Name Class Sample from For AQA General Certificate of Secondary Education Mathematics Paper 2A Calculator Higher Tier H For this paper you must have: a calculator mathematical instruments. Time allowed 2 hours Instructions and Information Write your name in the at the top of the page. Answer all questions in the spaces provided. The marks for questions are shown in brackets. The maximum mark for this paper is 105. If your calculator does not have a π button, take the value of π to be 3.14 unless another value is given in the question. The quality of your written communication is specifically assessed in questions 3, 8, 13 and 20. These questions are indicated with an asterisk (*) Advice In all calculations, show clearly how you work out your answer. Written by Shaun Armstrong Only to be copied for use in the purchaser's school or college 2012 AHA Paper 2 Page 1 Limited Turn over
Formulae Sheet: Higher Tier Sample from a Area of trapezium = 1 (a + b)h 2 h b Volume of prism = area of cross-section length cross- section length Volume of sphere = 4 3 πr3 r Surface area of sphere = 4πr 2 Volume of cone = 1 3 πr2 h l h Curved surface area of cone = πr l r In any triangle ABC C Area of triangle = 1 ab sin C 2 b a Sine rule a sin A = b sinb = c sin C A c B Cosine rule a 2 = b 2 + c 2 2cb cos A The Quadratic Equation The solutions of ax 2 + bx + c = 0, where a 0, are given by x = b± b 2 4ac 2a 2012 AHA Paper 2 Page 2 Limited
Answer all questions in the spaces provided. 1 Ghadah runs an online store. She bought 30 decorative mirrors for 15 each. Ghadah sold 16 of the mirrors on her website for 25 each. She then reduced the price by 5 and sold 12 more mirrors. She sold the last two mirrors on an online auction site for 16.50 and 9.20 Work out how much profit Ghadah made on the mirrors. Answer (5 marks) 2 A person can be right-handed, left-handed or ambidextrous. The probability of a person being right-handed is 0.88 The probability of a person being left-handed is three times the probability of a person being ambidextrous. Work out the probability of a person being ambidextrous. Answer (3 marks) 8 2012 AHA Paper 2 Page 3 Limited Turn over
3 Samaira asked 10 families in different towns to record the maximum temperature each day in January. She then worked out the mean of these maximum temperatures. Samaira also asked the families how much they spent on gas in January. The scatter graph shows her results. 40 Cost of Gas Used ( ) 35 30 25 20 0 2 4 6 8 10 Mean Maximum Temperature (ºC) 3 (a) What type of correlation does this scatter graph show? Answer (1 mark) 3 (b) Draw a line of best fit on the scatter graph. (1 mark) 3 (c) The mean maximum temperature in January in Ullapool was 0.4ºC. Explain why it might not be sensible to use your line of best fit to estimate the cost of the gas used by a family living in Ullapool. (1 mark) 2012 AHA Paper 2 Page 4 Limited
The table below summarises the maximum temperature for each day in January where Samaira lives. Maximum Temperature (ºC) Number of days 3 3 4 6 5 10 6 7 7 4 8 1 *3 (d) Estimate the cost of gas used by Samaira's family in January. Answer (4 marks) 4 A film was shown seven times over one weekend at a cinema with 120 seats. The number of tickets sold for five of the showings were 69 106 51 89 72 The median number of tickets sold was 78. The mean number of tickets sold was 81. Work out how many tickets were sold at the other two showings of the film. Answer and (3 marks) 2012 AHA Paper 2 Page 5 Limited Turn over 10
5 (a) A bag of potatoes weighs 2.5 kg. Approximately how much does the bag weigh in pounds? 5 (b) In 1985 petrol cost 1.95 per gallon. In 2005 petrol cost 80p per litre. Answer pounds (1 mark) Harry says that the price of petrol more than doubled from 1985 to 2005. Is Harry correct? Explain your answer. Answer (3 marks) 6 A new company had sales of 25 000 in total in its first two years. The ratio of its sales in first year to its second year was 2 : 3 The company's profit was 600 in the first year and 1200 in the second year. Find the ratio of the company's profit as a percentage of sales in its first year to its second year. Give your answer in its simplest form. Answer (5 marks) 2012 AHA Paper 2 Page 6 Limited
7 Magnus drives at 70 km/h for 45 minutes. How far does he travel? Answer km (3 marks) *8 Here are some patterns made with dots. Pattern 1 Pattern 2 Pattern 3 Work out how many dots there will be in Pattern 50. Show how you obtained your answer. Answer (4 marks) 16 2012 AHA Paper 2 Page 7 Limited Turn over
9 Dhakwan has an empty metal barrel. The barrel is in the shape of a cylinder. The height of the barrel is 1.2 m. The diameter of the base of the barrel is 80 cm. Dhakwan fills the barrel with water from a tap. The tap fills the barrel at the rate of 1 litre per second. 1.2 m Find how long it takes to fill the barrel. Give your answer to the nearest minute. 80 cm Answer minutes (5 marks) 2012 AHA Paper 2 Page 8 Limited
10 y 5 4 3 A 2 1 6 5 4 3 2 1 0 1 1 2 3 4 5 6 7 8 x 2 3 4 5 Triangle A is shown on the grid. 10 (a) Translate triangle A using the vector 6 1. Label the image B. (2 marks) 10 (b) Enlarge triangle A by scale factor 2 with centre of enlargement (0, 0). Label the image C. (2 marks) 9 2012 AHA Paper 2 Page 9 Limited Turn over
11 (a) Solve 11 (a) (i) 4p 7 = 37 Answer (2 marks) 11 (a) (ii) 3(1 2y) = 15 4y Answer (3 marks) 11 (b) Anna orders 2 cups of coffee and 4 cups of tea. She is charged 11. When Anna looks at her receipt she sees that she's been charged for 4 cups of coffee and 2 cups of tea. The cost should have been 10 so she is refunded 1. Work out the cost of a cup of coffee and the cost of a cup of tea. Answer Coffee Tea (5 marks) 2012 AHA Paper 2 Page 10 Limited
12 Dan and Erina are booking a holiday. The prices are shown in the table below. Full board includes breakfast, lunch and an evening meal. Price per person for 7 nights ( ) For 14 nights add 25% Week Beginning 24 Jul 31 Jul 7 Aug 14 Aug 21 Aug 28 Aug Self Catering 381 390 422 422 410 399 Bed and Breakfast 401 412 444 444 432 419 Full Board 478 494 530 530 516 499 They want to go on the 7 th August and stay for two weeks. They plan to book bed and breakfast. 12 (a) Work out the total cost of their holiday. Answer (3 marks) Dan wants to find out how much a taxi to the airport will cost. The distance to the airport is 35 miles to the nearest 5 miles. The cost will be 1.60 per mile to the nearest 10p. 12 (b) What is the most that the taxi to the airport will cost? Answer (3 marks) 16 2012 AHA Paper 2 Page 11 Limited Turn over
13 (a) Complete this table of values for y = x 2 + 3 x 3 2 1 0 1 2 3 y 12 7 4 (2 marks) 13 (b) On the grid, draw the graph of y = x 2 + 3 y 12 11 10 9 8 7 6 5 4 3 2 1 4 3 2 1 0 1 2 3 4 x (2 marks) 13 (c) Draw the graph of y = x on the same grid. (1 mark) 2012 AHA Paper 2 Page 12 Limited
*13 (d) Explain how your diagram shows that there are no solutions to the equation x 2 x + 3 = 0 Answer (2 marks) 14 Roger invested 2000 in a savings account. The account paid 5% compound interest per year. 14 (a) Work out how much was in the account after 3 years. Answer (3 marks) Lisa invested 400 in a different savings account. The account paid x % compound interest per year. 14 (b) Circle the expression below which gives the amount, in pounds, in the account after 3 years. 1 x 3 100 3 x 400 100 400 100 x 3 100 400 (1 mark) 11 2012 AHA Paper 2 Page 13 Limited Turn over
15 E A b Not drawn accurately B 120º a D 76º The points A, B, C, D and E lie on the circumference of a circle as shown. AC is parallel to ED. 15 (a) (i) Work out the size of angle a. C 15 (a) (ii) Give a reason for your answer. Answer degrees (1 mark) (1 mark) 15 (b) Work out the size of angle b. Answer degrees (3 marks) 2012 AHA Paper 2 Page 14 Limited
16 Just Clothes takes orders for its products on its website and from a catalogue. The manager of the company wants to do a survey of 100 customers who have ordered products in the last month. The table gives some information about all 840 customers over the last month. Website Catalogue Male 144 65 Female 348 283 The manager decides to use a sample stratified by gender and source of order. 16 (a) Write down one advantage of using a stratified sample. (1 mark) 16 (b) How many women who ordered from the catalogue should be in the sample. Answer (2 marks) 8 2012 AHA Paper 2 Page 15 Limited Turn over
17 Vicky is making a path using paving stones. It is made up of octagonal and square stones. The octagonal stones are made from a square by removing the four corners. The dimensions are shown below. The size of the square stones is such that they tesselate with the octagonal stones. 10 cm 10 cm Not drawn accurately 30 cm 30 cm 17 (a) Work out the area of this section of path. Not drawn accurately Answer cm 2 (5 marks) 2012 AHA Paper 2 Page 16 Limited
Vicky decides that the width of the path is to be three octagonal stones. She is not sure how long the path will be but there will be no square stones on the edges. 17 (b) Find an expression, in terms of n, for the number of square stones in the path when it has n octagonal stones. Show how you find your answer. Answer (3 marks) 2012 AHA Paper 2 Page 17 Limited Turn over 8
18 (a) Factorise a 2 6a + 8 18 (b) Express Answer (2 marks) 4 x 3 + 2 x 1 as a single fraction in its simplest form. Answer (3 marks) 18 (c) Simplify fully 4 x 6 4 x 2 9 Answer (3 marks) 2012 AHA Paper 2 Page 18 Limited
19 Here are 10 letters printed on plastic tiles. A A B C C D D D E F The tiles are put into a bag and two are picked out at random. Work out the probability that the tiles picked out have the same letter on them. Give your answer in its simplest form. Answer (4 marks) 12 2012 AHA Paper 2 Page 19 Limited Turn over
*20 A Not drawn accurately Q N 100 km A plane leaves an airport, A, and flies for 100 km on a bearing of 140º. The plane then turns and flies on a bearing of 045º until it is due East of A. The plane then flies directly back to A. Work out the total distance travelled by the plane. Answer km (7 marks) END OF QUESTIONS 7 2012 AHA Paper 2 Page 20 Limited