Mathematics Module N4 Paper 1 (Non-calculator) Higher Tier pm 2.30 pm [GMN41] 1 hour.

Transcription

1 Centre Number 71 Candidate Number General Certificate of Secondary Education 2009 Mathematics Module N4 Paper 1 (Non-calculator) Higher Tier [GMN41] GMN41 MONDAY 18 MAY 1.30 pm 2.30 pm TIME 1 hour. INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number in the spaces provided at the top of this page. Write your answers in the spaces provided in this question paper. Answer all eleven questions. Any working should be clearly shown in the spaces provided since marks may be awarded for partially correct solutions. You must not use a calculator for this paper. INFORMATION FOR CANDIDATES The total mark for this paper is 44. Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question. You should have a ruler, compasses, set-square and protractor. The Formula Sheet is on page For Examiner s use only Question Number Total

2 Formula Sheet Area of trapezium = 1 2 (a + b)h a h b Volume of prism = area of cross section length In any triangle ABC Cross section A length Area of triangle = 1 2 ab sin C a b c Sine rule : = = sin A sin B sin C Cosine rule: a 2 = b 2 + c 2 2bc cos A B c a b C Volume of sphere = 4 3 πr 3 Surface area of sphere = 4πr 2 r Volume of cone = 1 3 πr 2 h Curved surface area of cone = πrl l r h Quadratic equation: The solutions of ax 2 + bx + c = 0, where a 0, are given by x = 2 b± b 4ac 2a [Turn over

3 1 (a) Expand and simplify (3x 2)(2x + 1) Answer [2] (b) Solve the simultaneous equations 3x 2y = 14 0x + 2y = 10 Show your working. A solution by trial and improvement will not be accepted. Answer x =, y = [2] 2 Calculate Answer [3] 2x + 1 x Solve the equation = Show your working. A solution by trial and improvement will not be accepted. Answer x = [4] [Turn over

4 4 A glacier is losing 20% of its volume each year. What % of its original volume will be left after 3 years? Answer % [2] 5 30 B Diagram not drawn accurately A 50 O C D T O is the centre of a circle and A, B, C and D are points on the circumference of the circle. TA is a tangent to the circle. Angle BAD is 50. Angle ABO is 30. Calculate the size of (a) angle OAT, Answer [1] (b) angle BCD, Answer [1] (c) angle BOD, Answer [1] (d) angle TAD. Answer [2] [Turn over

5 6 (a) Factorise x 2 4 Answer [1] (b) Hence simplify x 2 4 2x 2 x 6 Answer [3] 7 Which of the three measures of central tendency ( average ) would be of most use to a shoe shop manager when placing an order for more shoes? Give a reason for your answer. Answer because [2] 8 Write down the equation of the straight line which passes through the point (0, 2) and is perpendicular to the line with equation y = 3x. Answer [2] 9 Evaluate (a) Answer [2] (b) Answer [2] [Turn over

6 10 The table gives information about the weights of schoolbags. Weight, w kg Number of schoolbags 2.0 w w w w w (a) Illustrate the data by drawing a histogram on the graph paper opposite, using the scale provided. [3] (b) A stratified sample of 20 schoolbags was taken from those whose weight was less than 4.0 kg. (i) How many of the sample were taken from the class interval 3.0 w 3.5? Answer [2] (ii) In this stratified sample, half the schoolbags weighed less than 3.2 kg. Estimate how many of the original full set of schoolbags weighed 3.2 kg or more. Answer [2] [Turn over

7 Weight, w kg 11 Solve the simultaneous equations y = x 2 + 3x 2 and 3x + 2y = 22. Answer [7] [Turn over

8 Centre Number 71 Candidate Number General Certificate of Secondary Education 2009 Mathematics Module N4 Paper 2 (With calculator) Higher Tier [GMN42] GMN42 MONDAY 18 MAY 2.45 pm 3.45 pm TIME 1 hour. INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number in the spaces provided at the top of this page. Write your answers in the spaces provided in this question paper. Answer all nine questions. Any working should be clearly shown in the spaces provided since marks may be awarded for partially correct solutions. INFORMATION FOR CANDIDATES The total mark for this paper is 44. Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question. You should have a calculator, ruler, compasses, set-square and protractor. The Formula Sheet is on page For Examiner s use only Question Number Total

9 Formula Sheet Area of trapezium = 1 2 (a + b)h a h b Volume of prism = area of cross section length In any triangle ABC Cross section A length Area of triangle = 1 2 ab sin C a b c Sine rule : = = sin A sin B sin C Cosine rule: a 2 = b 2 + c 2 2bc cos A B c a b C Volume of sphere = 4 3 πr 3 Surface area of sphere = 4πr 2 r Volume of cone = 1 3 πr 2 h Curved surface area of cone = πrl l r h Quadratic equation: The solutions of ax 2 + bx + c = 0, where a 0, are given by x = 2 b± b 4ac 2a [Turn over

10 1 Calculate the volume of a sphere of diameter 70 cm. Answer [3] [Turn over

11 2 Peter is a gardener. He recorded how much money he earned each week for 40 weeks. Money in (m) Frequency Money in Cumulative Frequency 180 m < < m < < m < < m < m < m < m < (a) Complete the table. [1] (b) Draw the cumulative frequency graph on the opposite page. [3] (c) Use the graph to estimate (i) the median, Answer [1] (ii) the inter-quartile range, Answer [2] (iii) in how many weeks Peter earned more than 225. Answer weeks [2] (d) The lowest amount Peter earned was 185 and the highest amount was 315. Draw a box plot opposite to illustrate Peter s earnings. [3] [Turn over

12 40 30 Cumulative frequency Money in less than [Turn over

13 3 Explain the difference between discrete data and continuous data and give one example of each. [2] 4 B 8 cm C Diagram not drawn accurately 5 cm 22 A cm D ABCD is a quadrilateral. AB = 8 cm, AD = 10 cm, CD = 5 cm. Angle BAD = 80 and angle BDC = 22. Calculate (a) the length of BD, Answer cm [3] (b) the area of triangle BCD. Answer cm 2 [2] [Turn over

14 5 A man walks x km East and then (x + 8) km North. He is now 12 km from his starting point. (a) Show that x satisfies the equation x 2 + 8x 40 = 0 [3] (b) Solve the equation to find x, giving your answer correct to 3 significant figures. Answer x = [3] [Turn over

15 6 (a) D Diagram not drawn accurately E 14 cm B 24 cm F C 7 cm A ABC and BDE are similar triangles. BE = 14 cm, BC = 24 cm, AC = 7 cm Find the length of DE. Answer cm [2] [Turn over

16 (b) The diagram below shows the frustum of a cone. The circular top of the frustum, centre E, is of radius 14 cm. The circular base of the frustum, centre F, is of radius 21 cm. E 14 cm B 24 cm F C 7 cm A Using the answer found in part (a), find the volume of the frustum of the cone. Answer cm 3 [4] [Turn over

17 7 The equation 3x 2 = 1 N can have rational or irrational solutions. (a) Write down a value for N which gives rational solutions. Answer N = [1] (b) Write down a value for N which gives irrational solutions. Answer N = [1] (c) Write down a value for N which gives no solutions. Answer N = [1] 8 Given that (x + b) 2 x 2 10x + c, find the values of b and c. Answer b = [3] c = [3] [Turn over

18 9 K J L I G E H D F C A B ABCDEF, GHIJKL, the base and top of the prism, are regular hexagons. AB = 20 cm, AG = 30 cm. Calculate the angle between AJ and the base ABCDEF. Answer [4] THIS IS THE END OF THE QUESTION PAPER