Bancroft's School 2017 Paper 1

IndependentCo-ed

37 questions
2 sections

Original PDFWorked solutions in progress

Questions

Section A
Questions 1–30
1. 1
  Fill in the missing numbers in the boxes.
  1.a
  $123 - \rtqMathsBoxedEmptyValueFourDigitsWide = 78$
  1.b
  $( 24 \div 3 ) + ( 12 \div 12 ) = \rtqMathsBoxedEmptyValueFourDigitsWide$
  1.c
  $18 - \rtqMathsBoxedEmptyValueFourDigitsWide + 22 = 37$
  1.d
  $\rtqMathsBoxedEmptyValueFourDigitsWide \times 3 \times 2 \times 1 = 48$
  1.e
  $125 \times 4 = 1000 \div \rtqMathsBoxedEmptyValueFourDigitsWide$
  1.f
  $1.1 + 2.2 + 3.3 + 4.4 = \rtqMathsBoxedEmptyValueFourDigitsWide$
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2. 2
  Add together $4867$ and $285$ .
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3. 3
  Divide $2412$ by $9$ .
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4. 4
  Multiply $257$ by $37$ .
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5. 5
  What number (written in digits) is two hundred and twenty two less than two thousand?
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6. 6
  6.a
  The tables in the Dining Hall can each seat $8$ pupils.
  
  How many tables are needed to seat $180$ pupils?
  6.b
  Jake paid a $\rtqMathsSymbolPound 50$ deposit for a bike, then monthly payments of $\rtqMathsSymbolPound 25$ each. The bike cost $\rtqMathsSymbolPound 275$ .
  
  How many monthly payments did Jake have to make to buy it?
  6.c
  There are $500$ pupils at Lily's school.
  
  There are $30$ more girls than boys.
  
  How many girls are there?
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7. 7
  7.a
  The sum of five consecutive whole numbers is $100$ .
  
  What is the smallest of these five numbers?
  7.b
  The sum of two numbers is $22$ and their difference is $4$ .
  
  What are the two numbers?
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8. 8
  Add the number of sides of a decagon to the number of sides of a pentagon, then multiply by the number of faces of a cuboid.
  
  What is your answer?
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9. 9
  It is $165 \rtqMathsUnit{minutes}$ before midnight. Put one digit into each of the four boxes to show the time on this $24\text{-hour}$ digital clock.
  
  $\rtqMathsSizeTen{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeTen{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSizeTen{\rtqMathsTimeSeparator} \rtqMathsSizeTen{\rtqMathsBoxedEmptyValueOneDigitWide} \rtqMathsSpaceQuarterEm \rtqMathsSizeTen{\rtqMathsBoxedEmptyValueOneDigitWide}$
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10. 10
  10.a
  In the boxes, write the numbers that their arrows are pointing to.
  
  10.b
  Write down (in simplest form) the fraction that the arrow is pointing to.
  
  10.c
  There is some liquid in the container.
  
  How many more millilitres must be added to fill it up to the $900 \rtqMathsUnit{ml}$ mark?
  
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11. 11
  11.a
  Write the following decimal numbers in order from smallest to largest:
  
  $\rtqMathsBoxedValueOneDigitPaddingEachSide{0.505} \rtqMathsListSeparator \rtqMathsBoxedValueOneDigitPaddingEachSide{0.05} \rtqMathsListSeparator \rtqMathsBoxedValueOneDigitPaddingEachSide{0.5005} \rtqMathsListSeparator \rtqMathsBoxedValueOneDigitPaddingEachSide{0.055}$
  11.b
  Write down the decimal number that is equivalent to $0.4 - \dfrac{1}{4}$ .
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12. 12
  12.a
  Calculate $50 \%$ of $20 \%$ of $6000$ .
  12.b
  Calculate $20172017 \div 2017$ .
  12.c
  Jen correctly worked out that $2793 \div 49 = 57$ .
  
  What is the value of $(49 \times 57) + 7$ ?
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13. 13
  At Ali's shop, a multipack of $8$ toilet rolls costs $\rtqMathsSymbolPound 2.40$ .
  
  At Mya's shop, the cost per toilet roll is twice as much.
  
  How much is a pack of $3$ toilet rolls at Mya's shop?
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14. 14
  Write down the number of lines of symmetry (mirror lines) for each shape.
  14.a
  Left-hand shape
  
  14.b
  Right-hand shape
  
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15. 15
  Each number in a sequence is calculated by multiplying the previous number by $100$ then adding $1$ .
  15.a
  If the first number in the sequence is $0$ , what is the fourth number?
  15.b
  If the second number in the sequence is $51$ , what is the first number?
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16. 16
  A sequence of numbers is formed by always adding the same number to get the next number in the sequence.
  
  The $10 ^ \text{th}$ number in the sequence is $23$ and the $15 ^\text{th}$ number is $38$ .
  
  What is the $12 ^ \text{th}$ number?
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17. 17
  Guy is training for a long distance cycle race.
  17.a
  He leaves home and cycles for $10 \rtqMathsUnit{km}$ at a speed of $30 \rtqMathsUnit{km per hour}$ .
  
  How many minutes does this take him?
  17.b
  He then cycles for a further $5 \rtqMathsUnit{km}$ at a speed of $20 \rtqMathsUnit{km per hour}$ .
  
  How many minutes does this take him?
  17.c
  Next, he returns home by the same route, cycling at $30 \rtqMathsUnit{km per hour}$ .
  
  How many minutes does his return journey take?
  17.d
  If Guy left home at $9.30 \rtqMathsTimeAm$ and had no stops, at what time did he arrive back home?
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18. 18
  Billy is $2 \rtqMathsUnit{metres}$ and $2 \rtqMathsUnit{centimetres}$ tall.
  
  Write his height as a decimal, in metres.
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19. 19
  The diagram shows a cross made from square tiles.
  
  The area of the cross is $245 \rtqMathsUnit{cm}^2$ .
  
  19.a
  What is the area of one tile?
  19.b
  What is the length of one side of a tile?
  19.c
  What is the perimeter of the cross?
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20. 20
  A square is folded exactly in half and then in half again.
  
  Which one of the following ( $\text{A, B, C, D}$ or $\text{E}$ ) could not be the resulting shape?
  
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21. 21
  It takes $9 \rtqMathsUnit{litres}$ of paint to cover the surface of the cube on the left.
  
  How many litres of paint would it take to cover the surface of the shape on the right?
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22. 22
  Twelve people (and no more) can sit evenly spaced around a square table.
  
  Deesha puts eight of these square tables together in a row to make one very long rectangular table.
  
  What is the maximum number of people that can sit evenly spaced around this long table?
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23. 23
  The school site covers an area of $8000 \rtqMathsUnit{m}^2$ .
  23.a
  Buildings take up $\dfrac{3}{5}$ of the area. How much area is this?
  23.b
  The playground takes up $\dfrac{1}{4}$ of what is left. How much area is this?
  23.c
  The rest of the site is footpaths and grass. How much area is this?
  23.d
  The area of the grass is seven times the area of the footpaths.
  
  What area is covered in grass?
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24. 24
  The bar chart shows the favourite cold drinks of the students in Class $6\text{A}$ .
  
  24.a
  How many students like squash best?
  24.b
  Four students prefer which drink?
  24.c
  How many more students prefer fizzy drinks to juice?
  24.d
  How many students are in Class $6\text{A}$ ?
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25. 25
  The diagram shows the coordinates of three points $A, B$ and $C$ .
  
  Shape $ABCD$ is a rectangle.
  
  What are the coordinates of point $D$ ?
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26. 26
  Each of the four different symbols stands for a number.
  
  Work out the number that each symbol stands for.
  
  $\begin{aligned} \rtqMathsSymbolBlackTriangle + \rtqMathsSymbolBlackTriangle + \rtqMathsSymbolBlackTriangle &= 27 \\\\ \rtqMathsSymbolBlackTriangle + \rtqMathsSymbolBeamedEighthNotes &= 26 \\\\ \rtqMathsSymbolBeamedEighthNotes - \rtqMathsSymbolBlackHeartSuit &= 9 \\\\ \rtqMathsSymbolBlackTriangle + \rtqMathsSymbolBeamedEighthNotes + \rtqMathsSymbolBlackHeartSuit &= \rtqMathsSymbolBlackSmilingFace \end{aligned}$
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27. 27
  Toby is given four bags of fruit.
  
  Bag A contains $2$ apples, $4$ oranges and $3$ pears.
  
  Bag B contains $4$ apples, $5$ oranges and $3$ pears.
  
  Bag C contains $3$ apples, $6$ oranges and $4$ pears.
  
  Bag D contains $5$ apples, $4$ oranges and $9$ pears.
  
  Toby is allowed to choose one bag and then he is given one piece of fruit from that bag at random.
  27.a
  Which bag should Toby choose to have the greatest chance of getting an apple?
  27.b
  Which bag should Toby choose to have the least chance of getting an orange?
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28. 28
  A wooden cube has edges $2 \rtqMathsUnit{cm}$ long.
  
  28.a
  What is the total length of all its edges?
  28.b
  If the cube is now cut into smaller cubes with edges $1 \rtqMathsUnit{cm}$ long, how many smaller cubes can be made?
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29. 29
  A rectangular garden is surrounded by a path of a fixed width.
  
  The perimeter of the garden is $24 \rtqMathsUnit{metres}$ less than the distance along the outside edge of the path.
  
  What is the width of the path?
  
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30. 30
  Look at the dial.
  
  30.a
  The pointer starts at $0$ and turns clockwise.
  
  Which number does it point to after turning through $270 \rtqMathsSpaceQuarterEm \text{degrees}$ ?
  30.b
  The pointer turns anticlockwise from $1$ to $6$ .
  
  Through how many degrees does it turn?
  30.c
  The pointer starts at $3$ and turns clockwise.
  
  Which number does it point to after turning through $10 \dfrac{1}{4}$ whole turns?
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Section D

Questions 1–7

1
Granny takes one a day of each of two types of tablet.

One type of tablet is in packets of $25$ and the other type is in packets of $20$ .

She starts new packets of both on $1 ^ \text{st}$ March.

On what date will she next start new packets of both?
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2
1. 2.a
  What is the product of the smallest two-digit prime number and the largest two-digit square number?
2. 2.b
  $585$ and $7227$ are examples of palindromic numbers as they read the same when the order of their digits is reversed.
  2.b.i
  Which three-digit number is palindromic, has the sum of its digits equal to $7$ and has the product of its digits equal to $12$ ?
  2.b.ii
  Which five-digit number is palindromic, has the sum of its digits equal to $27$ and has the product of its digits equal to $0$ ?
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3
Paddy is leading in a race.

He is $81 \rtqMathsUnit{metres}$ in front of Sam who is in last place.

Martin is between Paddy and Sam.

Martin is $40 \rtqMathsUnit{metres}$ from the finish line and is twice as far away from Sam as he is from Paddy.

How far has Sam left to run?
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4
Mr Patel and his sons Humza and Kian have the same birthday.

Today, Mr Patel is $34$ , Humza is $6$ and Kian is $3$ .

How old will they be when Mr Patel's age is the sum of his sons' ages?
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5.a
The diagram on the right is the net of a cube.

Which one of the six cubes shown below could not be made from this net?

5.b

A double-decker bus has just ten seats.

There are five seats in a line upstairs and five downstairs.

	$\rtqMathsEmptyValueThreeDigitsWide$	$\rtqMathsEmptyValueThreeDigitsWide$	$\rtqMathsEmptyValueThreeDigitsWide$	$\rtqMathsEmptyValueThreeDigitsWide$	$\rtqMathsEmptyValueThreeDigitsWide$
Front						Back

Dhanyal is sitting directly below Kim and in front of eight people.

Pranav is sitting right at the back, directly above Noor.

Lucy is directly in front of George and directly above Revan.

Chen is just behind Jo and directly below Becky.

5.b.i
Who is directly behind Kim?
5.b.ii
Who is directly in front of Noor?

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6
1. 6.a
  A lottery prize of $\rtqMathsSymbolPound 5555$ was shared equally between a number of people so that each person received a whole number of pounds.
  
  There were between $20$ and $100$ people.
  6.a.i
  How many people shared the prize?
  6.a.ii
  How much did each person receive?
2. 6.b
  Three boxes (A, B and C) contain red balls or yellow balls or both.
  
  Each box contains the same number of balls.
  
  Box A contains all twelve of the red balls and one-ninth of the yellow balls.
  6.b.i
  How many yellow balls are there altogether?
  6.b.ii
  How many balls are there in each box?
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7
1. 7.a
  The total of the numbers in the five boxes below is $222$ and the sum of the numbers in any three adjacent boxes is always the same.
  
  Fill in the numbers in the three empty boxes.
  
  $65$ $40$
2. 7.b
  In the addition sum shown below, different shapes represent different digits.
  
  What digit does each shape represent?
  Two one-digit pentagons and a two-digit number made from six-point stars are added to make a three-digit number made from triangles. To the right, a pentagon, a six-point star and a triangle each have a blank dotted answer line.
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Bancroft's School 2017 · Paper 1

Questions

Section A

Section D

Bancroft's School 2017 · Paper 1

Questions

Section A

Section D

Bancroft's School 2017 Paper 1

Bancroft's School 2017 Paper 1