City of London School Paper 1

IndependentBoys

22 questions

Original PDFWorked solutions in progress

Questions

1. 1
  For this question you can do rough working on the left hand side of the page if required.
  
  Put answers only in the spaces on the right.
  1.a
  $2.74 \times 10,000 = \rtqMathsUnderlineEmptyValueMedium$
  1.b
  $13^2 = \rtqMathsUnderlineEmptyValueMedium$
  1.c
  The square root of $49$ is $\rtqMathsUnderlineEmptyValueMedium$
  1.d
  The cube root of $125$ is $\rtqMathsUnderlineEmptyValueMedium$
  1.e
  $4^3 = \rtqMathsUnderlineEmptyValueMedium$
  1.f
  $\dfrac{240}{300}$ in its simplest form is $\rtqMathsUnderlineEmptyValueMedium$
  1.g
  $25\%$ of $68 = \rtqMathsUnderlineEmptyValueMedium$
  1.h
  $43 \times 38 = \rtqMathsUnderlineEmptyValueMedium$
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2. 2
  The calculator display below shows $\dfrac{2}{9}$ as a decimal.
  
  Complete the empty box to show how the calculator would display the answer to $\dfrac{2}{900}$ .
  
  You do not need to write your digits in the same style, but you should use $10$ digits.
  
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3. 3
  I buy $7$ drinks at $72 \rtqMathsUnitCurrencyPence$ each, and $9$ sandwiches at $\rtqMathsSymbolPound 1.21$ each.
  
  How much change do I get from a $\rtqMathsSymbolPound 20$ note?
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4. 4
  Reflect the letters in the mirror line below. Three letters have been done for you.
  
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5. 5
  Martin is given $\rtqMathsSymbolPound 240$ . He gives $\dfrac{1}{8}$ to his sister and $\dfrac{1}{5}$ of what remains to his little brother.
  
  How much does he keep himself?
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6. 6
  The thermometers below show the temperature recorded at midday yesterday and midnight last night.
  Two vertical thermometers compare midday and midnight temperatures. Each has ticks on both sides, Fahrenheit labels on the left and Celsius labels on the right.
  6.a
  What was the temperature midday yesterday in $\degree \text{F}$ ?
  6.b
  What was the temperature midnight last night in $\degree \text{C}$ ?
  6.c
  What was the difference in temperature between midday yesterday and midnight last night in $\degree \text{C}$ ?
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7. 7
  How many $\text{minutes}$ are there between $9.23 \rtqMathsTimeAm$ and $1.06 \rtqMathsTimePm$ ?
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8. 8
  8.a
  What fraction of the above design is shaded? Give your fraction in its simplest form.
  8.b
  How many more of the hexagons need to be shaded so that $\dfrac{3} {4}$ of the design is shaded?
  8.c
  What fraction of the large rectangle below is shaded?
  
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9. 9
  9.a
  Write $15\%$ as a fraction in its simplest form.
  9.b
  Rowan sends $7$ text messages each day.
  
  A $\rtqMathsSymbolPound 5$ credit buys him $140$ text messages.
  
  Today he received an extra $15\%$ free text messages when he bought his $\rtqMathsSymbolPound 5$ credit.
  
  How many days should the credit last? Show your working.
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10. 10
  In a sponsored walk: Adam took $4 \rtqMathsUnit{hours}, 39 \rtqMathsUnit{minutes}$ ;
  
  Billy took $274 \rtqMathsUnit{minutes}$ and Charlie took $4\dfrac{3}{5} \rtqMathsUnit{hours}$ .
  
  Who was the quickest and who was the slowest?
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11. 11
  The diagram below shows two overlapping rectangles.
  
  11.a
  Calculate the area of the larger rectangle only.
  11.b
  Calculate the total shaded area that the rectangles cover.
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12. 12
  The diagram below shows a rectangle and a square. The diagrams are not drawn to scale.
  
  If they have equal perimeters, what is the difference in their area?
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13. 13
  Calculate the size of the missing angle in this triangle. The diagram is not drawn to scale.
  
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14. 14
  14.a
  Find the size of angle $a$ in the diagram below.
  
  14.b
  How would you describe $100\degree$ ? Acute, obtuse or reflex?
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15. 15
  A right angled triangle is shown below. It is not drawn to scale.
  
  15.a
  Calculate the perimeter of the triangle.
  15.b
  Calculate the area of the triangle.
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16. 16
  
  The diagram above is not drawn to scale.
  16.a
  A box measures $20 \rtqMathsUnit{cm}$ by $11 \rtqMathsUnit{cm}$ by $15 \rtqMathsUnit{cm}$ .
  
  Calculate the volume of the box.
  16.b
  A string is tied around the box with a bow at the top as shown in the diagram.
  
  If the length of the bow is $8 \rtqMathsUnit{cm}$ , calculate the total length of string used.
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17. 17
  $20, \rtqMathsListSeparator 21, \rtqMathsListSeparator 22, \rtqMathsListSeparator 23, \rtqMathsListSeparator 24, \rtqMathsListSeparator 25, \rtqMathsListSeparator 26, \rtqMathsListSeparator 27, \rtqMathsListSeparator 28,$
  
  Write one number from $20$ to $30$ that satisfies the descriptions below. Some numbers are used more than once.
  17.a
  Prime?
  17.b
  Cube numbers?
  17.c
  Square numbers?
  17.d
  Fibonacci numbers?
  
  The Fibonacci numbers follow the sequence $1, 1, 2, 3, 5, 8, 13, \rtqMathsSequenceEllipsis$
  17.e
  Triangular numbers?
  
  The triangular numbers follow the sequence $1, 3, 6, 10, 15, \rtqMathsSequenceEllipsis$
  17.f
  Perfect numbers?
  
  A perfect number is a number whose factors (not including itself) add up to itself.
  
  e.g. $6$ is a perfect number because $1 + 2 + 3 = 6$ .
  17.g
  Powerful numbers?
  
  A powerful number has the property that for every prime number which divides into it, that prime number squared also divides into it.
  
  e.g. $16$ is a powerful number because both $2$ and $2^2$ are factors.
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18. 18
  What is $4 - ((4 + 4) \div 4)$ ?
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19. 19
  $1001 = 𝑎 \times 𝑏 \times 𝑐$ , where $a, b$ and $c$ are prime numbers, with $c$ bigger than $b$ , and $b$ bigger than $a$ .
  
  Find $a$ , $b$ and $c$ .
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20. 20
  Given that $2357 \times 99 = 233 \rtqMathsDigitGroupSeparator 343$ , find:
  20.a
  $233343 \div 99$
  20.b
  $235.7 \times 99$
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21. 21
  The symbol $\rtqMathsSymbolRightArrowWithCircledPlus$ has a special meaning in arithmetic.
  
  $a \rtqMathsBinaryOperatorRightArrowWithCircledPlus b$ means add $a$ and $b$ and then multiply by $a$ .
  
  For example:
  
  $\begin{aligned} 4 \rtqMathsBinaryOperatorRightArrowWithCircledPlus 2 &= 4 \times (4 + 2) \\\\ &= 4 \times 6 \\\\ &= 24 \end{aligned}$
  21.a
  Work out $4 \rtqMathsBinaryOperatorRightArrowWithCircledPlus 5$ .
  21.b
  Work out $4 \rtqMathsBinaryOperatorRightArrowWithCircledPlus (3 \rtqMathsBinaryOperatorRightArrowWithCircledPlus 2)$ .
  21.c
  Work out the value of $p$ such that $6 \rtqMathsBinaryOperatorRightArrowWithCircledPlus p = 78$ .
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22. 22
  Four bells ring at intervals of $2, 8, 7$ and $11 \rtqMathsUnit{seconds}$ .
  
  If they are all rung at the same time, how many seconds will pass before they all ring at the same time again?
  
  You should show some justification for your answer.
  
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