Independent Schools Examination Board 2009 Paper 2

IndependentCo-ed

18 questions

Original PDFWorked solutions in progress

Questions

1
1. 1.a
  Write down the sum of $28$ and $35$ .
2. 1.b
  Subtract $27$ from $72$ .
3. 1.c
  Which number is double $176$ ?
4. 1.d
  What is the remainder when $265$ is divided by $7$ ?
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2
The population of Sumford is $9080$ .
1. 2.a
  Write $9080$ correct to the nearest $100$ .
2. 2.b
  What is the value of $9$ in $9080$ ? Write your answer in words.
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3
Ten calculators have a total mass of $1500 \rtqMathsUnit{g}$ .
1. 3.a
  Write down the mass of one calculator.
2. 3.b
  3.b.i
  What is the total mass of $100$ calculators?
  3.b.ii
  Write your answer to part (ii) (a) in kilograms.
3. 3.c
  Each calculator costs $\rtqMathsSymbolPound 5.19$ .
  
  What is the cost of $10$ calculators?
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4

ICE CREAM
Cone $\rtqMathsSymbolPound 1.50$
Tub $\rtqMathsSymbolPound 1.90$
All drinks $65 \rtqMathsUnitCurrencyPence$
1. 4.i
  Anne buys a cone and a drink.
  
  How much does she spend?
2. 4.ii
  Brian buys $4$ tubs.
  4.ii.a
  How much does he pay?
  4.ii.b
  He pays with a $\rtqMathsSymbolPound 10$ note.
  
  How much change does he receive?
3. 4.iii
  Caley buys $3$ identical ice lollies and pays $\rtqMathsSymbolPound 1.92$ .
  
  What is the cost, in pence, of one ice lolly?
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ICE CREAM
Cone	$\rtqMathsSymbolPound 1.50$
Tub	$\rtqMathsSymbolPound 1.90$
All drinks	$65 \rtqMathsUnitCurrencyPence$

Sophie's grandmother has given her the family recipe to make a tray of $12$ scones.

Recipe for a tray of $12$ scones:
$2 \rtqMathsUnit{cups}$	flour
$4 \rtqMathsUnit{teaspoons}$	baking powder
$\dfrac{1}{2} \rtqMathsUnit{teaspoon}$	salt
$2 \rtqMathsUnit{tablespoons}$	sugar
$3 \rtqMathsUnit{tablespoons}$	butter
$1$	egg
$150 \rtqMathsUnit{ml}$	milk

5.a
How much flour will she need to make $24$ scones?
5.b
How much salt will she need to make $60$ scones?
5.c
Sophie has only half a litre of milk.
1. 5.c.i
  Write half a litre in millilitres.
2. 5.c.ii
  What is the maximum number of trays of scones which she can make?

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6
Rupert has a spinner which is divided into three sections, coloured white, grey and black.

He spins the spinner $60$ times and records the colour which the arrow points to.
A circular spinner has unequal white, grey and black sections. Its pointer is directed into the white section.
Here are his results:

colour tally frequency
white $21$
grey
black
total: $60$
1. 6.a
  Complete the frequency table.
2. 6.b
  Complete the bar chart to show his results.
  A blank square reading grid has colour categories white, grey and black, a frequency axis beginning 0, 2, 4, and no bars because drawing them is part of the question.
3. 6.c
  Rupert thinks that the spinner is fair.
  
  Do you agree?
  
  $\rtqMathsUnderlineEmptyValueMedium$ because $\rtqMathsUnderlineEmptyValueLong$
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7
1. 7.a
  Draw accurately triangle $ABC$ in which:
  
  $\begin{aligned} AB &= 10 \rtqMathsUnit{cm} \\\\ \text{angle} \rtqMathsSpaceQuarterEm BAC &= 35 \degree \\\\ AC &= 7 \rtqMathsUnit{cm} \end{aligned}$
  
  (Point $A$ is already marked for you.)
2. 7.b
  Measure and write down the size of angle $B$ in the triangle.
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8
The lunch break at Harry's school lasts $60 \rtqMathsUnit{minutes}$ . Harry spends $\dfrac{1}{3}$ of his lunch break eating his lunch.
1. 8.a
  How many minutes does he spend eating lunch?
2. 8.b
  He spends $75\%$ of the remaining time playing with his friends.
  
  How long does he spend playing with his friends?
3. 8.c
  What percentage of his total lunch break does Harry spend playing with his friends?
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9
Arrange these distances in size order, from smallest to largest:

$250 \rtqMathsUnit{m} \rtqMathsListSeparator 0.52 \rtqMathsUnit{km} \rtqMathsListSeparator 0.5 \rtqMathsUnit{km} \rtqMathsListSeparator 2.05 \rtqMathsUnit{km} \rtqMathsListSeparator 502 \rtqMathsUnit{m}$
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10
There are two maths classes in Year $6$ , called $6\text{A}$ and $6\text{B}$ .

boys girls total
$6\text{A}$ $14$
$6\text{B}$ $6$ $18$
total $48$
1. 10.a
  Complete the table showing the number of boys and girls in each class.
2. 10.b
  Which class has a higher proportion of boys?
3. 10.c
  What fraction of the children in $6\text{B}$ are girls?
  
  Give your answer in its simplest form.
4. 10.d
  Some boys leave Year $6$ to go to another school.
  
  Half the total number of pupils in Year $6$ are now boys.
  
  How many boys have left the school?
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11
Shapes $A$ and $D$ are drawn on the centimetre-square grid below.
1. 11.a
  Reflect shape $A$ in the dotted line.
  
  Label the new shape $B$ .
2. 11.b
  Translate shape $A$ $6$ units to the right and $4$ units up.
  
  Label the new shape $C$ .
3. 11.c
  Choose the word from the list below to describe the transformation from shape $A$ to shape $D$ :
  
  reflection
  
  rotation
  
  translation
4. 11.d
  Calculate the area of shape $A$ .
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12
The table below shows the maximum temperatures in New York City last year:

month Jan Mar May Jul Sept Nov
maximum temperature, in $\degree\text{C}$ $3$ $9$ $21$ $29$ $24$ $11$
1. 12.a
  Use the information in this table to work out:
  12.a.i
  the range of temperatures
  12.a.ii
  the median temperature
2. 12.b
  In January, the lowest temperature was $7 \degree \text{C}$ colder than the maximum temperature for that month.
  
  Calculate the lowest temperature in January.
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13
1. 13.a
  This is a square-based pyramid.
  
  It has $5$ faces, which are a square and four congruent isosceles triangles.
  
  In the space below, draw an accurate net for this pyramid.
  
  (One of the triangular faces has already been drawn for you.)
2. 13.b
  This solid shape is made from $1 \rtqMathsUnit{cm}$ cubes.
  
  Calculate the volume of the shape.
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14
Lucy has some fair dice.

She picks one and rolls it.

On the line below, mark the following probabilities with the letters shown:
1. 14.a
  she gets an even number on the top face.
2. 14.b
  she gets a $6$ on the top face.
3. 14.c
  she gets a number less than $7$ on the top face
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15
1. 15.a
  The cost of a bottle of lemonade in four different shops is $42 \rtqMathsUnitCurrencyPence, 38 \rtqMathsUnitCurrencyPence, 40 \rtqMathsUnitCurrencyPence$ and $36 \rtqMathsUnitCurrencyPence$ .
  
  Calculate the mean price of a bottle of lemonade.
2. 15.b
  Freshly-squeezed lemonade costs $57 \rtqMathsUnitCurrencyPence$ a bottle.
  
  How much would $13$ bottles of this lemonade cost?
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colour	tally	frequency
white		$21$
grey
black
total:		$60$

	boys	girls	total
$6\text{A}$	$14$
$6\text{B}$		$6$	$18$
total			$48$

month	Jan	Mar	May	Jul	Sept	Nov
maximum temperature, in $\degree\text{C}$	$3$	$9$	$21$	$29$	$24$	$11$

The area of a rectangle can be found using the formula below:

The area of each of these rectangles is $24 \rtqMathsUnit{m}^2$ .

16.a

Complete the table below for each rectangle.

rectangle	area	height	width	perimeter
$A$	$24 \rtqMathsUnit{m}^2$	$6 \rtqMathsUnit{m}$	$\rtqMathsUnderlineEmptyValueShort \rtqMathsUnit{m}$	$\rtqMathsUnderlineEmptyValueShort \rtqMathsUnit{m}$
$B$	$24 \rtqMathsUnit{m}^2$	$\rtqMathsUnderlineEmptyValueShort \rtqMathsUnit{m}$	$3 \rtqMathsUnit{m}$	$\rtqMathsUnderlineEmptyValueShort \rtqMathsUnit{m}$
$C$	$24 \rtqMathsUnit{m}^2$	$2 \rtqMathsUnit{m}$	$\rtqMathsUnderlineEmptyValueShort \rtqMathsUnit{m}$	$\rtqMathsUnderlineEmptyValueShort \rtqMathsUnit{m}$

16.b
Write down the height and width of a rectangle with area $24 \rtqMathsUnit{m}^2$ which has a larger perimeter than the $3$ rectangles above.

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17
Here are some factors of $28$ :

$1 \rtqMathsListSeparator 2 \rtqMathsListSeparator 4 \rtqMathsListSeparator \dots \rtqMathsListSeparator 14 \rtqMathsListSeparator 28$
1. 17.a
  Write down the missing factor of $28$ .
2. 17.b
  Write down a factor of $28$ which is also a prime number.
3. 17.c
  Write down a factor of $28$ which is also a square number.
4. 17.d
  Add up all the factors and halve the total.
  
  Write down your answer.
5. 17.e
  A perfect number is a special type of number.
  
  If you add up all of its factors and halve the total, the result is the original number.
  
  Find a perfect number which is less than $10$ .
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18
In each number puzzle below, the numbers along each side of the shape add up to the same total.

For example, in this number square each side adds to $12$ .
1. 18.a
  In this number triangle, the numbers $1, 2, 3, 4, 5$ and $6$ are used once each.
  
  Complete the triangle so that the numbers along each side add up to $9$ .
2. 18.b
  In this number pentagon, the numbers $1, 2, 3, 4, 5, 6, 7, 8, 9$ and $10$ are used once each.
  
  Complete the pentagon so that the numbers along each side add up to $14$ .
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ICE CREAM
Cone	$\rtqMathsSymbolPound 1.50$
Tub	$\rtqMathsSymbolPound 1.90$
All drinks	$65 \rtqMathsUnitCurrencyPence$

ICE CREAM

Cone

\rtqMathsSymbolPound 1.50

Tub

\rtqMathsSymbolPound 1.90

All drinks

65 \rtqMathsUnitCurrencyPence

Recipe for a tray of

12

scones:

2 \rtqMathsUnit{cups}

flour

4 \rtqMathsUnit{teaspoons}

baking powder

\dfrac{1}{2} \rtqMathsUnit{teaspoon}

salt

2 \rtqMathsUnit{tablespoons}

sugar

3 \rtqMathsUnit{tablespoons}

butter

1

egg

150 \rtqMathsUnit{ml}

milk

colour	tally	frequency
white		$21$
grey
black
total:		$60$

colour

tally

frequency

white

21

grey

black

total:

60

	boys	girls	total
$6\text{A}$	$14$
$6\text{B}$		$6$	$18$
total			$48$

boys

girls

total

6\text{A}

14

6\text{B}

6

18

total

48

month	Jan	Mar	May	Jul	Sept	Nov
maximum temperature, in $\degree\text{C}$	$3$	$9$	$21$	$29$	$24$	$11$

month

Jan

Mar

May

Jul

Sept

Nov

maximum temperature, in

\degree\text{C}

3

9

21

29

24

11

rectangle

area

height

width

perimeter

A

24 \rtqMathsUnit{m}^2

6 \rtqMathsUnit{m}

\rtqMathsUnderlineEmptyValueShort \rtqMathsUnit{m}

\rtqMathsUnderlineEmptyValueShort \rtqMathsUnit{m}

B

24 \rtqMathsUnit{m}^2

\rtqMathsUnderlineEmptyValueShort \rtqMathsUnit{m}

3 \rtqMathsUnit{m}

\rtqMathsUnderlineEmptyValueShort \rtqMathsUnit{m}

C

24 \rtqMathsUnit{m}^2

2 \rtqMathsUnit{m}

\rtqMathsUnderlineEmptyValueShort \rtqMathsUnit{m}

\rtqMathsUnderlineEmptyValueShort \rtqMathsUnit{m}

Independent Schools Examination Board 2009 · Paper 2

Questions

Independent Schools Examination Board 2009 · Paper 2

Questions

Independent Schools Examination Board 2009 Paper 2

Independent Schools Examination Board 2009 Paper 2