Dulwich College 11 Plus Maths Specimen Paper – B by smoothmaths | Jun 22, 2020 | 0 comments Welcome to your Dulwich College 11 Plus Maths Specimen Paper - B TIME allowed for this paper: 60 minutesInstructions Attempt all the questions. Do all your written work on this paper, showing all your working. Calculators must not be used. The numbers in square brackets are the marks available for each part of a question. You must not write in the squares at the bottom right of each page. There are 100 marks in total. 1. 543 + 284 827727627927525 2. 543 - 284259269359369341 3. 543 × 632583248305830483260 4. 3258 ÷ 9362462262358412 5. Arrange the following numbers from smallest to largest:\[\frac{3}{10}\] , 0.305, \[\frac{1}{3}\] , 0.3500.305 , \[\frac{3}{10}\] , \[\frac{1}{3}\] , 0.350\[\frac{1}{3}\] , \[\frac{3}{10}\] , 0.305, 0.350\[\frac{3}{10}\] , \[\frac{1}{3}\] , 0.305 , 0.3500.350 , \[\frac{1}{3}\] , 0.305, \[\frac{3}{10}\] 6. Fill in the missing numbers of these sequence:(a) 22 , 29 , 36 , , 50 , (b) 3 , 6 , 12 , , 48 ,43,5743,5541,5942,5640,54 7. A multipack of 15 packets of crisps costs £3.90. A packet of crisps costs 35 pence if they are bought individually. Calculate how much cheaper it is to buy a multipack of 15 packets of crisps than to buy 15 packets individually.24,9624,6018,5220,8034,96 8. The length of one statute mile is given as 1609.344 metres.(a) Circle which of the following describes the position of the 6 in the number above.£ 1.35£ 0.85£ 2.35£ 0.35£ 1.15 (b) Round the number 1609.344 to the nearest ten.hundredsunitsthousandstenthshundreths 9. (a) Circle which of the four options below shows a correct rotation of the word:16101609169116011608 (b) Circle which of the four options below show a correct reflection of the word: 10. The pie chart below represents data collected in a survey of the summer holiday destinations of a sample of school children. Half of the children went to Europe or the USA.(a) Write down the angle of the wedge representing the number of school children who did not go on holiday.30601304515 (b) Write down the fraction of the children who travelled to the USA, giving your answer in its simplest form.\[\frac{1}{8}\]\[\frac{1}{4}\]\[\frac{1}{3}\]\[\frac{2}{5}\]\[\frac{1}{7}\] (c) A total of 180 children were asked to complete the survey. Calculate how many of the children went on holiday to Africa.3040506020 (d) Estimate how many children would have visited Europe out of the whole school of 1600 pupils.600300400500700 11. On a long straight country road, there are four villages: Josham, Keston, Langham and Moreton, which are shown in the diagram below.Distances between the villages are shown by the arrows.(a) Work out the distance from: (i) Keston to Langham; 14km11km16km20km24km (ii) Langham to Moreton, giving your answer in metres.9000m7000m8000m6000m5000m (b) If a tourist cycles at 14 km per hour, work out how long her journey would take from Josham to Moreton in hours and minutes.2h 30min3h 20min2h 10min4h 30min3h 40min 12. A, B and C are three points on a grid. A is at (5, 2), B is at (4, 5) and C is at (3, 0).(a) Plot and label the other two points, B and C, and then join the three points and lightly shade the triangle you have formed. (b) State the name of the type of triangle that has been formed.ScaleneIsocelesEquilateralRight anglenone of the above A mirror line is marked as the dotted line at x = 3. The triangle can be reflected in this mirror line so that point A ends up at a new point D and point B ends up at a new point E. (c) Draw the reflected image of the triangle across this mirror line and label the two new points D and E. (d) Write down the co-ordinates of these new point D and E: Answer: D is at ( , 2) and E is at ( , )D=(1,2),E=(2,5)D=(1,1),E=(2,5)D=(1,2),E=(5,2)D=(2,2),E=(2,5)D=(1,3),E=(2,5) One of these new points, D or E, can be joined up to point A and to the origin to create an isosceles triangle.(e) Write down which new point completes this triangle in the diagram and explain briefly what it means for a triangle to be isosceles.Point will form an isosceles because an isosceles triangleE,because isoceles have 2 sides equalD,because isoceles have 3 sides equalB,because isoceles have 2 unequal sidesA,because isoceles have 2 sides equalnone of the above 13. A prime number has exactly 2 factors: itself and 1. The numbers from 1 to 20 inclusive are written on 20 cards. Write down the proportion of all the cards that have a prime number written on them, giving your answer as a decimal.0.40.30.50.20.1 14. The table and bar chart below shows the number of cars sold by a car showroom each day for a week. (a) Use the information in the table and the bar chart to complete the entry for Wednesday in the table and the bar for Friday on the chart. (b) The total number of cars sold in the week was 28. Use this information to help complete both the table and the bar chart with Sunday's entry. 15. The diagram shows a plan of the rectangular garden of local celebrity Louis Cowell-Cole, with an L-shaped fish pond in the middle. The dimensions of the garden and the pond are shown below. Diagram not drawn to scale.(a) Work out the area of the fish pond. Answer: m²24\[m^{2}\]50\[m^{2}\]96\[m^{2}\]42\[m^{2}\]38\[m^{2}\] (b) Work out the area of the lawn. Answer: m²72\[m^{2}\]62\[m^{2}\]96\[m^{2}\]24\[m^{2}\]82\[m^{2}\] Louis wants to put a stone path around the edge of the garden, just inside the existing perimeter fence. Each paving slab is a square with sides 1 metre.(c) Work out how many paving slabs are needed to complete this path. Answer:3640461620 15. continued: Louis hires a builder to lay the path. The builder charges £8 per hour basic labour for the job, and then £1.50 per slab he lays.(d) If he takes 3½ hours to finish the job, work out his overall fee.£ 82£ 72£ 79£ 75£ 85 Louis then decides to plant a row of bushes around the inside of the stone path.Each bush is to be planted 25 cm from the edge of the path, and 50 cm from itsneighbouring bushes. The diagram below display how this might look near a corner of the garden.(e) Calculate how many bushes are required to complete this in total.6028503080 16. In five of this mid-term tests, each out of 10 marks, Darshan scores 9 in Mathematics, 6 in English, 8 in Geography, 4 in History and 8 in Science.(a) Write down the mode of Darshan's five scores. Answer: marks864910 (b) Work out the range of marks that Darshan scores. Answer: marks51342 (c) Calculate the mean average score that he achieved in these five tests. Answer: marks76548 (d) After his French mark is announced, Darshan's average score from all six tests falls to 6.5 marks. Calculate the mark he score in his French test. Answer: marks41568 (e) The pass mark for each test is 50%. Write down what fraction of Darshan's six tests(including his French) he managed to pass, leaving your answer in its simplest form. Answer: marks\[\frac{2}{3}\]\[\frac{1}{3}\]\[\frac{1}{5}\]\[\frac{2}{7}\]\[\frac{1}{6}\] 16. continued: In the end of term tests, Darshan scores 15 out of 20 in his History.(f) Work out what his percentage improvement is in this subject. Answer:35%75%40%25%15% 17. Work out what time it is now if the time that has passed since nine o'clock this morning is five times as much as the time that is left before eleven o'clock this morning. Answer: :10:4010:2010:009:4011:15 18. In 1 tree, 2 chimps can eat 3 bananas in 4 minutes.(a) Work out how long it would take 2 chimps to eat 6 bananas. Answer: minutes8mins4mins12mins16mins6mins (b) Work out how many chimps would be required to eat 21 bananas in 8 minutes.(You can assume that the tree has a large number of bananas available and that the chimps all have big appetites!) Answer:798610 19. The sixteen shapes in the grid each contain a number with the following rules: The numbers in the circles are four more than the numbers in the squares on the same row. The numbers in the triangles are double those of the numbers in the squares on the same row. (a) Complete the missing numbers in the square. (b) Complete the missing numbers in the circles and triangles. (c) Identify the pattern that links the other numbers to the hexagonal numbers in each row. Write one of the four arithmetic symbols (+ , - , × , ÷) in each of the two gaps either side of the circle, to complete the following formula linking all the numbers in any row of shapes.Answer: (d) Complete the grid above by adding the appropriate number to the empty hexagon, using your formula. (e) If a fifth row is added below the four displayed, write down what number would be in the fifth hexagon. Time is Up!