James Allen's Girls' School Paper 1

IndependentGirls

22 questions

Original PDFWorked solutions in progress

Questions

1
$\rtqMathsColumnarArithmeticStyle \begin{array}{cccccccccccccc} & 2 & 7 & 5 \\ & 6 & 4 & 8 \\ {}+ & & 9 & 7 \\ \hline \end{array}$
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2
$\rtqMathsColumnarArithmeticStyle \begin{array}{cccccccccccccc} & 1 & 0 & 0 & 3 \\ {}- & & 8 & 3 & 7 \\ \hline \end{array}$
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3
$\rtqMathsColumnarArithmeticStyle \begin{array}{cccccccccccccc} & 5 & 8 & 7 \\ {}\times & & & 7 \\ \hline \end{array}$
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4
Long-division question showing 4716 divided by 9 in division-bracket notation.
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5
$2492 \div 28$
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6
Cheese costs $\rtqMathsSymbolPound 5.40 \rtqMathsUnit{per kg}$ . Jessica buys $0.6 \rtqMathsUnit{kg}$ of cheese. How much does Jessica pay?
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7
There are $31 \rtqMathsUnit{days}$ in July. Each day throughout July I picked $300 \rtqMathsUnit{g}$ of raspberries from my garden.

What was the total weight of the raspberries I picked that month? Give your answer in $\text{kilograms}$ .
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8
A sheet of graph paper is placed with its x-axis pointing due East and its y-axis pointing due North. A sluggish snail starts at point $(0, 0)$ and slowly, but smoothly, slithers $1$ unit North, $2$ units East, $3$ units South, $4$ units West, $5$ units North, $6$ units East, $7$ units South, $8$ units West, $9$ units North and (lastly!) $10$ units East.

At which point does the snail finally arrive?
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9
Write down the next term in each of these sequences.
1. 9.a
  $14, \rtqMathsListSeparator 25, \rtqMathsListSeparator 36, \rtqMathsListSeparator 47, \rtqMathsSpaceOneEm \rtqMathsSequenceEllipsis$
2. 9.b
  $7000, \rtqMathsListSeparator 700, \rtqMathsListSeparator 70, \rtqMathsListSeparator 7, \rtqMathsSpaceOneEm \rtqMathsSequenceEllipsis$
3. 9.c
  $2, \rtqMathsListSeparator 7, \rtqMathsListSeparator 22, \rtqMathsListSeparator 67, \rtqMathsSpaceOneEm \rtqMathsSequenceEllipsis$
4. 9.d
  $23, \rtqMathsListSeparator 16, \rtqMathsListSeparator 9, \rtqMathsListSeparator 2 , \rtqMathsSpaceOneEm \rtqMathsSequenceEllipsis$
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10
1. 10.a
  A tin of cookies costs $\rtqMathsSymbolPound 3.69$ and a bag of jelly babies costs $\rtqMathsSymbolPound 1.55$ . Tracey and Cat buy $2$ tins of cookies and a bag of jelly babies. They pay with a $\rtqMathsSymbolPound 20$ note.
  
  How much change should they get?
2. 10.b
  A normal tin contains $40$ cookies. A special offer tin contains $\dfrac{3}{10}$ more cookies.
  
  Work out how many cookies there are in a special offer tin.
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11
Roger drops his ball onto a hard surface. Each time it bounces, it rebounds to exactly one third of the height from which it fell. After the second bounce the ball rises to a height of $9 \rtqMathsUnit{cm}$ .

From what height was it originally dropped?
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Temperatures were taken on one day in each of five cities. The results are shown in the table.

City	Temperature at midnight	Temperature at midday
Bristol	$2 \degree \text{C}$	$8 \degree \text{C}$
Manchester	$-2 \degree \text{C}$	$8 \degree \text{C}$
Liverpool	$-4 \degree \text{C}$	$7 \degree \text{C}$
Norwich	$-3 \degree \text{C}$	$-1 \degree \text{C}$
York	$-7 \degree \text{C}$	$2 \degree \text{C}$

12.a
Which city had the lowest temperature at midnight?
12.b
Which city had the greatest rise in temperature between midnight and midday?
12.c
What is the greatest difference in temperature between any two cities at midnight?
12.d
Which of the five cities is being described here?

“Its temperature at midday is $6 \degree \text{C}$ higher than the temperature in York and its temperature at midnight is $2 \degree \text{C}$ higher than the temperature in Liverpool”.

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13
Calculate - remember to cancel your answers if possible.
1. 13.a
  $\dfrac{3}{4} + \dfrac{5}{6}$
2. 13.b
  $\dfrac{4}{5} - \dfrac{2}{3}$
3. 13.c
  $\dfrac{1}{7} \times \dfrac{2}{3} \times 21 =$
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14
A comb for horses has $100$ teeth, each $1 \rtqMathsUnit{mm}$ wide. The gaps between the teeth are also $1 \rtqMathsUnit{mm}$ wide.

How long is the comb in centimetres?
A long straight comb spine has three adjacent representative teeth at the left and the final tooth at the far right. A long open gap between the short lower stubs indicates the omitted repeated teeth.
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15
Here is a list of the ingredients to make $15$ Chocolate Brownies.

$50 \rtqMathsUnit{g}$ chocolate
$110 \rtqMathsUnit{g}$ butter
$225 \rtqMathsUnit{g}$ sugar
$50 \rtqMathsUnit{g}$ flour
$120 \rtqMathsUnit{g}$ nuts
1. 15.a
  Natasha made $60$ Chocolate Brownies. How much butter did she use?
2. 15.b
  Stella has $150 \rtqMathsUnit{grams}$ of flour and $300 \rtqMathsUnit{grams}$ of nuts, and plenty of the other ingredients. She makes as many Chocolate Brownies as she can.
  
  Which ingredient will she run out of, flour or nuts? Show how you decide.
3. 15.c
  Pauline wants to make $10$ Chocolate Brownies, how much sugar will she need?
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16
1. 16.a
  How big is angle $x$ in this diagram?
  The upper-left x and upper-right 113-degree labels are text-only sectors. The lower angle has a visible minor arc labelled 37 degrees. Decorative artwork from the source is omitted.
2. 16.b
  What is the value of $x$ in this diagram?
  The outlined concave network has a top point, left and right points, and an inward central notch. Visible minor arcs label 35 degrees at the top, 15 degrees on the left, 25 degrees on the right, and the inward notch sector x degrees.
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17
In a survey, $1000$ people were asked if they owned a computer. The pictogram shows the results of the survey.

Greece
Hong Kong
Italy
Korea
Kuwait
Malaysia

represents $50$ people who owned a computer.
1. 17.a
  In which country did the greatest number of people own a computer?
2. 17.b
  Write down the number of people in Italy who owned a computer.
3. 17.c
  In which country did $240$ people own a computer?
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18
Natasha is making a coloured tower as shown. She has thirty six small cubes, with equal numbers of red ( $\text{R}$ ), blue ( $\text{B}$ ) and yellow ( $\text{Y}$ ). Each row is of one colour, and no two rows which are next to each other are the same colour. The top three rows are coloured as indicated.

What colour must the bottom row be?

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19
1. 19.a
  Gill has $5$ pink, $7$ purple and $8$ orange counters in a bag. If she selects a counter without looking, what is the probability she chooses a pink counter?
2. 19.b
  If Gill wants to double her chances of choosing a pink counter, how many extra counters should she add to the bag?
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20
Natalie, Sara and Antonia catch $3$ different buses to go to the same destination.

Antonia catches the $19 \rtqMathsTimeSeparator 15$ bus.

Natalie's bus journey takes three times as long as Sara's. Natalie's bus leaves $20 \rtqMathsUnit{minutes}$ before Antonia's bus and arrives at $20 \rtqMathsTimeSeparator 10$ .

Sara catches the $19 \rtqMathsTimeSeparator 25$ bus.

What time does Sara arrive at the destination?
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21
How much smaller is the area of a $60 \rtqMathsUnit{cm}$ by $40 \rtqMathsUnit{cm}$ rectangle than that of a square with the same perimeter?
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22
Jack likes to eat lots of fruit. He finds that four apples and two oranges cost $\rtqMathsSymbolPound 1.54$ and that two oranges and four bananas cost $\rtqMathsSymbolPound 1.70$ .

How much would he have to pay if he bought one apple, one orange and one banana?
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Greece
Hong Kong
Italy
Korea
Kuwait
Malaysia

City

Temperature at midnight

Temperature at midday

Bristol

2 \degree \text{C}

8 \degree \text{C}

Manchester

-2 \degree \text{C}

8 \degree \text{C}

Liverpool

-4 \degree \text{C}

7 \degree \text{C}

Norwich

-3 \degree \text{C}

-1 \degree \text{C}

York

-7 \degree \text{C}

2 \degree \text{C}

Greece
Hong Kong
Italy
Korea
Kuwait
Malaysia

Greece

Hong Kong

Italy

Korea

Kuwait

Malaysia

$50 \rtqMathsUnit{g}$	chocolate
$110 \rtqMathsUnit{g}$	butter
$225 \rtqMathsUnit{g}$	sugar
$50 \rtqMathsUnit{g}$	flour
$120 \rtqMathsUnit{g}$	nuts