Dulwich College Specimen Paper B

IndependentBoys

19 questions

Original PDFWorked solutions in progress

Questions

1. 1
  $543 + 284$
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2. 2
  $543 - 284$
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3. 3
  $543 \times 6$
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4. 4
  $3258 \div 9$
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5. 5
  Arrange the following numbers from smallest to largest:
  
  $\dfrac{1}{3}, \rtqMathsListSeparator 0.305, \rtqMathsListSeparator 35\%, \rtqMathsListSeparator \dfrac{3}{10}$
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6. 6
  Fill in the missing numbers of these sequences:
  6.a
  $22, \rtqMathsListSeparator 29, \rtqMathsListSeparator 36, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator 50, \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
  6.b
  $3, \rtqMathsListSeparator 6, \rtqMathsListSeparator 12, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator 48, \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
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7. 7
  A multipack of $15$ packets of crisps costs $\rtqMathsSymbolPound 3.90$ .
  
  A packet of crisps costs $35 \rtqMathsUnit{pence}$ 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.
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8. 8
  The length of one statute mile is given as $1609.344 \rtqMathsUnit{metres}$ .
  8.a
  Circle which of the following describes the position of the $6$ in the number above.
  
  Units
  
  Tenths
  
  Hundredths
  
  Hundreds
  
  Thousands
  
  Tens
  
  8.b
  Round the number $1609.344$ to the nearest ten.
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9. 9
  9.a
  Circle which of the four options below shows a correct rotation of the word:
  QUESTION appears in upright capital letters. The word is shown in the source top-left option state: the whole word is half-turned except for the E glyph, which remains upright. The letters remain in forward source order and each individual glyph is half-turned. The whole word is reflected across a horizontal axis. The whole word is rotated through a half-turn.
  9.b
  Circle which of the four options below shows a correct reflection of the word:
  EXAMINATION appears in upright capital letters. The whole word is rotated through a half-turn. The whole word is reflected across a vertical axis. The whole word is reflected across a horizontal axis. The letters remain in forward source order and each individual glyph is reflected across a vertical axis.
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10. 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.
  The unshaded circle has five named sectors. Clockwise from the upward radius, they are USA, Europe, No holiday, Africa and Australia. USA is marked 45 degrees, Africa is marked 60 degrees, No holiday has an unlabelled angle arc, and Australia has a right-angle square. Europe and USA together occupy half of the circle.
  10.a
  Write down the angle of the wedge representing the number of school children who did not go on holiday.
  10.b
  Write down the fraction of the children who travelled to the USA, giving your answer in its simplest form.
  10.c
  A total of $180$ children were asked to complete the survey. Calculate how many of the children went on holiday to Africa.
  10.d
  Estimate how many children would have visited Europe out of the whole school of $1600$ pupils.
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11. 11
  On a long straight country road, there are four villages: Josham, Keston, Langham and Moreton, which are shown in the diagram below.
  
  Diagram not drawn to scale
  Josham, Keston, Langham and Moreton appear from left to right along a straight road. The spans show 12 kilometres from Josham to Keston, 26 kilometres from Josham to Langham, and 23 kilometres from Keston to Moreton.
  Distances between the villages are shown by the arrows.
  11.a
  Work out the distances from:
  11.a.i
  Keston to Langham;
  11.a.ii
  Langham to Moreton, giving your answer in metres.
  11.b
  If a tourist cycles at $14 \rtqMathsUnit{km per hour}$ , work out how long her journey would take from Josham to Moreton in hours and minutes.
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12. 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 $(3,0)$ .
  The positive coordinate grid runs from 0 to 8 horizontally and 0 to 6 vertically, with one-unit square spacing and arrowheads beyond the positive axes. A filled circular point A is at (5, 2). A dotted vertical mirror line passes through x equals 3 and extends slightly beyond the top and bottom of the grid. No other points are shown.
  12.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.
  12.b
  State the name of the type of triangle that has been formed.
  12.c
  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 $E$ .
  
  Draw the reflected image of the triangle across this mirror line and label the two new points $D$ and $E$ .
  12.d
  Write down the co-ordinates of these new points $D$ and $E$ :
  12.e
  One of these new points, $D$ or $E$ , can be joined up to point $A$ and to the origin to create an isosceles triangle.
  
  Write down which new point completes this triangle in the diagram and explain briefly what it means for a triangle to be isosceles.
  
  Point $\rtqMathsUnderlineEmptyValueShort$ will form an isosceles because an isosceles triangle $\rtqMathsUnderlineEmptyValueLong$
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13. 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.
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14. 14
  The table and bar chart below shows the number of cars sold by a car showroom each day for a week.
  
  Day Mon Tues Weds Thur Fri Sat Sun
  Number of cars sold $3$ $5$ $1$ $4$ $7$
  The horizontal categories are Monday through Sunday, and the vertical Number of Cars scale runs from 0 to 7 with one-unit grid lines. Hatched bars show Monday 3, Tuesday 5, Wednesday 2, Thursday 1 and Saturday 7. The Friday and Sunday bar positions are intentionally blank.
  14.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.
  14.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.
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15. 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.
  A double-outlined rectangular garden is 12 metres wide and 8 metres high. Its dotted lawn surrounds an unfilled L-shaped pond. The pond is marked 4 metres across the top, 5 metres down the left, 6 metres across the bottom and 2 metres on the short right-hand side.
  15.a
  Work out the area of the fish pond.
  15.b
  Work out the area of the lawn.
  15.c
  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 $1 \rtqMathsUnit{metre}$ .
  
  Work out how many paving slabs are needed to complete this path.
  15.d
  Louis hires a builder to lay the path. The builder charges $\rtqMathsSymbolPound 8$ per hour basic labour for the job, and then $\rtqMathsSymbolPound 1.50$ per slab he lays.
  
  If he takes $3 \dfrac{1}{2}$ hours to finish the job, work out his overall fee.
  15.e
  Louis then decides to plant a row of bushes around the inside of the stone path. Each bush is to be planted $25 \rtqMathsUnit{cm}$ from the edge of the path, and $50 \rtqMathsUnit{cm}$ from its neighbouring bushes. The diagram below displays how this might look near a corner of the garden.
  
  Calculate how many bushes are required to complete this in total.
  Three square paving slabs run across the top and three run down the left, sharing the corner slab. A double fence line follows their outer top and left edges. Four bushes run horizontally and four vertically inside the patterned lawn, sharing the corner bush. Bush centres are 25 centimetres from the paving edge and neighbouring bush centres are 50 centimetres apart.
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16. 16
  In five of his 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.
  16.a
  Write down the mode of Darshan's five scores.
  16.b
  Work out the range of marks that Darshan scores.
  16.c
  Calculate the mean average score that he achieved in these five tests.
  16.d
  After his French mark is announced, Darshan's average score from all six tests falls to $6.5$ marks. Calculate the mark he scored in his French test.
  16.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.
  16.f
  In the end of term tests, Darshan scores $15$ out of $20$ in his History.
  
  Work out what his percentage improvement is in this subject.
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17. 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.
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18. 18
  In $1$ tree, $2$ chimps can eat $3$ bananas in $4 \rtqMathsUnit{minutes}$ .
  18.a
  Work out how long it would take $2$ chimps to eat $6$ bananas.
  18.b
  Work out how many chimps would be required to eat $21$ bananas in $8 \rtqMathsUnit{minutes}$ . (You can assume that the tree has a large number of bananas available and that the chimps all have big appetites!)
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19. 19
  The sixteen shapes in the grid each contain a number with the following rules:
  
  The numbers in the circle 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.
  
  $1$ $3$
  $6$ $8$
  $6$
  $4$ $8$ $24$
  19.a
  Complete the missing numbers in the squares.
  19.b
  Complete the missing numbers in the circles and triangles.
  19.c
  Identify the pattern that links the other numbers to the hexagonal numbers in each row.
  
  Write one of the four arithmetic symbols ( $+, -, \times, \div$ ) 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.
  
  $\rtqMathsSpaceQuarterEm \rtqMathsUnderlineEmptyValueShort \rtqMathsSpaceQuarterEm$ $\rtqMathsSpaceQuarterEm \rtqMathsUnderlineEmptyValueShort \rtqMathsSpaceQuarterEm$ $=$
  19.d
  Complete the grid above by adding the appropriate number to the empty hexagon, using your formula.
  19.e
  If a fifth row is added below the four displayed, write down what number would be in the fifth hexagon.
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