Excel / Education. GCSE Mathematics. Paper 4B (Calculator) Foundation Tier. Time: 1 hour 30 minutes. Turn over

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1 Excel / Education GCSE Mathematics Paper 4B (Calculator) Foundation Tier Time: 1 hour 30 minutes 4B Materials required for examination Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser. Tracing paper may be used. Items included with question papers Formulae sheet Instructions to Candidates Answer ALL the questions in the spaces provided in this question paper. Supplementary answer sheets may be used. Information for Candidates The total mark for this paper is 100. The marks for questions and parts of questions are shown in round brackets: e.g.. Calculators may be used. Advice to Candidates Show all your working.

2 1. Write in figures the number one hundred and four thousand, three hundred and forty two A quadrilateral has all four sides the same length. It also has two pairs of parallel sides. Which two of the following could it be? A. Trapezium B. Square C. Kite D. Rhombus E. Pentagon. and In the space below, using the line AB, draw an angle of exactly 40 o. A B 4. Put the following sets of numbers in size order, starting with the smallest

3 (c) y B 10 8 C A x Write down the coordinates of; (i) (ii) (iii) Point A Point B Point C Mark on the diagram the position of the point with coordinates (3, -4). Label this point D.

4 6. Simplify; 4a + 3a + a 2xy + 4x + 3xy + 5x 7. What is the mathematical name given to this type of triangle? For the triangle below work out; b (i) Angle a 70 o a (ii) Angle b (c) Calculate the area of this triangle which has a height of 7.1cm and a base of 4.6cm. Remember to state the units in your answer. 7.1cm 4.6cm

5 8. Peter notes the number of people in each of 9 passing vehicles. The results are listed below What is the mode of these numbers? Find the median number of people (c) Calculate the mean number of people (d) What is the range of the number of people?

6 9. The number line below shows the Probability scale which goes from 0 to 1. Put the correct letter next to each cross. The first one has been done for you. Probability of.. A. Picking a RED counter from a bag containing 6 red and 4 white. B. Getting HEADS when throwing a coin once. C. Getting ALL 6 numbers correct on a National Lottery ticket D. NOT getting double 6 when throwing two dice E. Getting a FOUR when throwing one die b From the list above, write down one number which is; Prime A cube number (c) A factor of 60 (d) A square number (e) A multiple of Expand (i) 3(x + 6)

7 (ii) 4x(2x 3) Factorise fully (i) 8x + 12 (ii) 6x 2 4x 12. A sewerage pipe is made in the shape of a cylinder with diameter 1.5m and length 21.6m, as shown below 1.5m 21.6m Calculate the area of the circular end of the pipe. m 2 Hence calculate the volume of the pipe, giving your answer to a suitable degree of accuracy. m 3

8 (c) These pipes cost 225 to lay, plus 5.40 per metre length. Calculate the cost of laying the pipe above. 13. The table below shows languages studied by pupils in a school French German Spanish TOTAL Boys Girls TOTAL How many girls are in the survey?. What is the probability that a pupil chosen at random from the survey is a boy? Give your answer as a fraction in its simplest form.. (c) What is the probability that a pupil chosen at random from the survey is a boy who studies German? Give your answer as a fraction in its simplest form In a running club, 1 4 of the members are women and 3 5 marathon runners. of these women are

9 What fraction of the club are female marathon runners? There are 52 members of the club How many of the members are NOT women? 15. The circle has centre O, radius 3cm and AB is a tangent of length 8cm. O 3cm C A 8cm B (i) Use Pythagoras theorem to find the length of OB (ii) Hence find the length of the line BC.....cm

10 16. A motorbike is bought for 2200 and its value decreases by 12% per year. How much is it worth one year after it is bought? How much is it worth two years after it is bought? The diagram shows a regular octagon a b Calculate the size of angle a. Calculate the size of angle b.

11 X 14.4cm 4.2cm 6cm Y The octagon has lengths as shown in the diagram. (c) Calculate the area of the octagon. 18. Evaluate the following, rounding your answers to 2 decimal places....cm 2 (5) !

12 (c) 4 3! " b a 72 o 63 o Find the size of angle a. Give a reason for your answer. Find the size of angle b. Give a reason for your answer. o o 20. xy! 6y = 9z 7 Make z the subject of the formula...

13 Make x the subject of the formula. 21. The table gives population and total land area for three countries. Population Land area (km 2 ) Austria 8.11 x x 10 4 Italy 5.77 x x 10 5 Romania 2.2 x x What is the difference in land area between Italy and Austria? Give your answer in standard form.. What is the population density of Romania? (i.e. the number of people per km 2 ). Give your answer as an ordinary number.. End of Questions (Total Marks: 100)

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