City of London School for Girls Paper 1

IndependentGirls

36 questions
2 sections

Original PDFWorked solutions in progress

Questions

Section A
Questions 1–25
1. 1
  $3078 + 256$
  Worked solution
  Being written
2. 2
  $3078 - 256$
  Worked solution
  Being written
3. 3
  $158 \times 23$
  Worked solution
  Being written
4. 4
  $3072 \div 12$
  Worked solution
  Being written
5. 5
  What is the reading on the measuring cylinder?
  A vertical two-litre measuring cylinder is marked in 100-millilitre intervals. The liquid level is 1250 millilitres.
  Worked solution
  Being written
6. 6
  What number is twelve less than eight thousand two hundred and seven?
  Worked solution
  Being written
7. 7
  Both of these nets fold to make a cube.
  
  Shade the square that will be opposite the black square when the net is folded into a cube.
  7.a
  7.b
  Worked solution
  Being written
8. 8
  Work out the value of:
  8.a
  $3 \times 7 + 4$
  8.b
  $12 \div 6 \div 2$
  8.c
  $15 - 4 \times 2$
  Worked solution
  Being written
9. 9
  Shade in $\dfrac{3}{5}$ of this shape.
  
  Worked solution
  Being written
10. 10
  Write down the mathematical name for each of these $2\text{D}$ shapes:
  10.a
  10.b
  10.c
  Worked solution
  Being written
11. 11
  Here is a table showing how many minutes four children took to get to school last week:
  
  Maxine Ava Ellie Sara
  Monday $23$ $14$ $12$ $19$
  Tuesday $24$ $17$ $15$ $25$
  Wednesday $31$ $11$ $18$ $41$
  Thursday $26$ $16$ $12$ $22$
  Friday $19$ $16$ $16$ $23$
  11.a
  Who took over $40 \rtqMathsUnit{minutes}$ to get to school?
  11.b
  Which person has the shortest journey to school on any day?
  11.c
  On Thursday, what is the range of the times?
  Worked solution
  Being written
12. 12
  Round $12.05$ to:
  12.a
  The nearest whole number
  12.b
  $1$ decimal place
  Worked solution
  Being written
13. 13
  Here is a bar chart:
  
  The bar for strawberry is missing! Mr Gauss spent $\rtqMathsSymbolPound 15$ on Strawberry ice cream.
  13.a
  Draw a bar to show how much Mr Gauss spent on Strawberry ice cream.
  13.b
  How much did Mr Gauss spend on Vanilla Ice Cream?
  Worked solution
  Being written
14. 14
  Fill in the next two values in this sequence:
  
  $1\dfrac{3} {4}, \rtqMathsListSeparator 2\dfrac{1} {2}, \rtqMathsListSeparator 3\dfrac{1} {4}, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
  Worked solution
  Being written
15. 15
  Draw a net of a triangular prism.
  Worked solution
  Being written
16. 16
  How many edges does a cube have?
  Worked solution
  Being written
17. 17
  Which of the following is the best estimate for the length of a bus?
  
  $0.2 \rtqMathsUnit{km}$
  
  $2 \rtqMathsUnit{m}$
  
  $20 \rtqMathsUnit{cm}$
  
  $20 \rtqMathsDigitGroupSeparator 000 \rtqMathsUnit{mm}$
  
  Worked solution
  Being written
18. 18
  Reflect the grey shape in the dashed mirror line.
  
  Worked solution
  Being written
19. 19
  The temperature in Inverness is $12 \rtqMathsSpaceQuarterEm \text{degrees}$ lower than the temperature in London.
  
  The temperature in London is $5 \rtqMathsSpaceQuarterEm \text{degrees}$ .
  
  What is the temperature in Inverness?
  Worked solution
  Being written
20. 20
  Find the areas of the following shapes:
  20.a
  20.b
  Worked solution
  Being written
21. 21
  Max has more than $4$ apples but fewer than $7$ apples. Alex has more than $5$ apples and fewer than eight apples.
  
  How many apples do Max and Alex have altogether? Circle all the possible values:
  
  $4 \rtqMathsListSeparator 5 \rtqMathsListSeparator 6 \rtqMathsListSeparator 7 \rtqMathsListSeparator 8 \rtqMathsListSeparator 9 \rtqMathsListSeparator 10 \rtqMathsListSeparator 11 \rtqMathsListSeparator 12 \rtqMathsListSeparator 13 \rtqMathsListSeparator 14 \rtqMathsListSeparator 15$
  Worked solution
  Being written
22. 22
  Suki saves $\rtqMathsSymbolPound 12$ in January, $\rtqMathsSymbolPound 18$ in February and $\rtqMathsSymbolPound 5$ in March.
  
  What is her mean (average) monthly saving?
  Worked solution
  Being written
23. 23
  What is $\dfrac{1}{2}$ of $\dfrac{4}{5}$ of $35$ ?
  Worked solution
  Being written
24. 24
  Put the following numbers in order from smallest to largest:
  
  $\dfrac{3}{5} \rtqMathsListSeparator 0.58 \rtqMathsListSeparator \dfrac{5}{8} \rtqMathsListSeparator 62\% \rtqMathsListSeparator 0.508$
  Worked solution
  Being written
25. 25
  You are told that $82 \times 107 = 8774$ .
  
  Use this to work out the value of the following:
  25.a
  $8200 \times 107$
  25.b
  $8774 \div 107$
  25.c
  $8774 \div 41$
  25.d
  A bus can seat $82$ people.
  
  $8770$ people travel to a football match by bus.
  
  How many buses are needed?
  Worked solution
  Being written
Section B
Questions 1–11
1. 1
  Work out the number from the following clues:
  
  It is a whole number.
  
  It is less than $100$ .
  
  It is a square number.
  
  It is one less than a multiple of $5$ .
  
  $16$ is a factor of this number.
  
  Worked solution
  Being written
2. 2
  $\begin{aligned} B + A + T &= 17 \\\\ C + A + T &= 25 \\\\ C + O + A + T &= 29 \end{aligned}$
  
  What is the value of $B + O + A + T$ ?
  Worked solution
  Being written
3. 3
  A rectangle is $6 \rtqMathsUnit{cm}$ longer than it is wide. Its perimeter is $32 \rtqMathsUnit{cm}$ .
  
  Find its area.
  Worked solution
  Being written
4. 4
  On Planet Pythagoras, the people use a different money system to us.
  
  One pog is worth four pings.
  
  Three pings are worth five paz.
  
  Convert the following:
  4.a
  $3 \rtqMathsUnit{pog} = \rtqMathsUnderlineEmptyValueMedium \rtqMathsUnit{pings}$
  4.b
  $40 \rtqMathsUnit{paz} = \rtqMathsUnderlineEmptyValueMedium \rtqMathsUnit{pog}$
  4.c
  $3 \rtqMathsUnit{paz} = \rtqMathsUnderlineEmptyValueMedium \rtqMathsUnit{pog}$
  Worked solution
  Being written
5. 5
  What is the largest number of $15 \rtqMathsUnit{cm}$ by $30 \rtqMathsUnit{cm}$ by $20 \rtqMathsUnit{cm}$ shoe boxes that can fit in a $1 \rtqMathsUnit{m} \times 3 \rtqMathsUnit{m} \times 2 \rtqMathsUnit{m}$ crate?
  
  Be careful - you can't chop up the shoe boxes!
  
  Worked solution
  Being written
6. 6
  Miss Lovelace writes the following pattern on the whiteboard:
  
  $\begin{aligned} 6 \times 6 &= 36 \\\\ 5 \times 7 &= 35 = 36 - 1 \\\\ 4 \times 8 &= 32 = 36 - 4 \\\\ 3 \times 9 &= 27 = 36 - 9 \end{aligned}$
  6.a
  Write down the next line of the pattern.
  
  $\rtqMathsUnderlineEmptyValueShort \times \rtqMathsUnderlineEmptyValueShort = \rtqMathsUnderlineEmptyValueShort = 36 - \rtqMathsUnderlineEmptyValueShort$
  6.b
  Miss Lovelace says this works for other starting numbers as well and writes a second pattern:
  
  $\begin{aligned} 15 \times 15 &= 225 \\\\ 14 \times 16 &= 224 = 225 - 1 \\\\ 13 \times 17 &= 221 = 225 - 4 \end{aligned}$
  
  Complete the following line of the pattern:
  
  $9 \times \rtqMathsUnderlineEmptyValueShort = \rtqMathsUnderlineEmptyValueShort = 225 - \rtqMathsUnderlineEmptyValueShort$
  6.c
  You are told that $137^2 = 18769$ .
  
  Use this fact and the idea above to work out the value of $133 \times 141$ .
  
  (Note: Do not multiply $133$ by $141$ ).
  Worked solution
  Being written
7. 7
  Amy, Bella and Cara have twenty sweets altogether.
  
  Amy says she has ten of the sweets.
  
  Bella says that Cara has one more sweet than Amy.
  
  Cara says that she has the most sweets.
  
  Exactly one of them is lying.
  
  Who is lying? Explain briefly how you know.
  Worked solution
  Being written
8. 8
  The numbers in the following shapes must follow the rule:
  
  To find the number in the circle, multiply the number in the triangle by $3$ , multiply the number in the square by $4$ and find the difference
  
  Example:
  
  Work out the missing values:
  8.a
  8.b
  8.c
  8.d
  Worked solution
  Being written
9. 9
  A theme park wants to make more money. The director thinks that if she reduces the ticket price by one-third, the number of people who come to the theme park will double.
  9.a
  In $2016$ , the park made $\rtqMathsSymbolPound 360$ from ticket sales. Tickets were $\rtqMathsSymbolPound 4.50$ .
  
  How much money does the director think the theme park will make in $2017$ ?
  9.b
  In fact, the theme park makes $\rtqMathsSymbolPound 390$ .
  
  How many more people went to the theme park in $2017$ compared to $2016$ ?
  Worked solution
  Being written
10. 10
  Here is an example of a function machine:
  
  Rule: Multiply by three, then subtract $2$ .
  
  Fill in the gaps in this new function machine:
  
  Rule: .................................
  Worked solution
  Being written
11. 11
  This diagram shows a regular hexagon.
  
  What fraction of the hexagon is shaded?
  Worked solution
  Being written