The Haberdashers' Aske's Boys' School 2016 Paper 1

IndependentBoys

30 questions

Original PDFWorked solutions in progress

Questions

1. 1
  Add: $36 + 27$
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2. 2
  Subtract: $53 - 14$
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3. 3
  Multiply: $56 \times 8$
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4. 4
  Divide: $108 \div 4$
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5. 5
  Find the cost of downloading $5$ apps if each one costs $\rtqMathsSymbolPound 2.98$ .
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6. 6
  Work out the sum of: $9, 99, 999$ and $9999$ .
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7. 7
  Divide $3$ by $0.5$ .
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8. 8
  Shade $15\%$ of this shape
  
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9. 9
  There is an even chance that I will pick a toffee from a large bag of sweets containing toffees, jellies and chocolates.
  
  If the bag contains $17$ jellies and $8$ chocolates, how many toffees are there?
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10. 10
  The total attendance at Premier League football matches last season was $13{,}766{,}753$ .
  
  Round this number to the nearest ten thousand.
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11. 11
  Pens cost $7 \rtqMathsUnitCurrencyPence$ each and pencils cost $5 \rtqMathsUnitCurrencyPence$ each.
  
  I buy some pens and pencils which cost $55 \rtqMathsUnitCurrencyPence$ exactly.
  
  How many of each did I buy?
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12. 12
  Use the fact that $96{,}815 \times 123 = 11{,}908{,}245$ to work out $96{,}816 \times 123$ .
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13. 13
  Fill in the spaces with one of $+, - , \times, \div$ to make each statement correct.
  13.a
  $8 \rtqMathsSpaceQuarterEm \rtqMathsUnderlineEmptyValueShort \rtqMathsSpaceQuarterEm 2 = 5 \rtqMathsSpaceQuarterEm \rtqMathsUnderlineEmptyValueShort \rtqMathsSpaceQuarterEm 2$
  13.b
  $4 \rtqMathsSpaceQuarterEm \rtqMathsUnderlineEmptyValueShort \rtqMathsSpaceQuarterEm 3 = 60 \rtqMathsSpaceQuarterEm \rtqMathsUnderlineEmptyValueShort \rtqMathsSpaceQuarterEm 5$
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14. 14
  The three-digit number shown below can be divided by $3$ without a remainder.
  
  Fill in the box to show the largest possible value that the last digit could be.
  
  $\rtqMathsSizeEight{\rtqMathsBoxedValue{5}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedValue{3}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide}$
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15. 15
  At a busy railway station trains leave from platform $5$ every $6 \rtqMathsUnit{minutes}$ and from platform $8$ every $10 \rtqMathsUnit{minutes}$ . Trains leave from both platforms at $15 \rtqMathsTimeSeparator 57$ .
  
  When do trains next leave both platforms at the same time?
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16. 16
  The price of a one-day ticket to a theme park is $\rtqMathsSymbolPound 37.60$ .
  16.a
  Joe buys a ticket and experiences $8$ rides during the day.
  
  Work out the average cost per ride.
  16.b
  Rishi pays an additional $\rtqMathsSymbolPound 31$ for a special pass which gives front of line access to all rides throughout the day. He experiences $14$ rides.
  
  Does the special pass provide value for money? Give reasons for your answer.
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17. 17
  Draw lines to link each object to its correct height.
  
  Oak Tree $0.324 \rtqMathsUnit{km}$
  
  Eiffel Tower $1.41 \rtqMathsUnit{m}$
  
  Can of Soda $2390 \rtqMathsUnit{cm}$
  
  Car $122 \rtqMathsUnit{mm}$
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18. 18
  Mrs Catchpole gives the following instructions to her Year $6$ class:
  
  Think of a number.
  
  Subtract $13$ from this number to get the first result.
  
  Go back to the original number and subtract 5 to get the second result.
  
  Multiply the first and second results together to get the final answer.
  
  18.a
  Savan follows Mrs Catchpole's instructions starting with the number $23$ .
  
  Work out Savan's final answer.
  18.b
  Richard obtains a final answer of $0$ .
  
  What number might he have thought of? Give all possibilities.
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19. 19
  Write the words, square, rectangle, parallelogram, trapezium, kite and rhombus in the spaces below.
  
  19.a
  List all possible quadrilaterals from the list above which have the following properties:
  19.a.i
  Diagonals are of equal length.
  19.a.ii
  There is exactly one pair of parallel sides.
  19.a.iii
  Opposite angles are equal but are not right angles.
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20. 20
  A group of $48$ children are asked to choose their favourite subject from a list of three: English, Mathematics and Science.
  
  The results are displayed on a pie chart:
  
  20.a
  What fraction of the group chose English?
  20.b
  If $33 \dfrac{1}{3}\%$ chose Mathematics work out the angle of the Mathematics sector.
  20.c
  How many children chose Science?
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21. 21
  If it is a cold rainy day then I wear a raincoat. If it is a warm rainy day then I carry an umbrella. If I wear my raincoat then I also wear either gloves or a hat but not both. If I carry an umbrella I always wear gloves and sometimes wear my hat as well. I never carry an umbrella and wear my raincoat on the same day.
  
  For each of the following, state whether it is definitely true, false or uncertain.
  21.a
  It is a warm rainy day. I wear my raincoat and a hat.
  21.b
  It is a warm rainy day. I carry my umbrella and wear a hat but no gloves.
  21.c
  It is a cold rainy day. I wear my raincoat, hat and no gloves.
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22. 22
  A sunflower seed takes a week to germinate after it has been sown in the ground. After germination it grows the same number of centimetres each day.
  
  Maya sows a sunflower seed. She measures the height of the plant at midday on the $16 ^\text{th}$ August and again at midday on the $21 ^\text{st}$ August. These two measurements are recorded as $48 \rtqMathsUnit{cm}$ and $68 \rtqMathsUnit{cm}$ respectively.
  22.a
  Work out the height of the plant at midday on September $2 ^\text{nd}$ .
  22.b
  On what date did Maya sow the seed in the ground?
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23. 23
  The diagram shows a scale drawing of a rectangular school playground. The distance between consecutive marks shown on the diagram is $25 \rtqMathsUnit{metres}$ .
  
  23.a
  Work out the distance along the side $AB$ .
  23.b
  Work out the perimeter of the playground.
  23.c
  Ginny runs round and round the perimeter of the playground in a clockwise direction. She starts at the bottom left-hand corner labelled A on the diagram.
  
  Given that she runs a total distance of $1900 \rtqMathsUnit{m}$ , draw a cross on the diagram to show where she finishes her run.
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24. 24
  24.a
  Write down the time shown on this clock.
  
  24.b
  Alice looks at this clock in a mirror.
  
  Draw the hands on the clock face below to show the image that Alice sees.
  An empty circular clock face has longer ticks at 12, 3, 6 and 9 and shorter ticks at the other hours, ready for drawing mirror-image hands.
  24.c
  On another day Alice looks at the clock in the mirror and, without thinking, says that the time is $11 \rtqMathsTimeSeparator 30$ .
  
  What time is it really?
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25. 25
  Once upon a time, in the Ancient Wizarding World of Haberdasher's:
  
  One pound $= 20 \rtqMathsUnit{shillings}$
  
  One shilling $= 12 \rtqMathsUnit{pence}$
  
  A large Margarine-beer costs $1 \rtqMathsUnit{pound} \rtqMathsSpaceQuarterEm 4 \rtqMathsUnit{shillings}$ and $9 \rtqMathsUnit{pence}$ .
  
  A small Margarine-beer costs $14 \rtqMathsUnit{shillings}$ and $5 \rtqMathsUnit{pence}$ .
  25.a
  Work out the difference in price between a small and large beer.
  
  Give your answer in shillings and pence.
  25.b
  Work out the total cost of one large and two small beers.
  
  Give your answer in pounds, shillings and pence.
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26. 26
  An empty jug is filled with water at a constant rate. The graph shows how the height, $h$ , of the level of water varies over time, $t$ , as the jug fills up.
  A rising curve starts at the origin and gradually becomes less steep. The axes are labelled h vertically and t horizontally, with no numeric scale.
  For each of the following jugs draw the graph which shows how the height of water varies with time.
  26.a
  Blank arrowed axes labelled h and t are provided for drawing the first cup's filling graph.
  26.b
  Blank arrowed axes labelled h and t are provided for drawing the second cup's filling graph.
  26.c
  Blank arrowed axes labelled h and t are provided for drawing the third cup's filling graph.
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27. 27
  Helen works out the width of the base and the area of each of the following four shapes and then draws a corresponding blob showing these measurements on a graph.
  
  27.a
  Label four of the blobs on the graph with the letters $A, B, C$ and $D$ .
  27.b
  Draw a possible right-angled triangle, $E$ , which corresponds to the remaining blob on the graph.
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28. 28
  The diagram shows the one-way cycle paths in a park.
  
  Work out the total number of possible routes to go:
  
  28.a
  from $A$ to $C$
  28.b
  from $A$ to $D$
  28.c
  from $A$ to $E$
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29. 29
  A sequence of numbers which get multiplied (or divided) by a fixed amount each time is called a geometric progression ( $\text{GP}$ ). For example, the sequence
  
  $1^ \text{st}$ term $= 6$ , $2^ \text{nd}$ term $= 12$ , $3^ \text{rd}$ term $= 24$ , $4^ \text{th}$ term $= 48$
  
  is a $\text{GP}$ because you multiply by $2$ to go from one term to the next.
  29.a
  The $1^ \text{st}$ term of a $\text{GP}$ is $8$ and the $2^ \text{nd}$ term is $24$ .
  
  Work out the $3^ \text{rd}$ term.
  29.b
  The $1^ \text{st}$ term of a $\text{GP}$ is $20 \rtqMathsSpaceQuarterEm \text{million}$ and the $2^ \text{nd}$ term is $2 \rtqMathsSpaceQuarterEm \text{million}$ .
  
  Work out the $9^ \text{th}$ term.
  29.c
  The $1^ \text{st}$ term of a $\text{GP}$ is $8$ and the $3^ \text{rd}$ term is $200$ .
  
  Work out the $2^ \text{nd}$ term.
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30. 30
  Snow White and the seven dwarves work in a mining company.
  
  As Chief Executive, Snow White earns as much as all the dwarves put together. Sneezy gets $24$ gold galleons a day. Sleepy earns $50\%$ more than Happy. Bashful earns twice as much as Grumpy who earns one more galleon than Sneezy. Doc gets $24$ galleons a day more than Dopey and between them they get four times that of Sneezy. Sleepy earns seven-eighths of Sneezy's salary.
  
  Complete the table below to work out how much Snow White earns in a day.
  
  Gold Galleons
  Bashful
  Doc
  Dopey
  Grumpy
  Happy
  Sleepy
  Sneezy
  Snow White
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