The North London Independent Girls’ Schools’ Consortium 2016 Group 1

IndependentGirls

45 questions

Original PDFWorked solutions in progress

Questions

1
Work out $4689 + 2703$ .
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2
Work out $7305 - 946$ .
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3
Work out $3729 \times 6$ .
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4
Work out $4802 \div 7$ .
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5
Work out $\dfrac{3}{4}$ of $96$ .
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6
Write down the next number in the sequence.

$83, \rtqMathsListSeparator 76, \rtqMathsListSeparator 69, \rtqMathsListSeparator 62, \rtqMathsListSeparator \rtqMathsBoxedEmptyValueTwoDigitsWide$
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7
Write a number in each box to complete the statements.
1. 7.a
  $20.4 \times 100 = \rtqMathsBoxedEmptyValueFourDigitsWide$
2. 7.b
  $\rtqMathsBoxedEmptyValueFourDigitsWide \div 1000 = 1.05$
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8
Write in numerals, the number that is three hundred less than fourteen thousand and fifty.
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9
Write the missing sign $( = , <$ or $>)$ in the box.

$16 \times 7 \rtqMathsSpaceQuarterEm \rtqMathsRelationBoxedEmptyUnknown \rtqMathsSpaceQuarterEm 17 \times 6$
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10
In Moscow, the temperature is $-11 \degree \text{C}$ and in Paris the temperature is $14 \rtqMathsSpaceQuarterEm \text{degrees}$ warmer.

What is the temperature in Paris?
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11
Aisha thinks of a number.

She adds four and then multiplies by $8$ .

Her result is $56$ .

What was the number Aisha first thought of?
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12
What fraction of the shape below is shaded?
Two congruent centred squares, one turned through 45 degrees, form a symmetric eight-part outline. Five consecutive equal parts are shaded and the three parts on the left are unshaded.
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13
Georgie left home at $7.55 \rtqMathsTimeMeridiem{a.m.}$ and reached school $45 \rtqMathsUnit{minutes}$ later.

At what time did Georgie reach school?
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14
What is the difference between a tenth of $5$ and a fifth of $10$ ?
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15
1. 15.a
  The two-stage number machine below changes numbers according to the rule:
  
  “Add $7$ and then multiply by $4$ ”
  An input passes through add 7 and then multiply by 4 before reaching the output.
  15.a.i
  Work out the output when the input is $13$ .
  The input 13 passes through add 7 and then multiply by 4; the output is an answer blank.
  15.a.ii
  Work out the input when the output is $120$ .
  An answer blank passes through add 7 and then multiply by 4 to produce 120.
2. 15.b
  There are two possible function machines that will give the results shown below.
  
  Work out the rules for the two possible machines.
  The same two blank operation stages map 5 to 4 and 8 to 10.
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16
Jasmine has the six number cards shown below.

$\rtqMathsSizeTen{\rtqMathsBoxedValue{1}} \rtqMathsSpaceQuarterEm \rtqMathsSizeTen{\rtqMathsBoxedValue{9}} \rtqMathsSpaceQuarterEm \rtqMathsSizeTen{\rtqMathsBoxedValue{5}} \rtqMathsSpaceQuarterEm \rtqMathsSizeTen{\rtqMathsBoxedValue{3}} \rtqMathsSpaceQuarterEm \rtqMathsSizeTen{\rtqMathsBoxedValue{8}} \rtqMathsSpaceQuarterEm \rtqMathsSizeTen{\rtqMathsBoxedValue{4}}$

The cards can be placed side by side to form different numbers.

For example, using four of the cards, the largest $4$ -digit even number that can be made is $9854$ .

$\rtqMathsSizeTen{\rtqMathsBoxedValue{9}} \rtqMathsSpaceQuarterEm \rtqMathsSizeTen{\rtqMathsBoxedValue{8}} \rtqMathsSpaceQuarterEm \rtqMathsSizeTen{\rtqMathsBoxedValue{5}} \rtqMathsSpaceQuarterEm \rtqMathsSizeTen{\rtqMathsBoxedValue{4}}$
1. 16.a
  What is the smallest $5$ -digit multiple of $5$ that can be made?
2. 16.b
  Using five cards, what is the nearest number to $50000$ that can be made?
3. 16.c
  What is the largest $3$ -digit multiple of $3$ that can be made?
4. 16.d
  What is the largest $2$ -digit prime number that can be made?
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17
In a magic square the sum of the numbers in each row, column and diagonal is the same.

The numerals $1$ to $9$ are used in this magic square.

Complete the magic square.

$6$ $2$
$5$
$8$
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18
Sammy has correctly performed the following multiplication using her calculator:

$37 \times 42 = 1554$

Without doing any long multiplications, use Sammy's calculation to help you write down the results of the following:
1. 18.a
  $38 \times 42$
2. 18.b
  $37 \times 21$
3. 18.c
  $155.4 \div 42$
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19
Lily uses these ingredients to make strawberry sorbet:

For $6$ people
$300 \rtqMathsUnit{millilitres}$ water
$100 \rtqMathsUnit{grams}$ sugar
$450 \rtqMathsUnit{grams}$ strawberries
$2$ eggs
1. 19.a
  Calculate the ingredients needed to make this sorbet for $15$ people.
2. 19.b
  For how many people is Lily making this sorbet if she uses exactly $1 \rtqMathsUnit{kilogram}$ of sugar?
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20
Celia and Autumn have each thought of an integer (whole number) between $0$ and $20$ .

The product of their numbers is $72$ and the difference between the numbers is the same as Celia's number.

What is Autumn's number?
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21
The Venn diagram below is being used for sorting even numbers from $2$ to $20$ inclusive.
The left set is labelled multiples of a blank number and the right set multiples of 6. The visible values are 4, 8 and 16 in the left only region; 18 and 6 in the right only region; 12 in both; and 2 and 10 outside both.
1. 21.a
  Complete the label of the set.
2. 21.b
  Write the numbers $14$ and $20$ in the correct regions of the diagram.
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22
Kiwi fruits cost $78 \rtqMathsUnitCurrencyPence$ each; cherries cost $8 \rtqMathsUnitCurrencyPence$ each.

Gina buys as many kiwi fruits as she can for $\rtqMathsSymbolPound 5$ , and spends all of her change on cherries.
1. 22.a
  How many kiwi fruits does Gina buy?
2. 22.b
  How many cherries does Gina buy?
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23
Reflect the shape in the mirror line.
An eight-column by six-row staggered dot lattice contains an irregular shaded polygon on the right of a vertical mirror line. The mirror line passes through dots on the shifted rows. Two polygon vertices touch the mirror line. The reflected copy is not shown.
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For $6$ people
$300 \rtqMathsUnit{millilitres}$	water
$100 \rtqMathsUnit{grams}$	sugar
$450 \rtqMathsUnit{grams}$	strawberries
$2$	eggs

James missed the $4.20 \rtqMathsTimeMeridiem{p.m.}$ train by three minutes.

	Train A	Train B
London	$4.20 \rtqMathsTimeMeridiem{p.m.}$	$5.02 \rtqMathsTimeMeridiem{p.m.}$
Staplehurst	$5.16 \rtqMathsTimeMeridiem{p.m.}$	$5.59 \rtqMathsTimeMeridiem{p.m.}$

How long must he wait to catch the $5.02 \rtqMathsTimeMeridiem{p.m.}$ train?

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25
A square has perimeter $20 \rtqMathsUnit{cm}$ .

Work out the area of the square.
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26
What is the length of the pencil?
An inch ruler is labelled 1 to 4 with tenths and half-inch ticks. The pencil begins at 0.7 inches and its tip ends at 3.6 inches.
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27
Joanne's marks in five spelling tests are:

$7 \rtqMathsListSeparator 9 \rtqMathsListSeparator 8 \rtqMathsListSeparator 7 \rtqMathsListSeparator 6$

What is the range of her marks?
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28
The pictogram below shows the results of a survey into the numbers of woodlice found under pots in a greenhouse.

One symobol represents two woodlice.

Pot A
Pot B
Pot C
Pot D
Pot E
1. 28.a
  How many woodlice were found under pot A?
2. 28.b
  What was the total number of woodlice found?
3. 28.c
  Charlotte removes a third of the woodlice from pot B and $20\%$ of the woodlice from pot C. She puts these woodlice under a new pot, F.
  
  How many woodlice are under pot F?
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29
Mum, Dad and Granny have three cakes: chocolate, strawberry and coffee.

Mum likes chocolate or coffee.

Dad likes chocolate, and Granny likes all three.

How can it be arranged, so that they each get a cake that they like?
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30
Shade in four squares, so that the finished shape has exactly two lines of symmetry.
The middle row has five equal squares. Rows of three squares are centred above and below it. The leftmost square in the top row and the leftmost square in the middle row are shaded; the other squares are unshaded.
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31
The diagram shows a spinner with the numbers $1$ to $20$ .
A circular spinner divided into twenty equal sections, each labelled once with a number from 1 to 20, inside a square frame.
Vanessa spins the spinner.

The spinner is equally likely to land on each section of the disc.
Eleven equally spaced tick positions run from impossible at the left endpoint, through even chance at the centre, to certain at the right endpoint. No answer letters are marked.
On the likelihood scale above:
1. 31.a
  mark with letter $\text{A}$ the likelihood that the spinner lands on an even number.
2. 31.b
  mark with letter $\text{B}$ the likelihood that the spinner lands on a multiple of $5$ .
3. 31.c
  mark with letter $\text{C}$ the likelihood that the spinner lands on $21$ .
4. 31.d
  mark with letter $\text{D}$ the likelihood that the spinner lands on a cube number.
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32
Tick the correct box for each statement:

Always true Sometimes true Never true
A square has four right angles
A pentagon has five obtuse angles
A rhombus has all four sides different lengths
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33
The reading on the scale below shows the mass of a parcel.

Write down the mass:
A shallow curved dial is labelled 0, 1, 2, 3 and 4 kilograms, with five equal subdivisions between consecutive kilograms. Its needle points to the second small division after 2 kilograms, or 2.4 kilograms.
1. 33.a
  in kilograms
2. 33.b
  in grams
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34
Zoya has a jug of capacity $1.5 \rtqMathsUnit{litres}$ which is full of lemonade.

She has eight cups each of capacity $150 \rtqMathsUnit{ml}$ .

Zoya fills the cups with lemonade from her jug.
1. 34.a
  What volume of lemonade is left in the jug?
2. 34.b
  Zoya has five $2 \rtqMathsUnit{litre}$ bottles of lemonade.
  
  How many times could Zoya completely fill her jug from these bottles?
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35
1. 35.a
  On the centimetre square co-ordinate grid below, plot and label the points $P(3, 4), Q(6, 5)$ and $R(5, 8)$ .
  The square coordinate grid runs from 0 to 10 on both axes. A horizontal line segment joins A at (3, 2) to C at (7, 2). No other points or shapes are shown.
2. 35.b
  $PQRS$ is a square.
  
  Write down the co-ordinates of point $S$ .
3. 35.c
  $AC$ is the longer diagonal of kite $ABCD$ which has area $4 \rtqMathsUnit{cm}^2$ .
  
  $AB$ is longer than $BC$ .
  
  Draw kite $ABCD$ .
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36
Fred fits together two triangles to form a rectangle.
On a nine-column by six-row dot lattice, a six-by-three rectangle is shaded. A diagonal from its bottom-left corner to its top-right corner divides it into two congruent triangles.
1. 36.a
  On the grid below, show how Fred can fit together the same two triangles to make a parallelogram which is not a rectangle.
  A blank regular lattice has 10 columns and 8 rows of evenly spaced dots. No shapes or joining lines are drawn.
2. 36.b
  Fran fits together two isosceles triangles to make a parallelogram.
  On a six-by-six dot lattice, a shaded parallelogram has horizontal top and bottom edges. A diagonal joins its top-left vertex to its bottom-right vertex, dividing it into two congruent isosceles triangles.
  On the grid below, show how Fran can fit together the same two isosceles triangles to make a rhombus.
  A blank regular lattice has 10 columns and 8 rows of evenly spaced dots. No shapes or joining lines are drawn.
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37
Susan has a rectangular card that measures $18 \rtqMathsUnit{cm}$ by $6 \rtqMathsUnit{cm}$ .
1. 37.a
  What is the perimeter of the card?
2. 37.b
  What is the area of the card?
3. 37.c
  Rectangular stickers measure $3 \rtqMathsUnit{cm}$ by $2 \rtqMathsUnit{cm}$ .
  
  Susan wants to cover the front of the card with stickers, without any overlapping.
  
  What is the maximum number of stickers she can fit on the front of the card?
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38
Cube $A$ has a volume of $8 \rtqMathsUnit{cm}^3$ .
The front, top and right faces of cube A are each divided into a two-by-two grid of equal parts.
not to size

Another cube, $B$ , has edges which are twice the length of the edges of cube $A$ .

Work out the volume of cube $B$ .
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39
A tea leaf weighs $0.008 \rtqMathsUnit{grams}$ .
1. 39.a
  What would be the mass of $1000$ tea leaves?
2. 39.b
  How many tea leaves would you expect there to be in a $1 \rtqMathsUnit{kg}$ pack of tea?
3. 39.c
  A tea bag contains $250$ tea leaves.
  
  The tissue covering weighs $0.5 \rtqMathsUnit{g}$ .
  
  How many tea bags will there be in a $250 \rtqMathsUnit{g}$ packet of tea bags?
  
  (The $250 \rtqMathsUnit{g}$ includes the mass of the bags and not just the tea leaves.)
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Pot A
Pot B
Pot C
Pot D
Pot E

Myrtle wants to buy an ice-cream.

The options are:

container	cone	$20 \rtqMathsUnitCurrencyPence$	$(\text{C})$	tub	$15 \rtqMathsUnitCurrencyPence$	$(\text{T})$
flavour	mint	$60 \rtqMathsUnitCurrencyPence$	$(\text{M})$	vanilla	$50 \rtqMathsUnitCurrencyPence$	$(\text{V})$
topping	flake	$25 \rtqMathsUnitCurrencyPence$	$(\text{F})$	sprinkles	$20 \rtqMathsUnitCurrencyPence$	$(\text{S})$

40.a
Complete a table to show all the different combinations that Myrtle could choose.

A start has been made for you.

You may not need all of the lines in the table.

container flavour topping
$\text{C}$ (cone) $\text{M}$ (mint) $\text{F}$ (flake)
$\text{C}$ $\text{M}$
40.b
Myrtle has exactly $95 \rtqMathsUnitCurrencyPence$ and wishes to spend all her money.

Which two combinations of container, flavour and topping could she choose?

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41
The diagram below shows patterns drawn on a square dotted grid.
Pattern 1 is one softly shaded square. Pattern 2 is an L-shape of three softly shaded squares, with two across the top and one below the right square. Pattern 3 is a six-square staircase, with rows of three, two and one squares aligned down to the right. The area labelled pattern 4 is blank.
1. 41.a
  Draw pattern $4$ on the grid above.
2. 41.b
  Complete the table below.
  
  pattern number $1$ $2$ $3$ $4$ $5$
  number of squares $1$ $3$
  perimeter (units) $4$ $8$
3. 41.c
  Sarah suggests that the perimeter of a particular pattern can be worked out using the number machine below.
  The pattern number is multiplied by 4 to produce the perimeter.
  Use Sarah's idea to calculate the perimeter of pattern $10$ .
4. 41.d
  Emilia suggests that the number of squares in a pattern can be worked out by following these instructions, in order:
  
  Start with the pattern number, $n$ .
  
  Add $1$ to give a new number, $m$ .
  
  Multiply $m$ by $n$ .
  
  Divide by $2$
  
  Use the instructions to calculate the number of squares in pattern $100$ .
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42
Three hedgehogs, Rana, Sarah and Tina, are collecting leaves.

Rana collects twice as many as Sarah.

Sarah collects one and a half times as many as Tina.

Between them they collect $198$ leaves.

How many leaves did each hedgehog collect?
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43
Starting with a $2$ -digit number, Geraldine applies the rule:

Square the difference between the digits

repeatedly until her result is a single-digit number.

Examples:
The first chain is 72 to 25 to 9 in two steps, with transition labels 5 squared and 3 squared. The second is 90 to 81 to 49 to 25 to 9 in four steps, with labels 9 squared, 7 squared, 5 squared and 3 squared. The third is 19 to 64 to 4 in two steps.
1. 43.a
  Apply the rule to the following starting numbers:
  43.a.i
  $28$
  43.a.ii
  $73$
2. 43.b
  List all the starting numbers between $10$ and $30$ inclusive which give the single digit result $4$ in a single step.
3. 43.c
  For multiples of $11$ such as $22$ and $55$ , the result will be zero.
  
  For other starting numbers the numbers in the steps are all square numbers.
  
  List, in order, the possible single digit results.
4. 43.d
  What do you think will be the most common single digit result if you calculate the result for every $2$ -digit starting number?
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44
In the same time that Tom can run $100 \rtqMathsUnit{metres}$ , Jerry can run only $60 \rtqMathsUnit{metres}$ .

Tom and Jerry have a competition.

When Jerry has run $100 \rtqMathsUnit{metres}$ , Tom sets off in pursuit.

How many metres will Tom run before he catches Jerry?
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45
Paula has two counters, with different whole numbers on each side.

She throws them once and adds the numbers she sees:
A dark counter showing 6 plus a grey counter showing 7 equals 13.
Paula throws her counters several more times and gets the following totals:

$12, \rtqMathsListSeparator 15, \rtqMathsListSeparator 16$
1. 45.a
  What number is on the other side of the black counter?
2. 45.b
  What number is on the other side of the grey counter?
3. 45.c
  Irma gives Paula a third counter.
  
  When Paula throws all three counters together she can get the following totals:
  
  $13, \rtqMathsListSeparator 14, \rtqMathsListSeparator 16, \rtqMathsListSeparator 17, \rtqMathsListSeparator 20, \rtqMathsListSeparator 21, \rtqMathsListSeparator 23, \rtqMathsListSeparator 24$
  
  What are the two numbers on the third counter?
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pattern number	$1$	$2$	$3$	$4$	$5$
number of squares	$1$	$3$
perimeter (units)	$4$	$8$

For $6$ people
$300 \rtqMathsUnit{millilitres}$	water
$100 \rtqMathsUnit{grams}$	sugar
$450 \rtqMathsUnit{grams}$	strawberries
$2$	eggs

For

6

people

300 \rtqMathsUnit{millilitres}

water

100 \rtqMathsUnit{grams}

sugar

450 \rtqMathsUnit{grams}

strawberries

2

eggs

Train A

Train B

London

4.20 \rtqMathsTimeMeridiem{p.m.}

5.02 \rtqMathsTimeMeridiem{p.m.}

Staplehurst

5.16 \rtqMathsTimeMeridiem{p.m.}

5.59 \rtqMathsTimeMeridiem{p.m.}

Pot A
Pot B
Pot C
Pot D
Pot E

Pot A

Pot B

Pot C

Pot D

Pot E

Always true

Sometimes true

Never true

A square has four right angles

A pentagon has five obtuse angles

A rhombus has all four sides different lengths

container

cone

20 \rtqMathsUnitCurrencyPence

(\text{C})

tub

15 \rtqMathsUnitCurrencyPence

(\text{T})

flavour

mint

60 \rtqMathsUnitCurrencyPence

(\text{M})

vanilla

50 \rtqMathsUnitCurrencyPence

(\text{V})

topping

flake

25 \rtqMathsUnitCurrencyPence

(\text{F})

sprinkles

20 \rtqMathsUnitCurrencyPence

(\text{S})

container

flavour

topping

\text{C}

(cone)

\text{M}

(mint)

\text{F}

(flake)

\text{C}

\text{M}

pattern number	$1$	$2$	$3$	$4$	$5$
number of squares	$1$	$3$
perimeter (units)	$4$	$8$

pattern number

1

2

3

4

5

number of squares

1

3

perimeter (units)

4

8

container	flavour	topping
$\text{C}$ (cone)	$\text{M}$ (mint)	$\text{F}$ (flake)
$\text{C}$	$\text{M}$

The North London Independent Girls’ Schools’ Consortium 2016 · Group 1

Questions

The North London Independent Girls’ Schools’ Consortium 2016 · Group 1

Questions

The North London Independent Girls’ Schools’ Consortium 2016 Group 1

The North London Independent Girls’ Schools’ Consortium 2016 Group 1