The North London Independent Girls’ Schools’ Consortium 2016 Group 2

IndependentGirls

46 questions

Original PDFWorked solutions in progress

Questions

1
Work out $2015 + 329$ .
Worked solution
Being written
2
Work out $2015 - 329$ .
Worked solution
Being written
3
Work out $2898 \times 9$ .
Worked solution
Being written
4
Work out $2898 \div 6$ .
Worked solution
Being written
5
Work out $\dfrac{5}{7}$ of $84$ .
Worked solution
Being written
6
Write down the next two numbers in the sequence.

$5, \rtqMathsListSeparator 11, \rtqMathsListSeparator 23, \rtqMathsListSeparator 47, \rtqMathsListSeparator \rtqMathsBoxedEmptyValueTwoDigitsWide , \rtqMathsListSeparator \rtqMathsBoxedEmptyValueTwoDigitsWide$
Worked solution
Being written
7
Write a number in each box to complete the statements.
1. 7.a
  $16.7 \times 1000 = \rtqMathsBoxedEmptyValueFourDigitsWide$
2. 7.b
  $\rtqMathsBoxedEmptyValueFourDigitsWide \div 100 = 3.7$
Worked solution
Being written
8
Which number is one hundred less than three thousand and sixteen?
Worked solution
Being written
9
Write the missing sign $( = , <$ or $>)$ in the box.

$19 \times 3 \rtqMathsSpaceQuarterEm \rtqMathsRelationBoxedEmptyUnknown \rtqMathsSpaceQuarterEm 28 \times 2$
Worked solution
Being written
10
The temperature inside Nanook's igloo is $9 \degree \text{C}$ and the temperature outside is $-12 \degree \text{C}$ .

How many degrees warmer is it inside than outside?
Worked solution
Being written
11
Draw lines from the centre to help you shade $20\%$ of this shape.

Worked solution
Being written
12
Sherry's train to Bristol was scheduled to leave at $13 \rtqMathsTimeSeparator 40$ and to arrive at $14 \rtqMathsTimeSeparator 20$ .

However, the train left eight minutes late and then took $47 \rtqMathsUnit{minutes}$ .

At what time did Sherry arrive?
Worked solution
Being written
13
Which number between $60$ and $80$ is a multiple of both $3$ and $8$ ?
Worked solution
Being written
14
Lisa thinks of her favourite number.

She multiplies her favourite number by $2$ , subtracts $3$ and gets $19$ .

What is Lisa's favourite number?
Worked solution
Being written
15
1. 15.a
  Daniel and Bella are playing a game.
  
  When Daniel calls out a number, Bella multiplies it by $3$ and then subtracts $5$ and writes down the result.
  
  For example, when Daniel calls out $2$ , Bella writes down $1$ .
  
  They record the numbers in a table.
  
  Complete the table below.
  
  Daniel calls out Bella writes down
  $5$
  $19$
  $-2$
2. 15.b
  Claire and Erin play a similar game.
  
  They record their results in the table below.
  
  Claire calls out Erin writes down
  $-1$ $1$
  $0$ $4$
  $1$ $7$
  $2$ $10$
  
  Work out what Erin does to each number that Claire calls out.
Worked solution
Being written
16
Cameron has five number cards.

$\rtqMathsSizeEight{\rtqMathsBoxedValue{1}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedValue{2}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedValue{3}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedValue{4}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedValue{5}}$

The cards can be placed together to form a number.

For example, using three of his cards Cameron can create the smallest $3$ -digit multiple of $3$ .

$\rtqMathsSizeEight{\rtqMathsBoxedValue{1}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedValue{2}} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedValue{3}}$

In the questions that follow, choosing from Cameron's cards, write numbers on the blank cards to make:
1. 16.a
  the smallest possible $3$ -digit multiple of $6$
  
  $\rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide}$
2. 16.b
  the largest possible $2$ -digit prime number
  
  $\rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide}$
3. 16.c
  the largest possible $4$ -digit multiple of $5$
  
  $\rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeEight{\rtqMathsBoxedEmptyValueOneDigitWide}$
Worked solution
Being written

Daniel calls out	Bella writes down
$5$
	$19$
	$-2$

Claire calls out	Erin writes down
$-1$	$1$
$0$	$4$
$1$	$7$
$2$	$10$

The information on a pack of “Salmon pasta” is shown in the table.

NUTRITION per $100 \rtqMathsUnit{g}$
Protein	$10 \rtqMathsUnit{g}$
Carbohydrate	$15 \rtqMathsUnit{g}$
Fat	$5 \rtqMathsUnit{g}$
Fibre	$2 \rtqMathsUnit{g}$
Salt	$0.5 \rtqMathsUnit{g}$

17.a
How many grams of protein are in $100 \rtqMathsUnit{g}$ of “Salmon pasta”?
17.b
What percentage of the “Salmon pasta” is carbohydrate?
17.c
The mass of the fibre in a pack of “Salmon pasta” is $7 \rtqMathsUnit{grams}$ .

What is the mass of “Salmon pasta” in the whole pack?
17.d
What will be the mass of fat in a pack of “Salmon pasta”?

Worked solution

Being written

18
Mrs King asked all the children in Year $6$ if they play tennis.

This table shows some of the results.

play tennis do not play tennis total
Class $6 \text{A}$ $13$ $23$
Class $6 \text{B}$ $15$
total $25$ $48$
1. 18.a
  How many children are there in class $6 \text{B}$ ?
2. 18.b
  Complete the table.
3. 18.c
  What fraction of the children who do not play tennis are in class $6 \text{B}$ ?
Worked solution
Being written
19
It is known that $425 \times 134 = 56950$ .

Use this calculation to work out:
1. 19.a
  $4.25 \times 1.34$
2. 19.b
  $56950 \div 4.25$
3. 19.c
  $42.5 \times 67$
Worked solution
Being written
20
In a magic square, the sum of the numbers in each row, each column and each diagonal is the same.

Write numbers in the pale grey squares to complete this magic square.

pale grey $3$ $2$ pale grey
$5$ $10$ $11$ $8$
$9$ $6$ pale grey $12$
$4$ pale grey pale grey $1$
Worked solution
Being written
21
Barbara buys a box containing a selection of three types of biscuit.

There are eight chocolate biscuits.

A third of the other biscuits are custard creams.

There are twelve ginger biscuits.
1. 21.a
  How many custard creams are there?
2. 21.b
  How many biscuits are in the box?
Worked solution
Being written
22
In a box of shapes there are three times as many squares as there are circles.

There are twice as many triangles as squares.

If there are $45$ squares, how many shapes are there altogether?
Worked solution
Being written

	play tennis	do not play tennis	total
Class $6 \text{A}$	$13$		$23$
Class $6 \text{B}$		$15$
total		$25$	$48$

Which bus takes the shortest time from Elgin to Inverness and by how many minutes?

	Bus P	Bus Q
Elgin	$11.47 \rtqMathsTimeMeridiem{a.m.}$	$12.33 \rtqMathsTimeMeridiem{p.m.}$
Inverness	$1.06 \rtqMathsTimeMeridiem{p.m.}$	$1.50 \rtqMathsTimeMeridiem{p.m.}$

Worked solution

Being written

24
Janet's marks on five mental arithmetic tests are:

$15 \rtqMathsListSeparator 19 \rtqMathsListSeparator 13 \rtqMathsListSeparator 18 \rtqMathsListSeparator 20$

What is her mean (average) mark?
Worked solution
Being written
25
What number is indicated by the arrow on the scale?

Worked solution
Being written
26
A parallelogram has area $12 \rtqMathsUnit{cm}^2$ and all its vertices (corners) lie on the dots of the centimetre square dotted grid.

One side of the parallelogram, which is not a rectangle, is drawn for you.

Complete the drawing of the parallelogram.

Worked solution
Being written
27
Which is more likely, rolling a $3$ with an unbiased die with six faces, or getting a head with a fair coin?
Worked solution
Being written
28
Reflect the shaded shape in the mirror line.

Worked solution
Being written
29
In the long jump competition, children recorded their results in a bar chart:
1. 29.a
  Daya jumped $1.5 \rtqMathsUnit{m}$ .
  
  Draw the bar to represent Daya's jump.
2. 29.b
  By how many centimetres did Anna beat Clara?
Worked solution
Being written
30
Penny places $10 \rtqMathsUnitCurrencyPence$ coins, touching, in a straight line.

She hopes to make a line of coins that measures $1 \rtqMathsUnit{km}$ .

A $10 \rtqMathsUnitCurrencyPence$ coin has a diameter of $25 \rtqMathsUnit{mm}$ .
1. 30.a
  How long, in metres, is a line of forty $10 \rtqMathsUnitCurrencyPence$ coins?
2. 30.b
  What is the total value, in pounds, of forty $10 \rtqMathsUnitCurrencyPence$ coins?
3. 30.c
  How many coins will Penny need for a $1 \rtqMathsUnit{kilometre}$ line of $10 \rtqMathsUnitCurrencyPence$ coins?
4. 30.d
  What is the total value of a $1 \rtqMathsUnit{kilometre}$ line of $10 \rtqMathsUnitCurrencyPence$ coins?
Worked solution
Being written
31
Joanna was born on $19$ August $2004$ and her mother, Wendy, was born on the same date $26$ years earlier.
1. 31.a
  What is Joanna's age, on $1 ^\text{st}$ January, in $2016$ ?
2. 31.b
  In which year, on $1 ^\text{st}$ January, will Wendy's age be three times Joanna's age?
Worked solution
Being written
32
Six girls took a maths test.

Their marks were $13 \rtqMathsListSeparator 18 \rtqMathsListSeparator 14 \rtqMathsListSeparator 20 \rtqMathsListSeparator 7 \rtqMathsListSeparator 18$
1. 32.a
  What is the difference between the highest and lowest marks?
2. 32.b
  Ashleigh's mark was seven more than Bella's mark and six less than Connie's mark.
  
  What was Ashleigh's mark?
Worked solution
Being written
33
Amira checks the time when she sets off on her journey to school in the morning.
1. 33.a
  Write the time as a $12 \text{-hour}$ time.
2. 33.b
  At twenty minutes to eight, Amira stops to buy an apple from the shop.
  
  Write “twenty minutes to eight” as a $12 \text{-hour}$ clock time.
3. 33.c
  Amira spends five minutes at the shop before walking another twenty-three minutes to get to school.
  
  At what time does Amira reach school?
Worked solution
Being written
34
The diagram below shows information about the girls in Year $6$ who play in the hockey team and/or the netball team.

hockey not hockey
netball $9$ $6$
not netball $7$ $3$
1. 34.a
  How many girls are in Year $6$ ?
2. 34.b
  How many of the girls play in both teams?
3. 34.c
  What percentage of the girls play in the hockey team but not in the netball team?
4. 34.d
  What fraction of the girls who play netball also play hockey?
Worked solution
Being written
35
The diagram shows two squares. The larger square has perimeter $16 \rtqMathsUnit{cm}$ .

What is the area of the smaller, white square?
Worked solution
Being written
36
Bertie the Bee flies in straight lines from $A$ , $10 \rtqMathsUnit{cm}$ to $B$ and then from $B$ to $C$ which is $10 \rtqMathsUnit{cm}$ due south of $A$ .

Below is an accurate diagram of Bertie's route.
1. 36.a
  On the list below, circle the direction that Bertie flies to get from $B$ to $C$ .
  
  north-east $\rtqMathsListSeparator$ south-west $\rtqMathsListSeparator$ north-west $\rtqMathsListSeparator$ south-east
2. 36.b
  Bertie then flies from $C$ back to $A$ .
  
  Estimate the total distance that Bertie flies.
Worked solution
Being written
37
A matchbox measures $1 \rtqMathsUnit{cm}$ high, $3 \rtqMathsUnit{cm}$ wide and $5 \rtqMathsUnit{cm}$ long.
1. 37.a
  What is the maximum number of matchboxes that could fit, in one layer, onto a tray that is $20 \rtqMathsUnit{cm}$ long and $15 \rtqMathsUnit{cm}$ wide?
2. 37.b
  What is the maximum number of matchboxes that could be fitted into a box measuring $18 \rtqMathsUnit{cm}$ by $25 \rtqMathsUnit{cm}$ by $10 \rtqMathsUnit{cm}$ ?
Worked solution
Being written
38
A rhombus has been drawn on the grid below.

The co-ordinates of three points are listed below.

$P(5, 3) \rtqMathsListSeparator Q(5, 9) \rtqMathsListSeparator R(4, 4)$

Write the letter names of the points that lie inside the rhombus.
Worked solution
Being written
39
In order to convert from the imperial units ounces and pounds to the metric unit kilograms, you should use the following conversions:

$\begin{aligned} 16 \rtqMathsUnit{ounces} &= 1 \rtqMathsUnit{pound} \\ 2.2 \rtqMathsUnit{pounds} &= 1 \rtqMathsUnit{kg} \end{aligned}$

Newborn tiger cubs weigh about $56 \rtqMathsUnit{ounces}$ .

Circle the mass in kilograms which gives the best approximation of the mass of a newborn tiger cub.

$0.5 \rtqMathsUnit{kg}$

$1 \rtqMathsUnit{kg}$

$1.5 \rtqMathsUnit{kg}$

$2 \rtqMathsUnit{kg}$

$2.5 \rtqMathsUnit{kg}$

$3 \rtqMathsUnit{kg}$
Worked solution
Being written
40
Here is a pattern made with small equilateral triangles using centimetre dotted isometric paper.
1. 40.a
  Complete pattern $4$ on the isometric paper below.
2. 40.b
  Complete the table showing the number of lines, dots and small triangles in each pattern.
  
  pattern number $1$ $2$ $3$ $4$
  number of small triangles $1$ $4$
  perimeter (cm) $3$ $12$
  number of dots $3$ $10$
3. 40.c
  How many small triangles are there in pattern $6$ ?
4. 40.d
  What is the perimeter of pattern $10$ ?
5. 40.e
  Which pattern has $45$ dots?
Worked solution
Being written
41
Two icebergs, $A$ and $B$ , are floating in the ocean.

On $1$ January, iceberg $A$ weighs $4 \rtqMathsUnit{tonnes}$ , but loses $25 \rtqMathsUnit{kg}$ every day.

$1000 \rtqMathsUnit{kg} = 1 \rtqMathsUnit{tonne}$
1. 41.a
  After how many days will iceberg $A$ weigh $3850 \rtqMathsUnit{kg}$ ?
2. 41.b
  On $1$ January, iceberg $B$ weighs $4500 \rtqMathsUnit{kg}$ and loses $50 \rtqMathsUnit{kg}$ every day.
  
  After how many days will the two icebergs have the same mass?
Worked solution
Being written
42
1. 42.a
  In the tower of bricks below, the number on a brick is the sum of the numbers on the two bricks supporting it.
  
  What number is on the top brick?
2. 42.b
  In the tower of bricks below, the number on a brick is the product of the two bricks supporting it.
  
  What number is on the top brick?
3. 42.c
  In the tower of bricks below, the number on a brick is the product of the two bricks supporting it.
  
  The number on the top brick is $72$ and the numbers on the bricks are all different whole numbers.
  
  What number is on the middle brick in the bottom row?
Worked solution
Being written
43
A number machine works to the rule “cube each digit and then add the cubes together.”

For example:

input $46$ gives output $280$ , as shown below:

$\begin{aligned} &= 4^\text{3} + 6^\text{3} \\\\ &= 64 + 216 \\\\ &= 280 \end{aligned}$

input $123$ gives output $36$ :

$\begin{aligned} &= 1^\text{3} + 2^\text{3} + 3^\text{3} \\\\ &= 1 + 8 + 27 \\\\ &= 36 \end{aligned}$
1. 43.a
  Work out the output for input $25$ .
2. 43.b
  What three-digit input would give output $3$ ?
3. 43.c
  Input $153$ gives output $153$ .
  
  Which two numbers between $300$ and $400$ will also give output $153$ ?
Worked solution
Being written
44
Wendy has three spinners $A, B$ and $C$ .
1. 44.a
  However many times spinner $A$ is spun and the scores are added, you always get an even total.
  
  Write a different number (choosing from $1$ to $9$ ) in each section of the spinner.
  Spinner A is a quadrilateral divided into four sections with a central pointer.
2. 44.b
  When spinner $B$ is spun, the result is always a prime number.
  
  Write a different number (choosing from $1$ to $9$ ) in each section of the spinner.
  Spinner B is a quadrilateral divided into four sections with a central pointer.
3. 44.c
  When spinner $C$ is spun there is an equal chance of getting a cube number or a multiple of $3$ .
  
  Write a different number (choosing from $1$ to $8$ ) in each section of the spinner.
  Spinner C is a quadrilateral divided into four sections with a central pointer.
4. 44.d
  If each spinner is spun $100$ times and the $100$ scores added, which spinner is likely to score the highest total, and why?
Worked solution
Being written
45
A bird has $2$ legs, a cat has $4$ legs, an insect has $6$ legs and a spider has $8$ legs.

Claire looks at some animals and counts all their legs.

She counts $38$ legs.

There are twice as many birds as spiders and twice as many cats as insects.

How many of each type of animal can she see?
Worked solution
Being written
46
Tia adds three consecutive prime numbers:

$5 + 7 + 11 = 23$

She does this two more times:

$\begin{aligned} 7 + 11 + 13 &= 31 \\\\ 11 + 13 + 17 &= 41 \end{aligned}$

Tia is delighted to see that the sum of three consecutive prime numbers seems to give another prime number.
1. 46.a
  Complete the following statements:
  46.a.i
  $17 + 19 + 23 = \rtqMathsUnderlineEmptyValueMedium$
  46.a.ii
  $\rtqMathsUnderlineEmptyValueMedium + \rtqMathsUnderlineEmptyValueMedium + \rtqMathsUnderlineEmptyValueMedium = 71$
  46.a.iii
  $\rtqMathsUnderlineEmptyValueMedium + \rtqMathsUnderlineEmptyValueMedium + \rtqMathsUnderlineEmptyValueMedium = 83$
2. 46.b
  The prime numbers between $20$ and $140$ are:
  
  $23$ , $29$ , $31$ , $37$ , $41$ , $43$ , $47$ , $53$ , $59$ , $61$ , $67$ , $71$ , $73$ , $79$ , $83$ , $89$ , $97$ , $101$ , $103$ , $107$ , $109$ , $113$ , $119$ , $127$ , $131$ , $137$ and $139$ .
  
  Which two groups of three consecutive prime numbers, between $10$ and $50$ , have a sum which is not prime?
Worked solution
Being written