Mathematics (Modular) 43055/2H (Specification B) Module 5

Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Secondary Education Higher Tier June 0 Mathematics (Modular) 43055/H (Specification B) Module 5 Paper Calculator Friday 0 June 0 For this paper you must have: l a calculator l mathematical instruments. 9.00 am to 0.5 am H Pages 3 4 5 6 7 8 9 0 3 4 5 6 7 8 9 TOTAL Mark Time allowed l hour 5 minutes Instructions l Use black ink or black ball-point pen. Draw diagrams in pencil. l Fill in the es at the top of this page. l Answer all questions. l You must answer the questions in the spaces provided. around each page or on blank pages. l Use a calculator where appropriate. l Do all rough work in this book. l If your calculator does not have a π button, take the value of π to be 3.4 unless another value is given in the question. Information l The marks for questions are shown in brackets. l The maximum mark for this paper is 70. l You may ask for more answer paper, graph paper and tracing paper. These must be tagged securely to this answer booklet. Advice l In all calculations, show clearly how you work out your answer. 43055/H

Formulae Sheet: Higher Tier a Area of trapezium = (a +b)h h b Volume of prism = area of cross-section length crosssection length 4 Volume of sphere = π r 3 3 r Surface area of sphere = 4π r Volume of cone = 3 πr h Curved surface area of cone = πrl l r h In any triangle ABC Area of triangle = ab sin C a b c Sine rule = = sin A sin B sin C Cosine rule a = b + c bc cos A A b c C a B The Quadratic Equation The solutions of ax + bx + c = 0, where a 0, are given by x = b ± (b 4ac) a (0)

3 Answer all questions in the spaces provided. 6 identical circles are shown. A, B, C and D are centres of circles. ABCD is a square. A B Not drawn accurately D C The perimeter of ABCD is 60 cm. Work out the radius of a circle. Answer... cm Turn over for the next question 3 Turn over (03)

4 A quadrilateral is shown. 00 x Not drawn accurately 83 x Work out the value of x. Answer... degrees (4 marks) 3 This is a regular pentagon. Not drawn accurately w Work out the value of an exterior angle, marked w on the diagram. Answer... degrees ( marks) (04)

5 4 In this diagram, all lengths are in centimetres. 6 6 Not drawn accurately h h 4 8 The area of the shape is 56 cm. Work out the length marked h in the diagram. Answer... cm 5 The nth term of a sequence is 8n 5 How many terms of the sequence are less than zero? Answer... Turn over (05)

6 6 Use trial and improvement to find a solution to the equation Continue the table of results. Give your solution to decimal place. x 3 + 6x = 9 x x 3 + 6x 0 Comment Too small Answer x =... (4 marks) (06)

7 7 Enlarge the triangle by scale factor using (0,0) as the centre of enlargement. y 6 4 0 8 6 4 0 0 4 6 8 0 4 x ( marks) 6 Turn over (07)

8 8 Here is a right-angled triangle. x 7 cm Not to accurately Not drawn accurately 5 cm Work out the value of x. Answer... cm (08)

9 9 (a) Draw the graph of y = 3x for 4 x 4 y 4 0 8 6 4 4 3 O 3 4 x 4 6 8 0 4 9 (b) Shade the region on your graph that represents y 3x ( mark) 7 Turn over (09)

0 0 Here is a triangular prism. 4 cm 0 cm 6 cm Work out the volume of the prism. Answer... cm 3 (0)

The formula for the area, A, of a trapezium is a A = (a +b)h h b (a) A trapezium has an area of 30 cm. Work out a possible set of values for a, b and h for this trapezium. Answer a =... cm Answer b =... cm Answer h =... cm ( marks) (b) Rearrange the formula A = (a +b)h to make b the subject. Answer... 8 Turn over ()

(a) Solve 9c 3 = 4c + Answer c =... 3 (b) Solve x + 4 = Answer x =... 3 a, b and c represent lengths. π is a constant. For each expression put a tick to show whether it could represent a length, an area or a volume. Expression Length Area Volume πabc π(a + b) a + 3b ()

3 4 A and C are points on a circle, centre O. BA and BC are tangents. Angle ABO = 4 A Not drawn accurately O D 4 C B 4 (a) Work out the size of angle AOC. Answer... degrees ( marks) 4 (b) Which of these triangles are isosceles? Circle your answers. BDC ABC ABO ODA AOC ( marks) 3 Turn over (3)

4 5 (a) Show that x = is a solution of the equation 5x + 9 = 6x 7x 3 5 ( marks) 5 (b) Show that the equation 5x + 9 = 6x 7x 3 5 can be written as 4x 3x 7 = 0 ( marks) (4)

5 5 (c) Hence or otherwise, find a complete solution to the equation 5x + 9 = 6x 7x 3 5 Answer... ( marks) 6 Line L is perpendicular to the line y = x 3 L passes through the point (0, 4). Work out the equation of L. Answer... ( marks) Turn over for the next question 8 Turn over (5)

6 7 (a) (i) On the grid below, sketch the graph of y = 3 sin x for 0 x 360 The graph y = sin x is shown to help you. y 3 0 0 90 80 70 360 x 3 ( mark) 7 (a) (ii) On the grid below, sketch the graph of y = + sin x for 0 x 360 The graph y = sin x is shown to help you. y 3 0 0 90 80 70 360 x 3 ( mark) (6)

7 7 (b) The graph y = cos x is shown for 0 x 360 y 0.5 0 0.5 0 90 80 70 360 x You are given that cos 60 = 0.5 Work out the value of x between 80 and 360 such that 7 (b) (i) cos x = 0.5 Answer... degrees ( mark) 7 (b) (ii) cos x = 0.5 Answer... degrees ( mark) Turn over for the next question 4 Turn over (7)

8 8 Here is a triangle. 7 cm Not drawn accurately 53 0 cm Work out the area of the triangle. Give your answer to an appropriate degree of accuracy. Answer... cm (8)

9 9 Here are a square and a rectangle. All dimensions are in centimetres. x (3y x) (3y + x) The area of the square is equal to the area of the rectangle. Show that y is a multiple of x. (6 marks) END OF QUESTIONS 9 (9)