EXAMINATIONS COUNCIL OF SWAZILAND Swaziland General Certificate of Secondary Education

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1 EXAMINATIONS COUNCIL OF SWAZILAND Swaziland General Certificate of Secondary Education MATHEMATICS 6880/03 Paper 3 Calculator Structured Questions (Extended) October/November 2015 Additional Materials: Answer Paper Graph Paper (2 sheets) Electronic Calculator Geometrical instruments Mathematical Tables (optional) Tracing paper (optional) 2 hours 30 minutes READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions. All working should be clearly shown. It should be done on the same sheet as the rest of the answer. Marks will be given for working which shows that you know how to solve the problem even if you get the answer wrong. Electronic calculators should be used. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π use either your calculator value or The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100. This document consists of 9 printed pages and 3 blank pages. [Turn over

2 2 1 (a) Find the inverse of the matrix 2 3 x 7. [2] (b) Make h the subject of this formula. (c) y varies inversely as the square root of x. When x is 25, y is 1.6. p = g 2 2 gm h [3] (i) Form an equation connecting x and y. [2] (ii) Find the value of y when x 5 9. [2] 2 (a) Solve the following equations. (i) y [2] (ii) 8 x [2] (b) (i) Write the equation 2x 2 2 8x in the form (x 1 a) 2 5 k. [3] (ii) Hence or otherwise solve the equation 2x 2 2 8x [3] x21 (c) Given that f(x) x and g(x) 5 2, find the value of fg(23). [3] 3 (a) You are given that a , b 5 23 and c 5 k 34. Find the value of k if c is parallel to 2a 2 b. [2] (b) Without using a drawing, show that the points P(3, 2), Q(5, 8) and R( 2, 1) are not collinear. [3]

3 4 The diagram shows the speed-time graph of a boat moving straight across a dam. 3 (a) Calculate the acceleration in the first 10 seconds in terms of u. [1] (b) Express, in terms of u, the distance covered in the last 30 seconds. [2] (c) (i) Given that the distance covered in the last 30 seconds is also given by 60(u ) metres. Form an equation in, terms of u, and show that it reduces to u 2 2 u [2] (ii) Solve the equation u 2 2 u [3] (iii) Hence find the speed of the boat at t 5 0. [1] 5 The skirt sizes for 6 girls are listed below. 14 l m n where l < m < n The median size is 17. The modal size is 18. The mean size is 17. Find the values of l, m and n. [4] [Turn over

4 4 6 Clay is moulded to form a solid cone. (a) The circular base area of the clay cone is m 2. [Volume of a cone pr2 h. Curved surface area of a cone 5 prl] (i) If the volume of the cone is cm 3, find the height of the cone. [2] (ii) Find the radius of the cone. [2] (iii) Calculate the total surface area of the cone given that the slant height is cm. [2] (b) The clay is then remoulded into a sphere. [Volume of a sphere pr3. Surface area of a sphere 5 4pr 2 ] Calculate (i) the radius of the sphere. [2] (ii) the total surface area of the sphere. [2]

5 5 7 The speed of each of 90 cars that passed through a point was recorded. The table summarises this information. Speed (v km/h) Frequency 0 v v v v v v v 130 p 130 v < v (a) Find the value of p. [1] (b) The cumulative frequency table for the above distribution is shown below. Speed (v km/h) Cumulative frequency v 50 0 v 60 3 v v v 110 q v v 130 r v v (i) Find the values of q and r. [2] (ii) Using 2 cm to represent km/h on the horizontal axis and 2 cm to 10 cars on the vertical axis, draw a cumulative frequency curve. [5] (c) Use your curve to estimate the (i) median speed, [1] (ii) interquartile range. [3] (iii) the number of cars which exceeded 106 km/h. [2] (d) Find the probability that a car chosen at random was travelling at a speed higher than 120 km/h. [2] [Turn over

6 6 8 In the diagram STV is a straight line. ST 5 5 cm, TU 5 11 cm and UV 5 15 cm. (a) You are given that the area of triangle STU cm 2. Show that obtuse angle STU [3] (b) Calculate (i) the length SU, [3] (ii) the size of angle UVT. [3]

7 9 A container with a uniform triangular cross section is 2 m long. DF is horizontal. 7 You are given that DE 5 FE 5 1 m and DF m. (a) Calculate the volume of the container. [4] (b) The container has water up to level GH. Given that the area of triangle GHE is 0.06m 2, calculate the length of GH. [3] [Turn over

8 10 Mr Shabangu asked his class what they did over a weekend. The results are shown in the Venn diagram where ξ 5 {students in the class}, F 5 {students who watched Football}, S 5 {students who spent time Studying}, C 5 {students who attended Church}. ξ 8 There were 42 students in the class. There were 19 students who watched Football. There were 15 students who took part in exactly two activities. (a) Find the values of x, y and z. [3] (b) Find the number of students who (c) Find (i) watched Football and also attended Church, [1] (ii) neither attended Church nor watched Football. [1] (i) n(c F S ), [1] (ii) n(s F ). [1]

9 9 11 A farmer is to harvest x tonnes of sunflower and y tonnes of maize. It takes the farmer 2 hours per tonne to harvest sunflower and 3 hours per tonne to harvest maize. He has 1200 hours to finish the harvesting. This can be represented by the inequality 2x + 3y (a) (i) It takes the farmer 1 hour per ton to package each crop. The time available for packaging is 500 hours. Write this information as an inequality. [2] (ii) The farmer must produce more than 100 tonnes of maize. Write this information as an inequality. [1] (iii) Using a scale of 2 cm to represent 100 units for each axis, Draw x and y axes from 0 to 700. [1] (iv) On your axes, show the region represented by the three inequalities by shading the unwanted regions. [5] (b) Use your graph to find the maximum number of tonnes for each crop that can be harvested and packaged simultaneously within the given time. [2]

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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level www.xtremepapers.com * 7 7 7 2 2 5 1 5 3 4 * ADDITIONAL MATHEMATICS 4037/23 Paper 2 October/November 2013