Centre Number 71 Candidate Number General Certificate of Secondary Education 2009 Mathematics Module N3 Paper 1 (Non-calculator) Higher Tier [GMN31] GMN31 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 fourteen 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 2. 4560 For Examiner s use only Question Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Total
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 4560 2 [Turn over
1 Start Input N Is N divisible by 5? No Increase N by 1 Yes Is N divisible by 7? No Yes Print N Stop Starting with N = 64, use the flow chart to find the number printed. Answer Number Printed [2] 4560 3 [Turn over
2 On holiday Mark drinks 3 4 of a bottle of water each day. What is the least number of bottles Mark will have to buy for a 9 day holiday? Answer [3] 3 I buy y bars of chocolate at 42 pence each. Write an expression in terms of y for the change, in pence, I will get from 5. Answer p [2] 4560 4 [Turn over
4 The table shows the RRP (recommended retail price) and the sale price of some products in Jack s Discount Store. RRP ( ) 80 113 140 170 180 210 230 270 300 320 Sale price ( ) 58 85 105 130 132 155 178 200 232 240 Sale price ( ) 300 250 200 150 100 50 0 0 100 200 300 400 RRP ( ) The data in bold type has already been plotted. (a) Complete the scatter graph. [2] (b) Draw a line of best fit. [1] (c) Estimate the RRP of a product on sale for 150 Answer [1] (d) What type of correlation does your graph show? Answer [1] 4560 5 [Turn over
5 A E O B Diagram not drawn accurately D C ABCDE is a regular pentagon with centre O. Calculate the size of (a) angle AOB Answer [2] (b) angle ABC Answer [2] 6 The nth term of a sequence is represented by n 2 3 Which term of the sequence will equal 78? Answer [2] 4560 6 [Turn over
7 The heights of 100 students were recorded. Height, h, in cm Frequency 130 h 135 15 135 h 140 25 140 h 145 26 145 h 150 21 150 h 155 8 155 h 160 5 Draw a frequency polygon for the data. 30 25 20 Frequency 15 10 5 0 125 130 135 140 145 Height, h (cm) 150 155 160 165 [2] 4560 7 [Turn over
8 Write 80 as a product of its prime factors, giving your answer in index form. Answer [3] 9 Jack is x years old. His brother Dan is 5 years younger. In 3 years time the sum of their ages will be 15. (a) Write an equation in terms of x using the sum of their ages in 3 years time. Answer [2] (b) Solve the equation to find Jack s age now. Answer [1] 4560 8 [Turn over
10 The percentage marks in a class test were recorded in the following table: (%) Frequency 55 59 1 60 64 1 65 69 2 70 74 5 75 79 9 80 84 5 85 89 2 Calculate an estimate for the mean mark. Answer % [4] 11 (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] 4560 9 [Turn over
12 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 Calculate the size of (a) angle OAT, Answer [1] (b) angle BCD, Answer [1] (c) angle BOD. Answer [1] 13 Calculate 2 1 5 1 2 3 Answer [3] 4560 10 [Turn over
2x + 1 x + 1 14 Solve the equation = 3 3 5 Show your working. A solution by trial and improvement will not be accepted. Answer x = [4] THIS IS THE END OF THE QUESTION PAPER 4560 11 [Turn over
Centre Number 71 Candidate Number General Certificate of Secondary Education 2009 Mathematics Module N3 Paper 2 (With calculator) Higher Tier [GMN32] GMN32 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 twelve 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 2. 4561 For Examiner s use only Question Number 1 2 3 4 5 6 7 8 9 10 11 12 Total
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 4561 2 [Turn over
1 y 6 A 5 4 3 2 1 6 5 4 3 2 1 0 1 2 1 2 3 4 5 6 x 3 4 5 6 B A is the point ( 2, 4). B is the point (3, 6). Find the midpoint of AB. Answer (, ) [2] 4561 3 [Turn over
2 The heights (in centimetres) of twenty boys in a local hockey club are: 181 170 162 153 182 171 163 158 185 174 166 157 177 167 178 167 178 167 169 168 Construct a stem and leaf diagram to illustrate these heights. [3] 3 A wardrobe is priced at 640 In a sale its price was reduced by 35%. Calculate the sale price of the wardrobe. Answer [3] 4561 4 [Turn over
4 Construct a rhombus of side 6.5 cm which has one of its diagonals 5 cm in length. [4] 5 Katy wants to know how many times a month, on average, the people in her town go to the cinema. She asks 200 pupils in her school. Explain why Katy s sample may not be representative of the people in her town. Answer [1] 4561 5 [Turn over
6 (a) Expand and simplify 4(2a + 3) 7 Answer [2] (b) Factorise (i) 6a 10 Answer [1] (ii) a 2 + a Answer [1] 7 A man is filling his garden pond with water. He can fill a bucket of water and empty it into the pond every 25 seconds. The bucket holds 15 litres of water. It takes the man 4 minutes and 35 seconds to fill the pond. What volume of water does the pond hold? Answer [4] 8 Use trial and improvement to solve x 3 2x = 41 giving the answer correct to 1 decimal place. Show your working. Answer [4] 4561 6 [Turn over
9 2500 is placed in a bank account and gains 4% compound interest per year. What should be the total amount in the account at the end of 3 years? Answer [3] 10 B 25 cm C 7cm A (a) Calculate the length of BC in the right-angled triangle. Answer cm [3] (b) Calculate the size of angle BAC. Answer [3] 4561 7 [Turn over
11 The number of trees undamaged in an orchard after a hurricane was 220. It was observed that 12% had been damaged. How many trees were in the orchard before the hurricane? Answer [3] 12 Peter is a gardener. He recorded how much money he made each week for 40 weeks. Money in (m) Frequency Money in Cumulative frequency 180 m 200 4 200 4 200 m 220 7 220 11 220 m 240 12 240 240 m 260 9 260 m 280 5 280 m 300 2 300 m 320 1 (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] 4561 8 [Turn over
40 30 Cumulative frequency 20 10 0 180 200 220 240 260 280 300 Money in (less than) 320 THIS IS THE END OF THE QUESTION PAPER 4561 9 [Turn over