# Mathematics Paper 2 (Calculator)

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2 Answer ALL questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1 Frank, Mary and Seth shared some sweets in the ratio 4 : 5 : 7 Seth got 18 more sweets than Frank. Work out the total number of sweets they shared. 2 PQR is a right-angled triangle. Work out the size of the angle marked x. Give your answer correct to 1 decimal place. R x 14 cm... (Total for Question 1 is 3 marks) P 5 cm Q... (Total for Question 2 is 2 marks) Pearson Education Limited *S48574A0220* 2015

3 3 Here are the first four terms of an arithmetic sequence (a) Write an expression, in terms of n, for the nth term of this sequence. The nth term of a different arithmetic sequence is 3n + 5 (b) Is 108 a term of this sequence? Show how you get your answer.... (2) (2) (Total for Question 3 is 4 marks) *S48574A0320* 119 3

4 4 Axel and Lethna are driving along a motorway. They see a road sign. The road sign shows the distance to Junction 8 It also shows the average time drivers take to get to Junction 8 The speed limit on the motorway is 70 mph. Lethna says We will have to drive faster than the speed limit to drive 30 miles in 26 minutes. Is Lethna right? You must show how you get your answer. To Junction 8 30 miles 26 minutes (Total for Question 4 is 3 marks) Pearson Education Limited *S48574A0420* 2015

5 5 The table shows some information about the foot lengths of 40 adults. Foot length ( f cm) (a) Write down the modal class interval. Number of adults 16 f < f < f < f < f < 26 9 (b) Calculate an estimate for the mean foot length.... (1)... cm (3) (Total for Question 5 is 4 marks) *S48574A0520* 121 5

6 6 Triangles ABD and BCD are right-angled triangles. Work out the value of x. Give your answer correct to 2 decimal places. A 5 cm B x cm 10 cm D 4 cm C... (Total for Question 6 is 4 marks) Pearson Education Limited *S48574A0620* 2015

7 7 The graph of y = f(x) is drawn on the grid. (a) Write down the coordinates of the turning point of the graph. (b) Write down the roots of f(x) = 2 (c) Write down the value of f(0.5) y O x 1 (...,...) (1)... (1)... (1) (Total for Question 7 is 3 marks) *S48574A0720* 123 7

8 8 In a box of pens, there are three times as many red pens as green pens and two times as many green pens as blue pens. For the pens in the box, write down the ratio of the number of red pens to the number of green pens to the number of blue pens.... (Total for Question 8 is 2 marks) Pearson Education Limited *S48574A0820* 2015

9 9 ABCD is a rectangle. EFGH is a trapezium. All measurements are in centimetres. The perimeters of these two shapes are the same. Work out the area of the rectangle. H A D E 5x 3x + 4 x 3 4x 7x 3 B 4x C F 5x G... cm 2 (Total for Question 9 is 5 marks) *S48574A0920* 125 9

10 10 Katy invests 2000 in a savings account for 3 years. The account pays compound interest at an annual rate of 2.5% for the first year x% for the second year x% for the third year There is a total amount of in the savings account at the end of 3 years. (a) Work out the rate of interest in the second year. Katy goes to work by train. The cost of her weekly train ticket increases by 12.5% to 225 (b) Work out the cost of her weekly train ticket before this increase.... (4)... (2) 10 *S48574A01020* 126 (Total for Question 10 is 6 marks)

11 11 S S and T are points on the circumference of a circle, centre O. PT is a tangent to the circle. SOP is a straight line. Angle OPT = 32 Work out the size of the angle marked x. You must give a reason for each stage of your working. x O T 32 P (Total for Question 11 is 4 marks) *S48574A01120*

12 12 A and B are two sets of traffic lights on a road. The probability that a car is stopped by lights A is 0.4 If a car is stopped by lights A, then the probability that the car is not stopped by lights B is 0.7 If a car is not stopped by lights A, then the probability that the car is not stopped by lights B is 0.2 (a) Complete the probability tree diagram for this information. lights A stop not stop Mark drove along this road. He was stopped by just one of the sets of traffic lights. (b) Is it more likely that he was stopped by lights A or by lights B? You must show your working. lights B stop not stop stop not stop (2) (3) 12 *S48574A01220* 128 (Total for Question 12 is 5 marks)

13 13 d is inversely proportional to c When c = 280, d = 25 Find the value of d when c = Prove algebraically that (2n + 1) 2 (2n + 1) is an even number for all positive integer values of n. d =... (Total for Question 13 is 3 marks) (Total for Question 14 is 3 marks) *S48574A01320*

14 15 Prove algebraically that the recurring decimal has the value 16 Show that 1 1 simplifies to ax + b 2 2 6x + 7x 5 4x 1 cx + d (Total for Question 15 is 2 marks) where a, b, c and d are integers.... (Total for Question 16 is 3 marks) 14 *S48574A01420* 130

15 17 The diagram shows a sector of a circle of radius 7 cm cm 7 cm Work out the length of arc AB. Give your answer correct to 3 significant figures. A B... cm (Total for Question 17 is 2 marks) *S48574A01520*

16 18 m = s t s = 3.47 correct to 3 significant figures t = correct to 4 significant figures By considering bounds, work out the value of m to a suitable degree of accuracy. Give a reason for your answer. (Total for Question 18 is 5 marks) 16 *S48574A01620* 132

17 19 The graph of y = f(x) is shown on both grids below. y y = f(x) O x 2 4 (a) On the grid above, sketch the graph of y = f( x) (1) y y = f(x) O x 2 4 (b) On this grid, sketch the graph of y = f(x) + 3 (1) (Total for Question 19 is 2 marks) *S48574A01720*

18 20 Solve algebraically the simultaneous equations x 2 + y 2 = 25 y x = *S48574A01820* 134 (Total for Question 20 is 5 marks)

19 21 In triangle RPQ, RP = 8.7 cm PQ = 5.2 cm Angle PRQ = 32 (a) Assuming that angle PQR is an acute angle, calculate the area of triangle RPQ. Give your answer correct to 3 significant figures....cm 2 (b) If you did not know that angle PQR is an acute angle, what effect would this have on your calculation of the area of triangle RPQ? (1) (4) (Total for Question 21 is 5 marks) *S48574A01920*

20 22 A frustum is made by removing a small cone from a large cone as shown in the diagram. 10 cm 12 cm The frustum is made from glass. The glass has a density of 2.5 g / cm 3 15 cm Work out the mass of the frustum. Give your answer to an appropriate degree of accuracy. 1 2 Volume of cone = 3 πr h h... g (Total for Question 22 is 5 marks) TOTAL FOR PAPER IS 80 MARKS r 20 *S48574A02020* 136

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Centre No. Candidate No. Paper Reference 4 4 0 0 3 H Surname Signature Paper Reference(s) 4400/3H London Examinations IGCSE Mathematics Paper 3H Higher Tier Monday 18 May 2009 Afternoon Time: 2 hours Initial(s)

### Paper Reference. Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser. Tracing paper may be used.

Centre No. Candidate No. Paper Reference 5 5 2 3 0 3 Paper Reference(s) 5523/03 Edexcel GCSE Mathematics A 1387 Paper 3 (Non-Calculator) Intermediate Tier Tuesday 6 November 2007 Morning Time: 2 hours

### You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

Write your name here Surname Other names Pearson Edexcel International GCSE Mathematics A Paper 2FR Thursday 9 June 2016 Morning Time: 2 hours Centre Number Candidate Number Foundation Tier Paper Reference

### Higher Tier Friday 10 November 2006 Morning Time: 2 hours

Centre No. Candidate No. Paper Reference 5 5 2 5 0 6 Paper Reference(s) 5525/06 Edecel GCSE Mathematics A 1387 Paper 6 (Calculator) Higher Tier Friday 10 November 2006 Morning Time: 2 hours Surname Signature

### Paper Reference H. 1380/3H Edexcel GCSE Mathematics (Linear) 1380 Paper 3 (Non-Calculator)

Centre No. Candidate No. Paper Reference 1 3 8 0 3 H Paper Reference(s) 1380/3H Edexcel GCSE Mathematics (Linear) 1380 Paper 3 (Non-Calculator) Higher Tier Monday 18 May 2009 Afternoon Time: 1 hour 45

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

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

### You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

Write your name here Surname Other names Pearson Edexcel International GCSE Mathematics A Paper 2FR Centre Number Tuesday 17 January 2017 Morning Time: 2 hours Candidate Number Foundation Tier Paper Reference

### You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

Write your name here Surname Other names Pearson Edexcel Certificate Pearson Edexcel International GCSE Mathematics A Paper 2F Thursday 9 June 2016 Morning Time: 2 hours Centre Number Candidate Number

### General Certificate of Secondary Education Higher Tier

Centre Number Surname Other Names Candidate Number For Examiner s Use Examiner s Initials Candidate Signature General Certificate of Secondary Education Higher Tier Pages 3 4-5 Mark GCSE Mathematics Unit

### 43055/2H. General Certificate of Secondary Education June 2009

Surname Other Names For Examiner s Use Centre Number Candidate Number Candidate Signature General Certificate of Secondary Education June 2009 MATHEMATICS (MODULAR) (SPECIFICATION B) 43055/2H Module 5