You must have: Ruler, protractor, compasses, pen, pencil, eraser. Formulae: Higher Tier. where a 0, are given by

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1 For Edexcel GCSE Mathematics Paper 1J (Non-Calculator) Higher Tier Time : 1 hour 45 minutes You must have: Ruler, protractor, compasses, pen, pencil, eraser. Instructions, Information and Advice Do not write on this question paper use blank paper and the answer sheets provided. The total mark for this paper is 100. Calculators must not be used. Questions labelled with an asterisk (*) are ones where the quality of your written communication will be assessed. Read each question carefully before you start to answer it. Check your answers if you have time at the end. Formulae: Higher Tier Volume of prism = area of cross section length Volume of sphere = 4 3 πr3 Surface area of sphere = 4πr 2 In any triangle ABC Sine Rule a sin A = b sin B = c sin C Cosine Rule a 2 = b 2 + c 2 2bc cos A Area of trapezium = 1 (a + b)h 2 Volume of cone = 1 3 πr2 h Curved surface area of cone = πrl The Quadratic Equation The solutions of ax 2 + bx + c = 0 where a 0, are given by Area of triangle = 1 2 ab sin C x = b± b2 4ac 2a Written by Shaun Armstrong Only to be copied for use in the purchaser's school or college 2012 EHJ Paper 1 short Page 1 Churchill Maths Limited

2 Answer ALL questions. You must write down all stages in your working. 1 Use the information that to find the value of = 1820 (a) (b) (c) m 8 m 14 m The diagram shows Mr. Maharoof's garden. He wants to plant grass seed over the whole garden. The seed will cost 1 for every 3 square metres of garden. Work out how much Mr. Maharoof must spend on grass seed EHJ Paper 1 short Page 2 Churchill Maths Limited

3 3 70 children have to choose to go to either the Science Museum or the Planetarium. 22 of the 36 boys choose the Planetarium. In total, 33 children choose the Science Museum. Complete the two-way table on the answer sheets. 4 Manal takes 60 CDs to sell at a fete. Each CD is priced at 2.50 or 1.50 The ratio of CDs priced at 2.50 to those priced at 1.50 is 2 : 3 Work out how much money Manal makes if he sells all his CDs. 5 Here are the first 4 terms of a sequence Find an expression, in terms of n, for the nth term of this sequence. 6 (a) Express 98 as the product of its prime factors. (b) Find the lowest common multiple (LCM) of 42 and (a) What decimal is halfway between 0.36 and 0.42? (b) What fraction is halfway between 1 2 and 2 3? 2012 EHJ Paper 1 short Page 3 Churchill Maths Limited

4 *8 Jon has these five number cards Miranda has these five number cards Jon and Miranda each mix up their own number cards and pick one of them at random. Find the probability that the card Jon picks has the same number on it as the card Miranda picks. *9 D B 42º 48º A C AC and BD are parallel lines. Prove that triangle ABC is isosceles. 10 Water is poured at a constant rate into the four containers shown on the answer sheets. The containers are all the same height. The graphs show the height of the water in each container, h cm, after t seconds. The graphs are drawn to the same scale. Draw a line linking each container to its graph EHJ Paper 1 short Page 4 Churchill Maths Limited

5 11 10 Speed (v metres per second) 8 Car P 6 Car Q 4 2 O Time (t seconds) The graph shows the speed, v metres per second, of car P and car Q, t seconds after a traffic light turns red. (a) (b) (c) (d) Which car stopped first? How long was it after the light turned red that car P began to slow down? At what speed was car Q travelling when car P was travelling at 6 metres per second? Write down a formula for the speed (v metres per second) of car Q at time t seconds after the light turned red EHJ Paper 1 short Page 5 Churchill Maths Limited

6 12 (a) Factorise fully 4pq + 8p (b) Make x the subject of the following. x 4w = ax 6 *13 A company sells plastic trays. The top of each tray is a rectangle measuring 20 cm by 15 cm. The perpendicular height of each tray is 10 cm. 20 cm 15 cm 10 cm 2 cm The sides of the tray are sloped so that they can be stacked. When a tray is stacked on top of others, the height of the stack increases by 2 cm. The trays are packed into crates which are cubes of side 60 cm. Work out the maximum number of trays that can be packed in a crate. (6) 2012 EHJ Paper 1 short Page 6 Churchill Maths Limited

7 14 x + 5 x 2 2x + 1 In the shape shown above, all of the corners are right angles. All of the measurements are in centimetres. Find and simplify an expression for the perimeter of the shape. 15 Shape A is shown on the grid on the answer sheets. (a) Translate shape A using the vector 0 5. Label the image B. (b) Enlarge shape A by scale factor 2 with centre of enlargement (3, 1). Label the image C EHJ Paper 1 short Page 7 Churchill Maths Limited

8 *16 A restaurant recorded the number of main meals it served each day in August. The restaurant recorded the same information for October. The data recorded is displayed in this back-to-back stem and leaf diagram. August October Key for August: 3 4 Key for October: 3 5 means 43 meals means 35 meals Compare the number of main meals ordered each day in August with the number ordered each day in October. (6) cm 6 cm The diagram shows a square piece of card. The four shaded shapes are identical. They are cut out from the card and thrown away to leave the net of a pyramid. Work out the percentage of the square piece of card that is thrown away. (5) 2012 EHJ Paper 1 short Page 8 Churchill Maths Limited

9 18 Anne and Zia are discussing how much they each saved last week towards their holiday. Anne saved 4 more than Zia. If Anne had saved twice as much, between them they would have saved 50. Find out how much Zia saved last week. (5) 19 B O C aº A 62º D A and B are points on the circumference of a circle, centre O. CAD is a tangent to the circle. BOC is a straight line. Angle BAD = 62º. Angle BCD = aº. Work out the value of a. 20 Express 4 x x 1 as a single fraction in its simplest form. 21 (a) Estimate to the nearest whole number the value of (b) Work out the value of EHJ Paper 1 short Page 9 Churchill Maths Limited

10 *22 The histogram on the answer sheets shows information about the amount of money spent by 28 people in a record shop. Work out how many people could have spent more than 25. Write down all the possible answers. 23 (a) Express x 2 4x 2 in the form (x + a) 2 + b (b) y O B x A The diagram is a sketch of the curve with equation y = x 2 4x 2 (i) Write down the coordinates of the point A. (ii) Find the x-coordinate of the point B in the form p + q. END 2012 EHJ Paper 1 short Page 10 Churchill Maths Limited