Dulwich College Specimen Paper A

IndependentBoys

23 questions

Original PDFWorked solutions in progress

Questions

1. 1
  Calculate $546 + 287$ .
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2. 2
  Calculate $546 - 287$ .
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3. 3
  Calculate $546 \times 4$ .
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4. 4
  Calculate $2184 \div 7$ .
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5. 5
  Calculate how much bigger $3\dfrac{1}{4}$ is than $1\dfrac{3}{4}$ , writing your answer as a decimal.
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6. 6
  Fill in the missing numbers of these sequences:
  6.a
  $14, \rtqMathsListSeparator 17, \rtqMathsListSeparator 20, \rtqMathsListSeparator 23, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
  6.b
  $14, \rtqMathsListSeparator 13.25, \rtqMathsListSeparator 12.5, \rtqMathsListSeparator 11.75, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
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7. 7
  7.a
  Work out $\dfrac{1}{4}$ of $48$ .
  7.b
  Work out $\dfrac{1}{2}$ of $\dfrac{1}{3}$ of $\dfrac{1}{4}$ of $48$ .
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8. 8
  Draw the reflection of this triangle in the mirror line shown.
  An unnumbered equal-unit grid has 15 columns and 10 rows. It contains a right triangle below and to the left of a dashed diagonal mirror line. The triangle has vertices at grid positions (3, 0), (3, 6) and (6, 0). The mirror line crosses the top and bottom grid edges at (2, 10) and (12, 0), extends beyond both edges and is labelled Mirror line below the grid. Only the original triangle is shown.
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9. 9
  The pie chart below represents data collected in a survey by a PE teacher about the favourtie sports of a sample of school children.
  The unshaded circle has five named sectors. Clockwise from the upward radius, they are Tennis, Football, Cricket, Other and Rugby. The central angle is marked 45 degrees in Tennis, 60 degrees in Cricket and 30 degrees in Other. Rugby has a right-angle square at the centre. Football has no angle label.
  9.a
  Write down the fraction of the school children who liked tennis, giving your answer in its lowest form.
  9.b
  A total of $240$ children were asked to complete the survey. Calculate how many of the children preferred cricket.
  9.c
  Estimate how many children would say their favorite sport was football out of the whole school of $1200$ pupils.
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10. 10
  I buy $6$ bags of chocolate coins from a shop and count the number of coins in each bag. The quantities were as follows:
  
  $8, \rtqMathsListSeparator 7, \rtqMathsListSeparator 11, \rtqMathsListSeparator 6, \rtqMathsListSeparator 9, \rtqMathsListSeparator 7$
  10.a
  Write down the mode of the quantities.
  10.b
  Work out the mean (average) of the number of chocolate coins.
  10.c
  Work out the range of the quantities in the $6$ bags.
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11. 11
  A multipack of $12$ cans of Ned's Cola costs $\rtqMathsSymbolPound 6.95$ .
  
  A single can of Ned's Cola costs $65 \rtqMathsUnit{pence}$ if bought individually.
  
  Calculate how much cheaper it is to buy a multipack of $12$ cans than to buy $12$ cans individually, giving your answer in pence.
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12. 12
  Arrange the following fraction in numerical size order, starting with the smallest.
  
  $\dfrac{3}{10}, \rtqMathsListSeparator \dfrac{1}{5}, \rtqMathsListSeparator \dfrac{3}{2}, \rtqMathsListSeparator \dfrac{1}{20}, \rtqMathsListSeparator \dfrac{1}{4}$
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13. 13
  13.a
  An equilateral triangle is divided into smaller equilateral triangles as shown below. State how many angles of $60\degree$ there are in the diagram.
  An upright equilateral triangle has a horizontal base. Two internal lines parallel to the base and diagonal lines in both directions form three rows of smaller equilateral triangles. The interiors are unshaded.
  13.b
  The diagram is now squashed to make the top angle $90\degree$ , turning all the triangles into right-angled isosceles triangles.
  
  Calculate how many acute angles there are in the diagram now.
  A wide triangle has a horizontal base, equal sloping sides and a right-angle marker at its top vertex. Two internal lines parallel to the base and sloping lines divide it into three rows of smaller right-angled isosceles triangles. The interiors are unshaded.
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14. 14
  On the axes below, point $A$ has coordinates $(3,1)$ .
  The horizontal axis is labelled from minus 5 to 5 and the vertical axis from 1 to 8, with one-unit square grid spacing and arrowheads on the positive axes. A filled circular point A is at (3, 1), and a filled circular point C is at (-3, 4). No other points or construction lines are shown.
  14.a
  Write down the coordinates of point $C$ .
  14.b
  Plot the points with coordinates $(5,4)$ onto the axes and label it $B$ .
  14.c
  Plot another point $D$ , and then join $ABCD$ in that order so that you can form a quadrilateral shape with one line of symmetry.
  14.d
  Write down the common name for the quadrilateral $ABCD$ .
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15. 15
  Each shape in this grid is hiding a particular number so that the three shapes in any row or column add up to the value written at the end of that row or column.
  
  $16$
  $12$
  $18$
  $15$ $14$ $\rtqMathsQuestionMarkPlaceholder$ $+$
  
  Work out the number that should replace the question mark.
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16. 16
  Rhys and Sarah are on their bicycles and start $90 \rtqMathsUnit{miles}$ apart on a road, riding towards each other. Rhys is travelling at $10 \rtqMathsUnit{mph}$ and Sarah is travelling at $20 \rtqMathsUnit{mph}$ . They set off at the same time and both keep moving at constant speeds until they meet.
  16.a
  Work out at what distance each rider has cycled by the time they meet.
  16.b
  Write down the time taken for them to meet.
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17. 17
  17.a
  Find the area of rectangle shown below.
  The lower side of the rectangle is labelled 60 mm and the right side is labelled 20 mm.
  17.b
  George cuts the rectangle up into an exact number of right-angled triangles, each with sides as shown in the diagram below.
  The horizontal lower side is labelled 12 mm and the left vertical side 5 mm. They meet at the marked lower-left right angle. The sloping side is labelled 13 mm.
  Calculate the number of triangles that he cuts from the rectangle.
  17.c
  Find the combined perimeter of all triangles that have been cut from the rectangle.
  17.d
  Convert this distance from millimetres into metres.
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18. 18
  On the island of Pythageuleria all vehicle number plates have $2$ letters from the selection $\text {A, B, C, D}$ followed by a number $1, 2, 3$ or $4$ .
  
  For example:
  
  $\rtqMathsSizeSeven{ \rtqMathsBoxedValue{ \text {A D 1} }} \rtqMathsSpaceOneEm \rtqMathsSizeSeven{ \rtqMathsBoxedValue{ \text {A D 4} }} \rtqMathsSpaceOneEm \rtqMathsSizeSeven{ \rtqMathsBoxedValue{ \text {C A 3} }} \rtqMathsSpaceOneEm \rtqMathsSizeSeven{ \rtqMathsBoxedValue{ \text {D D 2} }}$
  
  Note that repeated letters are allowed.
  18.a
  Calculate how many plates start with a double $\text{B}$ .
  18.b
  Calculate how many plates there are that start with any repeated letter.
  18.c
  Calculate how many plates contain just one vowel and an odd number.
  18.d
  Given that there are $64$ possible codes in total, calculate what fraction of the number plates have their own two letters in alphabetical order, giving your answer in its lowest form.
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19. 19
  A new design for a novelty watch gives the time in $24\text{-hour}$ clock format by showing a particular combination of lights below a set of numbers. The lit-up numbers are added together to find the actual time, with the first row showing the hour and the second row displaying the minutes.
  
  For example, the display below represents the time $05 \rtqMathsTimeSeparator 26$ since:
  
  $32$ $16$ $8$ $4$ $2$ $1$
  Hr
  Mn
  
  $\begin{aligned} \text{Hr} &= 4 + 1 \\\\ &= 5 \\\\ \text{Mn} &= 16 + 8 + 2 \\\\ &= 26 \end{aligned}$
  19.a
  Write down the time (in $24\text{-hour}$ format) represented by the display:
  
  $32$ $16$ $8$ $4$ $2$ $1$
  Hr
  Mn
  19.b
  Mark the grid below to show the time “a quarter to ten in the evening”.
  
  $32$ $16$ $8$ $4$ $2$ $1$
  Hr
  Mn
  19.c
  Calculate how long it is between the times displayed on watch A and watch B below:
  
  Watch A
  
  $32$ $16$ $8$ $4$ $2$ $1$
  Hr
  Mn
  
  Watch B
  
  $32$ $16$ $8$ $4$ $2$ $1$
  Hr
  Mn
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20. 20
  In four years time, Sam will be twice as old as he was four years ago. Calculate Sam's current age.
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21. 21
  A packet containing seeds says it produces white, pink and blue flowers in such a proportion that, on average, for every one white flower grown there will be two pink and three blue flowers.
  21.a
  I plant some seeds and get three white flowers. Write down how many blue flowers I should expect to grow.
  21.b
  I plant a total of $30$ seeds in another patch of the garden. Calculate how many white flowers I would expect to grow in this patch.
  21.c
  In another area of the garden, $24$ blue flowers are grown. Calculate how many pink flowers I should expect to find here.
  21.d
  A packet of different types of seed produces red, orange or yellow flowers. Some students in a biology class plant $150$ seeds. All $150$ grow to produce flowers and the students draw up the results of the flower colours into a table and a bar chart as below.
  
  Complete the table and bar chart for the students' findings.
  
  Flower Colour Red Orange Yellow
  Number of flowers $72$
  The categories are Red, Orange and Yellow. The vertical Number of Flowers scale runs from 0 to 80. Only the supplied Red bar is present and reaches 20; Orange and Yellow are intentionally blank.
  21.e
  If I pick a flower at random from the $150$ grown in the test, list the following possible outcomes in order of likelihood, starting with the least likely:
  
  picking a red or orange flower
  
  picking a purple flower
  
  picking an orange or yellow flower
  
  picking a yellow flower
  
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22. 22
  22.a
  Shade in one more section on the grid below so that the overall shape has a single line of symmetry, marking your mirror line on the diagram.
  Three concentric circles are crossed by three diameters, forming six equal-angle sectors in each of three radial bands. One diameter is horizontal. The upper-left section of the outer band, lower-left section of the middle band and upper-right section of the inner disk are shaded. All other sections are unshaded.
  22.b
  Now shade two sections in this second grid so that the overall shape has an order of rotational symmetry of two.
  Three concentric circles are crossed by three diameters, forming six equal-angle sectors in each of three radial bands. One diameter is horizontal. The upper-left section of the outer band, lower-left section of the middle band, and top and bottom sections of the inner disk are shaded. All other sections are unshaded.
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23. 23
  The diagram below is made from three squares.
  
  Calculate the fraction of the larger square that is shaded, giving your answer in its lowest form.
  The middle square is turned through 45 degrees, with its vertices at the midpoints of the outer square's sides. The inner square is aligned with the outer square, with its vertices at the midpoints of the middle square's sides. The regions inside the middle square and outside the inner square are shaded.
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