Mathematics Module N3 Paper 1 (Non-calculator) Higher Tier am am [GMN31] 1 hour.

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1 Centre Number 71 Candidate Number General Certificate of Secondary Education January 2009 Mathematics Module N3 Paper 1 (Non-calculator) Higher Tier [GMN31] GMN31 FRIDAY 9 JANUARY 9.15 am am TIME 1 hour. INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number in the spaces provided at the top of this page. Write your answers in the spaces provided in this question paper. Answer all eleven questions. Any working should be clearly shown in the spaces provided since marks may be awarded for partially correct solutions. You must not use a calculator for this paper. INFORMATION FOR CANDIDATES The total mark for this paper is 44. Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question. You should have a ruler, compasses, set-square and protractor. The Formula Sheet is on page For Examiner s use only Question Number Total

2 Formula Sheet Area of trapezium = 1 2 (a + b)h a h b Volume of prism = area of cross section length In any triangle ABC Cross section A length Area of triangle = 1 2 ab sin C a b c Sine rule : = = sin A sin B sin C Cosine rule: a 2 = b 2 + c 2 2bc cos A B c a b C Volume of sphere = 4 3 πr 3 Surface area of sphere = 4πr 2 r Volume of cone = 1 3 πr 2 h Curved surface area of cone = πrl l r h Quadratic equation: The solutions of ax 2 + bx + c = 0, where a 0, are given by x = 2 b± b 4ac 2a [Turn over

3 1 (a) 4.8 cm 7 cm Diagram not drawn accurately 10 cm Calculate the area of the triangle. Answer cm 2 [2] (b) Convert 8.4 m 2 to cm 2 Answer cm 2 [2] [Turn over

4 2 Joe uses 3 4 of a tin of paint to paint a garden shed. What is the least number of tins he requires to paint 10 similar sheds? Answer [3] [Turn over

5 3 A survey was carried out in Belfast City centre to find out the opinions of people on the subject of healthy living. A sample of 100 people was questioned. (a) (i) Explain why these 100 people might not represent the opinions of the Belfast public on healthy living. [1] (ii) One of the questions used in the survey was Do you not think that thin people are healthier than fat people? Give a reason why this question may not have been a suitable question for the survey. Reason [1] (b) The same survey was carried out inside a leisure centre in Lisburn. Give two reasons why the survey should not have been carried out in this location. Reason [1] Reason [1] [Turn over

6 4 The heights, in cm, of 11 children in a nursery class were: Illustrate this using a stem and leaf diagram. [3] 5 (a) Factorise (i) 28 7y Answer [1] (ii) p pt Answer [1] (b) (i) Expand 5(3 y) Answer [1] (ii) Expand and simplify (x 3) (x + 1) Answer [2] (c) Write down an expression for the nth term of the sequence 2, 7, 12, 17,... Answer [2] [Turn over

7 6 The PSNI recorded the speeds of a number of vehicles passing under a bridge on the M2 motorway during a 2 minute period one morning. The speeds recorded are in miles per hour (mph). Speed x (mph) Frequency f 44 x < x < x < x < x < x < 80 1 (a) Which of the class intervals contains the median speed? Answer [1] (b) On the graph paper draw a frequency polygon for the data. [2] Frequency Speed (mph) [Turn over

8 7 Two identical regular polygons join with a square to form a tiling pattern. Explain why these polygons must be regular octagons. [3] 8 Write 120 as a product of prime factors and express your answer in index notation. Answer [3] [Turn over

9 BLANK PAGE (Questions continue overleaf) [Turn over

10 9 Eileen constructed a cumulative frequency table from her mobile phone bill to display her call times over the previous month. The results are shown in the table below. Time in minutes Cumulative frequency <5 29 <10 62 < < < < (a) Draw a cumulative frequency graph, on the opposite page, to display the data. [3] (b) From your graph, estimate the interquartile range. Answer minutes [2] (c) Eileen s pricing plan with the phone company allows her free calls provided that they last no more than 12 minutes. From your graph, estimate the number of calls which will be charged to Eileen s account by the phone company. Answer calls [2] [Turn over

11 Cumulative frequency Time in minutes ( ) [Turn over

12 10 Calculate Give your answer as a mixed number. Answer [3] 11 Solve the equation x+ 2 2x 1 = Show your working. A solution by trial and improvement will not be accepted. Answer x = [4] [Turn over

13 THIS IS THE END OF THE QUESTION PAPER [Turn over

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17 Centre Number 71 Candidate Number General Certificate of Secondary Education January 2009 Mathematics Module N3 Paper 2 (With calculator) Higher Tier [GMN32] GMN32 FRIDAY 9 JANUARY am am TIME 1 hour INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number in the spaces provided at the top of this page. Write your answers in the spaces provided in this question paper. Answer all thirteen questions. Any working should be clearly shown in the spaces provided since marks may be awarded for partially correct solutions. INFORMATION FOR CANDIDATES The total mark for this paper is 44. Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question. You should have a calculator, ruler, compasses, set-square and protractor. The Formula Sheet is on page 2. For Examiner s use only Question Number Total

18 Formula Sheet Area of trapezium = 1 2 (a + b)h a h b Volume of prism = area of cross section length In any triangle ABC Cross section A length Area of triangle = 1 2 ab sin C a b c Sine rule : = = sin A sin B sin C Cosine rule: a 2 = b 2 + c 2 2bc cos A B c a b C Volume of sphere = 4 3 πr 3 Surface area of sphere = 4πr 2 r Volume of cone = 1 3 πr 2 h Curved surface area of cone = πrl l r h Quadratic equation: The solutions of ax 2 + bx + c = 0, where a 0, are given by x = 2 b± b 4ac 2a [Turn over

19 1 Calculate the area of a circle of radius 2.5 cm. Answer [3] 2 A new table is priced at 140 In a sale it is reduced by 35% Calculate the sale price. Answer [3] [Turn over

20 3 The table shows the engine capacity in litres and the fuel consumption (number of miles per gallon (mpg)) for a selection of new cars. Car Engine capacity (litres) Fuel consumption (mpg) Aster Viva Megro Lazio Torino Serene (a) Draw a scatter graph on the grid opposite to show the data in the table. [2] (b) Draw a line of best fit for the data. [1] (c) Using your line of best fit, what fuel consumption in mpg would you expect from a car with an engine capacity of 2.2 litres? Answer mpg [1] [Turn over

21 50 40 Fuel consumption (mpg) Engine capacity (litres) [Turn over

22 4 (a) q Diagram not drawn accurately p 108 Calculate (i) angle p Answer [1] (ii) angle q Answer [1] [Turn over

23 (b) Measure the bearing of L from M. L N M Answer [1] [Turn over

24 5 In a game of Foozball a player scores 2 Goals worth x points each, 3 Overs worth y points each and 1 Nearly worth z points. (a) Write down an expression in terms of x, y and z for the total number of points scored by this player. Answer [2] (b) If the total points scored by this player were 19, how many points could each of the 3 scores have been worth? Give one possible solution. Points 1 Goal = 1 Over = 1 Nearly = [2] 6 Ciara is using Trial and Improvement to find a value of x to satisfy the equation x + 1_ x = 6 The table shows her first trial. Value of x x + 1_ x Comment Too Low Complete the table to help her find the correct value of x to 1 decimal place. Answer x = [4] [Turn over

25 7 Carol leaves 1200 in the bank for three years. It earns compound interest of 6% each year. Calculate the total amount Carol has in the bank at the end of the three years. Answer [3] 8 The PSNI recorded the speeds of a number of vehicles passing under a bridge on the M2 motorway during a 2 minute period one morning. The speeds recorded are in miles per hour (mph). Speed s (mph) Frequency 44 s < s < s < s < s < s < 80 1 Calculate an estimate for the mean speed. Answer mph [4] [Turn over

26 9 15 cm 12 cm A straw of length 15 cm just fits inside a cylindrical container of length 12 cm as shown. Calculate the diameter of the cylinder. Answer cm [3] [Turn over

27 10 y l x (a) (i) Find the gradient of the line l Answer [1] (ii) Hence write down the equation of this line in the form y = mx + c. Answer [2] (b) Here are the equations of another 4 lines Line 1: y = 2x Line 2: y = 2 Line 3: y = x 3 Line 4: y = 2x 2 Which one of these lines is parallel to the line with equation y = x 2? Answer [1] [Turn over

28 11 A coat has a sale price of which is a saving of 15% on the original price. What was the original price of the coat? Answer [3] [Turn over

29 12 The diagram shows a trapezium. D 8 cm C Diagram not drawn accurately 6 cm A 13 cm B AB is parallel to DC. AB = 13 cm, AD = 6 cm and CD = 8 cm. Calculate the size of angle B. Answer [3] [Turn over

30 13 S 52 P Diagram not drawn accurately O R Q O is the centre of the circle. (a) Explain why angle PQR = 90 [1] (b) Calculate (i) angle PRQ, Answer [1] (ii) angle POQ. Answer [1] THIS IS THE END OF THE QUESTION PAPER [Turn over

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