Alleyn's School Paper 1

IndependentCo-ed

26 questions

Original PDFWorked solutions in progress

Questions

1. 1
  How many minutes are there in three and a half hours?
  
  $4$
  
  $60$
  
  $210$
  
  $180.5$
  
  $3600$
  
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2. 2
  Which of these fractions is equal to $0.8$ ?
  
  $\dfrac{1}{8}$
  
  $\dfrac{4}{5}$
  
  $\dfrac{8}{100}$
  
  $\dfrac{0.8}{10}$
  
  $\dfrac{2}{5}$
  
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3. 3
  Which of these is the smallest?
  
  $0.0801$
  
  $0.08$
  
  $0.081$
  
  $0.08001$
  
  $0.0888$
  
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4. 4
  The most likely length of a television remote control is:
  
  $0.17 \rtqMathsUnit{cm}$
  
  $1.7 \rtqMathsUnit{cm}$
  
  $17 \rtqMathsUnit{cm}$
  
  $170 \rtqMathsUnit{cm}$
  
  $1700 \rtqMathsUnit{cm}$
  
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5. 5
  $12 - 2 \times 4 + 3 =$
  
  $7$
  
  $-2$
  
  $43$
  
  $70$
  
  $1$
  
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6. 6
  One of the angles in an isosceles triangle is $30 \degree$ . Which of these is a possible other angle in the triangle:
  
  $90 \degree$
  
  $80 \degree$
  
  $150 \degree$
  
  $60 \degree$
  
  $75 \degree$
  
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7. 7
  One quarter of the pupils in a class are girls. The rest are boys. What is the ratio of girls to boys?
  
  $1 \rtqMathsRatioSeparator 1$
  
  $1 \rtqMathsRatioSeparator 2$
  
  $1 \rtqMathsRatioSeparator 3$
  
  $1 \rtqMathsRatioSeparator 4$
  
  $1 \rtqMathsRatioSeparator 5$
  
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8. 8
  How long is it, in hours and minutes, between $09 \rtqMathsTimeSeparator 34$ and $13 \rtqMathsTimeSeparator 21$ ?
  
  $4 \rtqMathsUnit{hrs} \rtqMathsSpaceQuarterEm 57 \rtqMathsUnit{mins}$
  
  $3 \rtqMathsUnit{hrs} \rtqMathsSpaceQuarterEm 47 \rtqMathsUnit{mins}$
  
  $4 \rtqMathsUnit{hrs} \rtqMathsSpaceQuarterEm 37 \rtqMathsUnit{mins}$
  
  $22 \rtqMathsUnit{hrs} \rtqMathsSpaceQuarterEm 55 \rtqMathsUnit{mins}$
  
  $4 \rtqMathsUnit{hrs} \rtqMathsSpaceQuarterEm 13 \rtqMathsUnit{mins}$
  
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9. 9
  What is the value of the digit $9$ in the number $32.597$ ?
  
  nine hundred
  
  nine
  
  nine tenths
  
  nine hundredths
  
  nine thousandths
  
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10. 10
  I buy a pen and a pencil for $\rtqMathsSymbolPound 1.10$ . The pen costs $50 \rtqMathsUnitCurrencyPence$ more than the pencil. How much is the pen?
  
  $50 \rtqMathsUnitCurrencyPence$
  
  $60 \rtqMathsUnitCurrencyPence$
  
  $70 \rtqMathsUnitCurrencyPence$
  
  $80 \rtqMathsUnitCurrencyPence$
  
  $90 \rtqMathsUnitCurrencyPence$
  
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11. 11
  Show your working when answering these questions.
  11.a
  $454 + 297 =$
  11.b
  $604 - 447 =$
  11.c
  $32 \times 74 =$
  11.d
  $4184 \div 8 =$
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12. 12
  12.a
  $\dfrac{5}{9} + \dfrac{2}{9} =$
  12.b
  $\dfrac{3}{4} + \dfrac{1}{8} =$
  12.c
  $\dfrac{5}{6} - \dfrac{1}{2} =$
  12.d
  $7 - \dfrac{3}{7} =$
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13. 13
  Write down the next two numbers in these sequences:
  13.a
  $7, \rtqMathsListSeparator 10, \rtqMathsListSeparator 13, \rtqMathsListSeparator 16, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
  13.b
  $53, \rtqMathsListSeparator 49, \rtqMathsListSeparator 45, \rtqMathsListSeparator 41, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
  13.c
  $6, \rtqMathsListSeparator 10, \rtqMathsListSeparator 15, \rtqMathsListSeparator 21, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
  13.d
  $60, \rtqMathsListSeparator 58, \rtqMathsListSeparator 63, \rtqMathsListSeparator 61, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
  13.e
  $0.5, \rtqMathsListSeparator 2, \rtqMathsListSeparator 8, \rtqMathsListSeparator 32, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
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14. 14
  Put the following in order, starting with the smallest:
  
  $3.55, \rtqMathsListSeparator 53.5, \rtqMathsListSeparator 35.5, \rtqMathsListSeparator 5.35, \rtqMathsListSeparator 55.3, \rtqMathsListSeparator 5.53$
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15. 15
  Draw any lines of symmetry on these shapes. Some may have none or more than one.
  15.a
  An unfilled outer circle surrounds an unfilled inner circular boundary. A narrow diagonal band runs from upper left to lower right, interrupting the inner boundary at both ends. No line of symmetry has been added.
  15.b
  A wide rounded speech bubble has a pointed tail extending down and left from its lower-left boundary. The bubble is empty and no line of symmetry has been added.
  15.c
  One unfilled concave outline forms a vertical arrow pointing upward joined through a right-angle bend to a horizontal arrow pointing left. No line of symmetry has been added.
  15.d
  A wide unfilled parallelogram has horizontal top and bottom edges and two matching sides sloping up and to the right. No line of symmetry has been added.
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16. 16
  The coordinate grid runs from minus 6 to 6 horizontally and minus 4 to 4 vertically, with one-unit square spacing and axes crossing at the origin. Triangle A has vertices at (1, 2), (3, 1) and (4, 3). Only the original triangle A is shown.
  16.a
  Reflect shape $A$ in the x-axis and label the new shape $B$ .
  16.b
  Reflect shape $B$ in the y-axis and label the new shape $C$ .
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17. 17
  Steve counts the number of goals he scores in six $5$ -a-side football games. The counts were:
  
  $3, \rtqMathsListSeparator 4, \rtqMathsListSeparator 2, \rtqMathsListSeparator 0, \rtqMathsListSeparator 1, \rtqMathsListSeparator 8$
  17.a
  What was the mean score for the games he counted?
  17.b
  What was the range?
  17.c
  In the next game he scored enough goals to increase his mean to $4$ . How many goals did he score in the seventh game?
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18. 18
  18.a
  On a train there are $140$ men and $200$ women. What is the ratio of men to women written in its simplest form?
  18.b
  I am making a scale model of The Eye-Full Tower, which is $120 \rtqMathsUnit{m}$ tall. If the scale is $1 \rtqMathsRatioSeparator 50$ , how long will the model be (in cm)?
  18.c
  My friend Sanjay is making a scale model of the London Ear (a famous landmark in London). The London Ear is $80 \rtqMathsUnit{m}$ tall and his model is $150 \rtqMathsUnit{cm}$ tall. What is the scale of the model, in its simplest form?
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19. 19
  19.a
  My other friend Minka was doing some gardening when she snapped a bamboo cane. The cane was $2.05 \rtqMathsUnit{m}$ long and is now $156 \rtqMathsUnit{cm}$ long. What length of cane snapped off?
  19.b
  In her garden, Ying-Ge is sowing some grass seed. The garden has an area of $158 \rtqMathsUnit{m}^2$ and each packet has enough seed for $12 \rtqMathsUnit{m}^2$ . How many packets does Ying-Ge need to buy?
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20. 20
  Farmer Giles has two legs and each of his cows have four legs. In the picture below, there are six legs in total.
  A colour illustration shows Farmer Giles with two legs beside a cow with four legs, making six legs altogether.
  Fill in the table below for the total number of legs if Farmer Giles is always present, but the number of cows increases.
  
  Number of Cows $1$ $2$ $3$ $4$ $10$ $100$
  Total Number of Legs $6$ $14$
  20.a
  Hillary is trying to find a formula that links the Number of Cows, $C$ , to the number of Legs, $L$ .
  
  Fill in the gaps to help her.
  
  $L = \rtqMathsUnderlineEmptyValueShort \times C + \rtqMathsUnderlineEmptyValueShort$
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21. 21
  On my wall I want to put some stickers of my favourite pop star Singing Steve. The space I have available is $55 \rtqMathsUnit{cm}$ by $60 \rtqMathsUnit{cm}$ and the stickers are each $15 \rtqMathsUnit{cm}$ by $5 \rtqMathsUnit{cm}$ . What is the maximum number of stickers I can fit on the wall?
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22. 22
  Two runners are having a race. Gary starts running from the start line at $10 \rtqMathsUnit{m/s}$ . Two seconds later Andy starts running from the start line at $12 \rtqMathsUnit{m/s}$ .
  22.a
  How long after Gary starts running does Andy catch up with him?
  22.b
  How far are they both from the start line when Andy catches up with Gary?
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23. 23
  These pictures show parts of a scale with equal gaps between each marking. What number should replace each letter?
  23.a
  A horizontal number line has three equally spaced upward ticks. The left tick is labelled 0.2, the middle tick A and the right tick 1.2.
  23.b
  A horizontal number line has three equally spaced upward ticks. The left tick is labelled 0.7, the middle tick B and the right tick 1.8.
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24. 24
  The coordinate grid runs from minus 6 to 6 horizontally and minus 4 to 4 vertically, with one-unit square spacing and axes crossing at the origin. A filled circular point A is at (4, 1). No other points or joining lines are shown.
  The point $A (4,1)$ has been marked.
  24.a
  Mark the point $B$ with co-ordinates $(0,4)$ .
  24.b
  Mark the point $C$ with co-ordinates $(-3,0)$ .
  24.c
  The point $D$ forms a square “ $ABCD$ ”. Write down the coordinates of point $D$ .
  24.d
  What is the area of the square $ABCD$ ?
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25. 25
  This graph shows the progress of two cars in a race from Leeds to Blackpool and back again. Car $A$ is the bold line. Car $B$ is the dotted line.
  The horizontal axis shows time from 2 pm to 7 pm in quarter-hour grid intervals. The vertical axis shows distance from Leeds from 0 to 120 kilometres, labelled every 10 kilometres with lighter grid lines every 2 kilometres. Car A is a solid piecewise line and Car B is dotted. Both start at Leeds at 2 pm, travel outward with stops and turnarounds shown by the line segments, then return to Leeds at different times.
  25.a
  How far is it from Leeds to Blackpool?
  25.b
  Which car was winning at $3.30 \rtqMathsTimePm$ ?
  25.c
  Which car was winning at $4.15 \rtqMathsTimePm$ ?
  25.d
  What was the distance between the cars at $4.45 \rtqMathsTimePm$ ?
  25.e
  What happened just after $6 \rtqMathsTimePm$ ?
  25.f
  Which car achieved the highest speed, and between which times did this happen?
  25.g
  Which car won the race?
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26. 26
  26.a
  Can you find numbers to replace $A, B$ and $C$ in this sum?
  
  ( $A, B$ and $C$ are all different numbers)
  
  $\rtqMathsColumnarArithmeticStyle \begin{array}{ccccccc} & A & B & C \\ & A & B & C \\ {}+ & A & B & C \\ \hline & B & B & B \\ \hline \end{array}$
  26.b
  Can you find a four digit number which is reversed when multiplied by $9$ ?
  
  (i.e. $ABCD \times 9 = DCBA$ )
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