width by 3 metre, the new area will be 532m 2. Determine the dimensions of the original rectangle. [3] Question 19 (I) Stem a) Use the stem and leaf plot to answer the questions below: [3] Vehicle speed in Km/ hr Leaves 0 5 5 7 7 7 9 9 9 9 9 5 6 2 3 3 4 4 6 6 6 8 8 9 9 9 9 9 7 0 1 1 1 1 4 6 8 8 8 9 i. How many vehicles had their speeds measured? ii. If the maximum speed limit was 60km/hr, how many vehicles were exceeding the limit? iii. What was the range of the speed? BCSE/Math/2014 Page 29 of 36
b) Estimate the value of the correlation coefficient for each scatter plot: [3] i. 6 5 4 3 2 1 0 0 1 2 3 4 ii. 10 8 6 4 2 0 0 1 2 3 4 5 iii. 10 8 6 4 2 0 0 0.5 1 1.5 2 2.5 3 BCSE/Math/2014 Page 30 of 36
Question 19 (II) OR a) The frequency table below shows the lifespan in hours of 324 light bulbs that were tested at a Light Bulb Manufacturing Company. [3] Lifespan (hours) Frequency (No.of light bulbs) 300-400 20 400-500 40 500-600 56 600-700 75 700-800 78 800-900 55 i. Create a histogram and a frequency polygon. ii. Describe the shape of the frequency polygon. BCSE/Math/2014 Page 31 of 36
b) Sketch the corresponding box and whisker plot for each histogram given below. [3] i. ii. iii. Question 20 (I) a) A car travels 3km at a bearing of 90 0, then turns and travels 4 km at a bearing of 180 0. Use a single vector to describe the trip. Find the distance of the single vector and the bearing to describe the vector. [3] BCSE/Math/2014 Page 32 of 36
b) Calculate the area of the given composite shape using the trigonometric identities. [3] 136 0 43 0 4cm 7cm Question 20 (II) OR a) A boy looks at the top of a tree from a window 12m above the ground at an angle of elevation of 30 0. He also looks at the base of the tree at an angle of depression of 45 0. Find the height of the tree? [3] BCSE/Math/2014 Page 33 of 36
b) Represent each trip as a single vector. Find its bearing and distance. [3] i. 3.4km ii. 5km 2.8km 7km BCSE/Math/2014 Page 34 of 36
Question 21 (I) a) i. Construct PQR: PQ = 6.5cm, Q = 30 0 and QR = 8.5cm (Use of protractor is not permitted) [3] ii Construct the circumcircle on the same triangle. b) Use deductive reasoning to prove that a regular polygon has an order of turn symmetry equal to its number of sides. [3] BCSE/Math/2014 Page 35 of 36
Question 21 (II) OR a) i. Construct triangle ABC where AB = 8cm, BC = 5cm and AC = 7cm. [3] ii. Determine its area by constructing the altitude of a triangle. b) Solve i. How many axis of rotation are there in a regular hexagon based prism? [3] ii. Describe the turn symmetry for each axis of rotation in a regular hexagon based prism. BCSE/Math/2014 Page 36 of 36