Sevenoaks School 2020 Paper 1

IndependentCo-ed

20 questions

Original PDFWorked solutions in progress

Questions

1. 1
  Mark’s reading group has read a total of $112$ books so far. The group has $7$ members including Mark.
  1.a
  Each member has read the same number of books. How many books has each member read?
  1.b
  On average each member reads $150$ pages during each group meeting. What are the total number of pages read by the group during each meeting?
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2. 2
  2.a
  Jill subtracts $18$ from $33$ and divides this by $5$ . What is the number Jill obtains?
  2.b
  Calculate:
  
  $3^2 \times (9 - 4) \div 3$
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3. 3
  Here is some flour on a weighing scale.
  A mound of flour rests on the tray of a kitchen scale. The linear display runs from 0 to 3 kilograms in tenths, and its pointer indicates 0.4 kilograms.
  3.a
  How many grams of flour are on the weighing scale?
  3.b
  How much more flour must be added to the scale to make $1.7 \rtqMathsUnit{kg}$ ?
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4. 4
  In each of the shapes below, make a pattern by shading with exactly
  4.a
  two lines of symmetry.
  Nine equal square cells are provided for making a pattern with two lines of symmetry.
  4.b
  three lines of symmetry.
  An unshaded equilateral triangular lattice has three equal subdivisions along each outside edge, forming nine equal small triangles for the requested symmetric pattern.
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5. 5
  5.a
  Round $6.275$ to $2$ decimal places.
  5.b
  Round $208{,} 567$ to the nearest $100$ .
  5.c
  Round $0.2499$ to $3$ decimal places.
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6. 6
  The total cost of Helen’s pencil case including stationery is $\rtqMathsSymbolPound 6.25$ .
  6.a
  How much would $12$ of these pencil cases cost?
  6.b
  The ruler costs $75 \rtqMathsUnitCurrencyPence$ . What percentage of the total cost of the pencil case is the ruler?
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7. 7
  What is the smallest number which is both a multiple of $12$ and $15$ ?
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8. 8
  Evaluate the following fractions giving your answer in its simplest form.
  
  Show clearly your working.
  8.a
  $\dfrac{2}{3} + \dfrac{4}{5}$
  8.b
  $3 \dfrac{2}{5} - 1 \dfrac{1}{2}$
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9. 9
  Calculate the angles in the diagrams below.
  9.a
  Three rays meet at one point. The angle between the two upper rays is labelled a, the angle on the right is 88 degrees, and the reflex angle around the left and lower side is 192 degrees.
  9.b
  The top-left angle is 51 degrees, the bottom-right angle is 37 degrees, and the bottom-left angle is labelled b.
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10. 10
  Below are the ingredients needed to make $16$ gingerbread men. Sam wants to make $24$ gingerbread men.
  
  Work out how much of each ingredient he needs.
  
  Ingredients
  to make $16$ gingerbread men
  $180 \rtqMathsUnit{g}$ flour
  $40 \rtqMathsUnit{g}$ ginger
  $110 \rtqMathsUnit{g}$ butter
  $30 \rtqMathsUnit{g}$ sugar
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11. 11
  Calculate $x$ in the following equations.
  11.a
  $17 - x = 3$
  11.b
  $3x = 72$
  11.c
  $\dfrac{5x}{4} = \dfrac{1}{2}$
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12. 12
  What goes in the boxes to complete the calculations below?
  12.a
  $\dfrac{2}{5} \times \rtqMathsBoxedEmptyValueFraction = \dfrac{1}{3}$
  12.b
  $\rtqMathsBoxedEmptyValueFraction \div 1 \dfrac{1}{3} = \dfrac{3}{5}$
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13. 13
  Calculate the area of this compound shape.
  The compound shape is 10 cm wide. Its rectangular part is 2¼ cm high and its triangular top is 1¼ cm high.
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14. 14
  Fill in the missing numbers of the following sequences:
  14.a
  $3, \rtqMathsListSeparator 5, \rtqMathsListSeparator 7, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator 13, \rtqMathsListSeparator 15$
  14.b
  ${-}33, \rtqMathsListSeparator {-}6, \rtqMathsListSeparator 21, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator 102, \rtqMathsListSeparator 129$
  14.c
  $10, \rtqMathsListSeparator 11, \rtqMathsListSeparator 15, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator 65, \rtqMathsListSeparator 101$
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15. 15
  Below is a coordinate grid including a point $A$ labelled below.
  The square coordinate grid has dashed one-unit grid lines and x- and y-axes labelled from negative 5 to positive 5. The axes have small integer tick marks and arrowheads at their positive ends. Filled circular point A is at (-1, 2).
  15.a
  Give the coordinates of the point $A$ .
  15.b
  Mark the coordinate $({-}4, 3)$ and label this point $B$ .
  15.c
  The point $C$ is obtained by reflecting the point $A$ in the x-axis followed by a reflection in the y-axis.
  
  Give the coordinates of the point $C$ .
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16. 16
  One clock gains $5 \rtqMathsUnit{minutes}$ every hour and another clock loses $10 \rtqMathsUnit{minutes}$ every hour.
  
  After one week how many hours will the slow clock have lost to the fast clock?
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17. 17
  17.a
  The volume of the cuboid below is $64 \rtqMathsUnit{cm}^3$ . Calculate the value of the unknown length, $x$ .
  A projected cuboid has a front vertical edge labelled 2 cm, its front lower edge labelled 4 cm and its lower-right receding edge labelled x cm. Three hidden edges are dashed.
  17.b
  A cube has the same volume as the cuboid above. Calculate the surface area of the cube.
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18. 18
  The diagram shows a design formed by drawing six lines in a regular hexagon. The lines divide each edge of the hexagon into three equal parts.
  
  What fraction of the hexagon is shaded?
  
  You must show relevant working to obtain marks.
  Six chords join points one third and two thirds of the way along the hexagon edges. Two horizontal, two rising and two falling chords intersect to form a shaded six-pointed star at the centre.
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19. 19
  The standard Fibonacci sequence $1, 1, 2, 3, 5, 8, 13, \rtqMathsSequenceEllipsis$ begins with two $1$ s and each later number in the sequence is the sum of the previous two numbers.
  
  Other Fibonacci-like sequences can be constructed by starting with any two numbers $a$ and $b$ (not necessarily $1$ and $1$ ) and using the same rule for creating the other numbers in the sequence.
  
  What is the first term of the Fibonacci-like sequence whose second term is $4$ and whose fifth term is $22$ ?
  
  You must show relevant working to obtain marks.
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20. 20
  A rectangle is made by placing together three smaller rectangles $P, Q$ and $R$ , without gaps or overlaps. Rectangle $P$ measures $3 \rtqMathsUnit{cm} \times 8 \rtqMathsUnit{cm}$ and rectangle $Q$ measures $2 \rtqMathsUnit{cm} \times 5 \rtqMathsUnit{cm}$ .
  
  Give all the possible measurements of $R$ .
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