Mathematics. Sample from Churchill Maths. For Edexcel GCSE. Unit 2 : Number, Algebra, Geometry 1 (Non-Calculator) Higher Tier

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1 Name Class For Edexcel GCSE Mathematics Unit 2 : Number, Algebra, Geometry 1 (Non-Calculator) Paper A Time : 1 hour 15 minutes Higher Tier You must have: Ruler, protractor, compasses, pen, pencil, eraser. Total Marks Instructions and Information Write your name in the box at the top of the page. Answer all the questions in the spaces provided. The total mark for this paper is 60. The marks for each question are shown in brackets. Calculators must not be used. Questions labelled with an asterisk (*) are ones where the quality of your written communication will be assessed. Advice Read each question carefully before you start to answer it. Keep an eye on the time. Try to answer every question. Check your answers if you have time at the end. Written by Shaun Armstrong Only to be copied for use in the purchaser's school or college 2012 EHA Unit 2 Page 1 Limited Turn over

2 GCSE Mathematics Formulae: Higher Tier You must not write on this formulae page. Volume of prism = area of cross section length Area of trapezium = 1 (a + b)h 2 a cross section length h b Volume of sphere = 4 3 πr3 Surface area of sphere = 4πr 2 Volume of cone = 1 3 πr2 h Curved surface area of cone = πrl r l h r In any triangle ABC C The Quadratic Equation The solutions of ax 2 + bx + c = 0 where a 0, are given by b a x = b± b2 4ac 2a A c B Sine Rule a sin A = b sin B = c sin C Cosine Rule a 2 = b 2 + c 2 2bc cos A Area of triangle = 1 2 ab sin C 2012 EHA Unit 2 Page 2 Limited

3 Answer ALL questions. Write your answers in the spaces provided. You must write down all stages in your working. 1 In 1985 petrol cost 1.95 per gallon. In 2005 petrol cost 80p per litre. Harry says that the price of petrol more than doubled from 1985 to Is Harry correct? Explain your answer. (Total for Question 1 is 3 marks) 2 (a) Simplify 2p q + 3p + 4q (b) Simplify m 9 m 2 (1) (c) Factorise fully 9xy 2 6y 3 (Total for Question 2 is 5 marks) 2012 EHA Unit 2 Page 3 Limited Turn over

4 3 (a) Complete this table of values for y = 3x 1 x y 4 (b) On the grid, draw the line y = 3x 1 y O x (c) Here are the equations of three more lines. y = 2x 1 y = 2 3x y = 3x 3 Tick the box under each equation of a line that is parallel to the line y = 3x 1 (1) (Total for Question 3 is 5 marks) 2012 EHA Unit 2 Page 4 Limited

5 4 P Diagram NOT accurately drawn O R Q P and Q are points on a circle, centre O. The tangents to the circle at P and Q intersect at the point R. Angle PRQ = 53º. Work out the size of angle POQ. º (Total for Question 4 is 2 marks) 2012 EHA Unit 2 Page 5 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. (a) Calculate how much less Badri charges for a 1 hour job. 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 O Time at job (t hours) The total that Martin charges is given by the formula C = 25 20t (b) Write down a formula for the total that Badri charges. (1) 2012 EHA Unit 2 Page 6 Limited

7 (c) Write down the value of t at the point where the two graphs intersect. (1) t = (d) Explain how your answer to part (c) is useful to someone choosing between Martin and Badri to do a plumbing job. (1) *6 Lanika needs a sheet of card that is at least 3 10 mm thick. (Total for Question 5 is 5 marks) 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. (Total for Question 6 is 3 marks) 2012 EHA Unit 2 Page 7 Limited Turn over

8 7 (a) Diagram NOT accurately drawn xº 32º The shape in the diagram above is made up of six identical isosceles triangles. Work out the value of x. (3) x = (b) Diagram NOT accurately drawn yº The diagram shows four sides of a regular polygon. A dotted line is drawn between two of the vertices of the polygon. Find, in terms of y, an expression for the number of sides of the polygon. (3) (Total for Question 7 is 6 marks) 2012 EHA Unit 2 Page 8 Limited

9 8 (a) Write 63 as a product of its prime factors 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. *(b) Marlon's step is between 40 cm and 80 cm in length. Find all the possible lengths of Marlon's step. (6) (Total for Question 8 is 8 marks) 2012 EHA Unit 2 Page 9 Limited Turn over

10 9 y F G (5, 6, 0) I H (5, 6, 4) E D O A x z (0, 0, 8) C B Diagram NOT accurately drawn The diagram shows a prism on a 3-dimensional grid. The point D is the midpoint of BG. (a) Find the coordinates of the points (i) I, (1) (,, ) (ii) D. (,, ) 1 unit on the grid represents 1 cm. (b) Work out the volume of the prism. (3) cm 3 (Total for Question 9 is 6 marks) 2012 EHA Unit 2 Page 10 Limited

11 10 Find the value of (a) (1) (b) (Total for Question 10 is 3 marks) 11 (a) Express 4 x x 1 as a single fraction in its simplest form. (3) (b) Simplify fully 4 x 6 4 x 2 9 (3) (Total for Question 11 is 6 marks) 2012 EHA Unit 2 Page 11 Limited Turn over

12 12 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 Diagram NOT accurately drawn 30 cm 30 cm (a) Work out the area of this section of path. Diagram NOT accurately drawn (5) cm EHA Unit 2 Page 12 Limited

13 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. (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. (3) (Total for Question 12 is 8 marks) TOTAL FOR PAPER IS 60 MARKS 2012 EHA Unit 2 Page 13 Limited Turn over