For AQA. Mathematics. General Certificate of Secondary Education. Non-calculator

Transcription

1 Name Class For AQA General Certificate of Secondary Education Mathematics Paper 1A Non-calculator Higher Tier H For this paper you must have: mathematical instruments. You must not use a calculator. Time allowed 1 hour 30 minutes 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 70. The quality of your written communication is specifically assessed in questions 3, 6 and 11. 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 1 Page 1 Churchill Maths Limited Turn over

2 Formulae Sheet: Higher Tier 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 1 Page 2 Churchill Maths Limited

3 Answer all questions in the spaces provided. Do not write 1 SIDE FRONT The diagram shows a prism. The cross-section of the prism is a regular hexagon. 1 (a) Sketch the front elevation of the prism from the direction shown. (2 marks) 1 (b) Sketch the side elevation of the prism from the direction shown. (1 mark) AHA Paper 1 Page 3 Churchill Maths Limited Turn over

4 2 (a) Simplify 2p q + 3p + 4q 2 (b) Simplify m 9 m 2 Answer (2 marks) 2 (c) Factorise fully 9xy 2 6y 3 Answer (1 mark) Answer (2 marks) *3 Holly is carrying out a survey about healthy eating. This is one of the questions. How many pieces of fruit did you eat yesterday? Tick one 1 to 2 3 to 4 4 or more 3 (a) Write down two criticisms of the response section for this question. First criticism Second criticism.. Holly carries out her survey by asking her questions of several groups of people. After asking each question, she goes round the group and records each person's answer. 3 (b) Give one reason why this is not a good survey method. (2 marks) (1 mark) 2012 AHA Paper 1 Page 4 Churchill Maths Limited

5 4 (a) xº Not drawn accurately 32º The shape in the diagram above is made up of six identical isosceles triangles. Work out the value of x. Answer (3 marks) 4 (b) Use a ruler and pair of compasses to construct the bisector of this angle. Leave in your constuction lines. (2 marks) AHA Paper 1 Page 5 Churchill Maths Limited Turn over

6 5 Martin and Badri are plumbers. Martin charges a 25 call-out fee and 20 per hour of work. Badri doesn't charge a call out fee but charges 30 per hour of work. 5 (a) Calculate how much less Badri charges for a 1 hour job. Answer (2 marks) The total charge ( C) for a job taking t hours is shown on the graph below for each plumber. Badri Total cost ( C) 100 Martin Time at job (t hours) 2012 AHA Paper 1 Page 6 Churchill Maths Limited

7 The total that Badri charges is given by the formula C = 30t 5 (b) Write down a formula for the total that Martin charges. Answer (2 marks) 5 (c) Write down the value of t at the point where the two graphs intersect. Answer (1 mark) 5 (d) Explain how your answer to part (c) is useful to someone choosing between Martin and Badri to do a plumbing job. (1 mark) *6 Lanika needs a sheet of card that is at least 3 10 mm thick. At home, she finds some card but she doesn't know how thick it is. Lanika finds that there are 45 sheets of card with a total thickness is 14 mm. Is the card thick enough for Lanika to use? Show how you decide. Answer (3 marks) AHA Paper 1 Page 7 Churchill Maths Limited Turn over

8 7 In a game, two players take it in turns to roll two ordinary dice. The dice are fair and numbered from 1 to 6. If, on one turn, the number on one of the dice is twice the number on the other dice, the player receives a bonanza card. In one game, each player had 42 turns before the game ended. Work out an estimate for the number of bonanza cards each player received in the game. Answer (4 marks) 2012 AHA Paper 1 Page 8 Churchill Maths Limited

9 Price ( ) Number of Leaflets 6000 The graph above shows the price of printing A4 colour leaflets. 8 (a) What is the price for 1000 leaflets? 8 (b) A company spends 380 on leaflets. How many leaflets do they have printed? Answer (1 mark) Answer (1 mark) 8 (c) Rhona is thinking of ordering 1500 leaflets. Angela says that for an extra 50%, Rhona could get 3 times as many leaflets. Is Angela correct? You must show how you decided. Answer (3 marks) AHA Paper 1 Page 9 Churchill Maths Limited Turn over

10 9 (a) Write 63 as a product of its prime factors. Answer (2 marks) Hisham and Marlon are comparing how far they step when walking. Hisham's step is 63 cm in length, from the heel of one foot to the heel of the other foot. 63 cm Hisham and Marlon start walking with their left heels exactly in line. After walking 6.3 metres, one of Hisham's heels is exactly in line with one of Marlon's heels. 9 (b) The length of Marlon's step is an exact number of centimetres between 40 and 80. Find all the possible lengths of Marlon's step. Answer (5 marks) 2012 AHA Paper 1 Page 10 Churchill Maths Limited

11 10 (a) Find the value of 10 (a) (i) (a) (ii) Answer (1 mark) Answer (2 marks) 10 (b) Show that k 6 where k is a fraction to be found. Answer k = (3 marks) AHA Paper 1 Page 11 Churchill Maths Limited Turn over

12 11 Residents who live on Stratton Avenue complain of cars driving too fast on their road. In a study, the speed of 100 cars is recorded and the results are shown in this cumulative frequency diagram. 100 Cumulative frequency Speed (miles per hour) 60 The speed limit on Stratton Avenue is 30 miles per hour. 11 (a) What percentage of the cars in the study were breaking the speed limit? Answer % (1 mark) 11 (b) Use the graph to estimate the median speed of the cars in the study. Answer mph (1 mark) 11 (c) Use the graph to estimate the interquartile range of the speed of the cars in the study. Answer mph (2 marks) Following the study, speed cameras are put up on Stratton Avenue. A second study records the speed of 100 cars one month later. The results are summarised in the table on the next page AHA Paper 1 Page 12 Churchill Maths Limited

13 Speed (v miles per hour) Frequency 0 < v < v < v < v < v < v 60 2 *11 (d) Use the data and the grid below to find out if the speed cameras have had an effect. Comment on your findings. (5 marks) AHA Paper 1 Page 13 Churchill Maths Limited Turn over

14 12 y (0, 5) y = f(x) (8, 0) x The graph of y = f(x) intersects the x-axis at (8, 0) and the y-axis at (0, 5). 12 (a) Write down the coordinates of the point where each of these graphs intersects the y-axis. 12 (a) (i) y = f(x) (a) (ii) y = 2f(x) Answer (, ) (1 mark) 12 (a) (iii) y = f(3x) Answer (, ) (1 mark) Answer (, ) (1 mark) 12 (b) Write down the coordinates of the point where each of these graphs intersects the x-axis. 12 (b) (i) y = f(x + 6) 12 (b) (ii) y = f(2x) Answer (, ) (1 mark) 12 (b) (iii) y = f( x) Answer (, ) (1 mark) Answer (, ) (1 mark) 2012 AHA Paper 1 Page 14 Churchill Maths Limited

15 13 Not drawn accurately 4 cm An ornament is in the shape of a tetrahedron. Each face is an equilateral triangle of side 4 cm. 13 (a) Show that the surface area of the ornament is 16 3 cm 2. (5 marks) A larger version of the ornament is similar in shape and has sides of length 12 cm. 13 (b) Find the exact surface area of the larger ornament. Answer cm 3 (3 marks) END OF QUESTIONS AHA Paper 1 Page 15 Churchill Maths Limited Turn over