Independent Schools Examination Board 2016 Paper 1

IndependentCo-ed

22 questions

Original PDFWorked solutions in progress

Questions

1. 1
  Write down the answers to these questions.
  
  (You may work them out in your head).
  1.a
  $48 + 35$
  1.b
  $613 - 123$
  1.c
  $28 \div 4$
  1.d
  $2^3$
  1.e
  twenty-five percent of eighty
  1.f
  $6.3 \times 100$
  1.g
  $398 + 297$
  1.h
  $27 \times 5$
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2. 2
  2.a
  Write down all the prime numbers between $10$ and $20$ .
  2.b
  Write down the first three multiples of $12$ .
  2.c
  Write down all the factors of $16$ .
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3. 3
  A box of $7$ grapefruit costs $\rtqMathsSymbolPound 3.29$ .
  3.a
  What is the cost of one grapefruit?
  
  Give your answer in pence.
  3.b
  Patrick buys $2$ boxes of grapefruit and pays with a $\rtqMathsSymbolPound 20$ note.
  
  How much change should he receive?
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4. 4
  These thermometers show the temperatures inside and outside a window at $10 \rtqMathsTimeMeridiem{a.m.}$ one winter's day.
  A horizontal thermometer runs from minus 5 to 25 degrees Celsius in one-degree steps, with its filled level at about 21 degrees. An outside thermometer runs from minus 5 to 25 degrees Celsius in one-degree steps. Its reading is minus 3 degrees Celsius.
  4.a
  How many degrees warmer was it inside than outside the window?
  4.b
  At $10 \rtqMathsTimeMeridiem{p.m.}$ , the temperature outside had fallen by $2 \degree \text{C}$ .
  
  What was the temperature outside the window at $10 \rtqMathsTimeMeridiem{p.m.}$ ?
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5. 5
  Fill in the boxes to make the following statements true:
  5.a
  $8 + 4 \times \rtqMathsBoxedEmptyValueOneDigitWide = 36$
  5.b
  $5 \times(4 - \rtqMathsBoxedEmptyValueOneDigitWide ) = 15$
  5.c
  $10 - (5 + \rtqMathsBoxedEmptyValueOneDigitWide ) = -3$
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6. 6
  Shape $P$ is drawn on the centimetre-square grid below.
  
  6.a
  Reflect shape $P$ in the dashed line.
  
  Label the new shape $Q$ .
  6.b
  Translate shape $P$ $3$ units right and $4$ units up.
  
  Label the new shape $R$ .
  6.c
  Work out the area of shape $P$ .
  
  Give your answer with the correct units.
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7. 7
  7.a
  Write down the value of these Roman numerals:
  7.a.i
  $\text{V}$
  7.a.ii
  $\text{M}$
  7.b
  Which year is written in Roman numerals as $\text{MMXVII}$ ?
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8. 8
  8.a
  Work out the following:
  8.a.i
  $3579 + 1824$
  8.a.ii
  $3579 - 1824$
  8.a.iii
  $264 \times 27$
  8.a.iv
  $1595 \div 11$
  8.b
  Round $2089$ to the nearest $100$ .
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9. 9
  Calculate the mean of these numbers:
  
  $9 \rtqMathsListSeparator 14 \rtqMathsListSeparator 7 \rtqMathsListSeparator 17 \rtqMathsListSeparator 8$
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10. 10
  Here is a list of fractions:
  
  $\dfrac{3}{4} \rtqMathsListSeparator \dfrac{5}{8} \rtqMathsListSeparator \dfrac{15}{11} \rtqMathsListSeparator \dfrac{8}{12} \rtqMathsListSeparator \dfrac{4}{5}$
  
  Choose from the list:
  10.a
  a fraction which is greater than $1$
  10.b
  a fraction equivalent to $80\%$
  10.c
  a fraction equivalent to $0.75$
  10.d
  a fraction which is not in its simplest form
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11. 11
  A sunflower is $150 \rtqMathsUnit{cm}$ tall.
  
  How tall will it be if its height increases by $10\%$ ?
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12. 12
  Here are $5$ number cards:
  
  $\rtqMathsSizeTen{\rtqMathsBoxedValue{6}} \rtqMathsListSeparator \rtqMathsSizeTen{\rtqMathsBoxedValue{3}} \rtqMathsListSeparator \rtqMathsSizeTen{\rtqMathsBoxedValue{7}} \rtqMathsListSeparator \rtqMathsSizeTen{\rtqMathsBoxedValue{5}} \rtqMathsListSeparator \rtqMathsSizeTen{\rtqMathsBoxedValue{9}}$
  
  The cards can be put together to form numbers.
  
  For example, the smallest number which could be made using $4$ of the cards is:
  
  $\rtqMathsSizeTen{\rtqMathsBoxedValue{3}}\rtqMathsSizeTen{\rtqMathsBoxedValue{5}}\rtqMathsSizeTen{\rtqMathsBoxedValue{6}}\rtqMathsSizeTen{\rtqMathsBoxedValue{7}}$
  12.a
  Using all $5$ cards:
  12.a.i
  what is the largest possible even number?
  12.a.ii
  what is the number which is closest to $80000$ ?
  12.b
  Use exactly $2$ of the cards to make the smallest possible prime number.
  12.c
  Arrange any $4$ of the cards to show a sum below which will give the smallest possible answer.
  
  $\rtqMathsSizeTen{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeTen{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm + \rtqMathsSpaceQuarterEm \rtqMathsSizeTen{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeTen{\rtqMathsBoxedEmptyValueOneDigitWide}$
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13. 13
  Put these distances in order from smallest to largest:
  
  $27.8 \rtqMathsUnit{km} \rtqMathsListSeparator 2.087 \rtqMathsUnit{km} \rtqMathsListSeparator 2778 \rtqMathsUnit{m} \rtqMathsListSeparator 2.708 \rtqMathsUnit{km}$
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14. 14
  14.a
  Draw accurately triangle $ABC$ where $AB = 5.5 \rtqMathsUnit{cm}, \text{angle} \rtqMathsSpaceQuarterEm A = 45 \degree$ and $\text{angle} \rtqMathsSpaceQuarterEm B = 90 \degree$
  
  (Point $A$ is already drawn for you.)
  
  14.b
  Measure and write down the length of side $BC$ .
  14.c
  Circle any appropriate words from the list to describe triangle $ABC$ .
  
  Give reasons for your answer.
  
  equilateral
  
  isosceles
  
  scalene
  
  right-angled
  
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15. 15
  15.a
  Two identical rectangles are divided into $15$ equal squares.
  15.a.i
  Shade $\dfrac{3}{5}$ of this rectangle:
  
  15.a.ii
  Shade $\dfrac{2}{3}$ of this rectangle:
  
  15.a.iii
  Which is larger: $\dfrac{3}{5}$ or $\dfrac{2}{3}$ ?
  
  Give a reason for your answer.
  15.b
  Arrange these fractions in order from smallest to largest:
  
  $1 \dfrac{1}{3} \rtqMathsListSeparator \dfrac{2}{3} \rtqMathsListSeparator \dfrac{4}{5} \rtqMathsListSeparator \dfrac{13}{15} \rtqMathsListSeparator \dfrac{3}{5}$
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16. 16
  Work out:
  16.a
  $\dfrac{2}{3} - \dfrac{1}{6}$
  16.b
  $\dfrac{2}{5} \times 3$
  
  Write your answer as a mixed number.
  
  (You may use the diagrams to help you).
  
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17. 17
  In a box of $24$ pens, one eighth are green, $25\%$ are red and the rest are blue.
  
  What fraction of the pens is blue?
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18. 18
  18.a
  Jake hangs a peg basket on a washing line.
  
  Find the size of one of the shaded angles in the diagram above, if both are the same size.
  18.b
  The diagram below shows two straight lines.
  
  Find the sizes of the angles marked $a, b$ and $c$ .
  
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19. 19
  Sarah measured the temperature of a beaker of liquid every $10 \rtqMathsUnit{minutes}$ during a science experiment.
  
  She plotted her results on the graph below.
  
  19.a
  What was the lowest temperature of the beaker?
  19.b
  At what time was the temperature of the beaker $15 \degree \text{C}$ ?
  19.c
  Sarah measured the temperature of the beaker again $4 \rtqMathsUnit{hours}$ and $30 \rtqMathsUnit{minutes}$ after the last reading on the graph.
  
  At what time did she take this measurement?
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20. 20
  Farmer Jack and Farmer Giles each have a rectangular field.
  
  Farmer Jack's field has an area of $24 \rtqMathsUnit{m}^2$ .
  
  Its length is $8 \rtqMathsUnit{m}$ .
  20.a
  Work out the width of Farmer Jack's field.
  20.b
  Work out the perimeter of Farmer Jack's field.
  20.c
  Farmer Giles' field has a perimeter of $20 \rtqMathsUnit{m}$ .
  
  The width of Farmer Giles' field is $4 \rtqMathsUnit{m}$ .
  
  Work out the length of Farmer Giles' field.
  20.d
  Work out the area of Farmer Giles' field.
  20.e
  Farmer Josephine also has a rectangular field.
  
  The width of Farmer Josephine's field is $x \rtqMathsUnit{m}$ and the length is $y \rtqMathsUnit{m}$ .
  
  Farmer Josephine builds a fence along the perimeter of her field.
  
  If the total length of this fence is $30 \rtqMathsUnit{m}$ , write down two possible values of $x$ and $y$ .
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21. 21
  Sanjay is making purple paint.
  
  21.a
  If he uses $6 \rtqMathsUnit{litres}$ of red paint, how much blue paint should he use?
  21.b
  How much blue paint is needed to make $35 \rtqMathsUnit{litres}$ of purple paint?
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22. 22
  22.a
  Annie and Bradley each think of a number.
  
  The difference between their numbers is $6$ .
  
  The sum of their numbers is $20$ .
  
  What are the two numbers?
  22.b
  Alice thinks of a number.
  
  Alice calls her number $a$ .
  
  Alice adds $7$ to her number, and then doubles her answer.
  
  Write an expression, using $a$ , to show what Alice does.
  22.c
  Jack thinks of a number.
  
  Jack calls his number $n$ .
  
  Jack multiplies his number by $3$ , and then subtracts $5$ .
  
  He gets the answer $16$ .
  
  Use this information to write down an equation, and then solve it to find $n$ .
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