Merchant Taylors' School Paper 1

IndependentBoys

31 questions

Original PDFWorked solutions in progress

Questions

1
Write down what the $4$ stands for in $3427$ .
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2
1. 2.a
  What is the eighth even number?
2. 2.b
  What is the fifth prime number?
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3
What is the smallest number which can be divided by $3, 4, 5$ and $6$ exactly?
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4
A child's heart beats $80 \rtqMathsUnit{times per minute}$ .

How many times will it beat between $05 \rtqMathsTimeSeparator 30$ and $15 \rtqMathsTimeSeparator 30$ on the same day?
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5
I think of a number and multiply it by $3$ and then subtract $6$ .

If the result is $15$ what number was I thinking of?
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6
Write down the next two terms in each of the sequences below:
1. 6.a
  $10, \rtqMathsListSeparator 13, \rtqMathsListSeparator 16, \rtqMathsListSeparator 19, \rtqMathsListSeparator 22, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
2. 6.b
  $60, \rtqMathsListSeparator 59, \rtqMathsListSeparator 57, \rtqMathsListSeparator 54, \rtqMathsListSeparator 50, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
3. 6.c
  $1, \rtqMathsListSeparator 2, \rtqMathsListSeparator 6, \rtqMathsListSeparator 24, \rtqMathsListSeparator 120, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
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7
Fill in the missing operations in the boxes:
1. 7.a
  $2 \longrightarrow \rtqMathsBoxedCellFourDigitsWideOneDigitHigh{\times 5} \longrightarrow \rtqMathsBoxedCellFourDigitsWideOneDigitHigh{} \longrightarrow \rtqMathsBoxedCellFourDigitsWideOneDigitHigh{\times 3} \longrightarrow 39$
2. 7.b
  $7 \longrightarrow \rtqMathsBoxedCellFourDigitsWideOneDigitHigh{} \longrightarrow \rtqMathsBoxedCellFourDigitsWideOneDigitHigh{\div 3} \longrightarrow 5$
3. 7.c
  Give both solutions:
  
  $24 \longrightarrow \rtqMathsBoxedCellFourDigitsWideOneDigitHigh{} \longrightarrow \rtqMathsBoxedCellFourDigitsWideOneDigitHigh{\times 4} \longrightarrow \rtqMathsBoxedCellFourDigitsWideOneDigitHigh{-6} \longrightarrow 26$
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8
Each pupil in a class was asked their favourite colour. The bar graph shows these results.
1. 8.a
  What was the most common favourite colour?
2. 8.b
  How many pupils were in the class?
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9
The following table shows the runs that Michael scored in each of the $11$ cricket matches he played for the school team.

Runs $0$ $25$ $15$ $40$ $52$ $15$ $6$ $8$ $25$ $35$ $10$
1. 9.a
  What was the mean number of runs he scored per innings?
2. 9.b
  What was the median number of runs scored?
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10
If you roll an ordinary six sided die what is the probability of obtaining:
1. 10.i
  10.i.a
  A six
  10.i.b
  An even number
2. 10.ii
  10.ii.a
  If I roll the die $60$ times how many times would you expect to get a $2$ or $3$ ?
  10.ii.b
  If I roll a red die and a blue die together in how many different ways can I get a total of $7$ ?
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11
Angela works for a computer firm. She is paid $\rtqMathsSymbolPound 10000$ , plus $\rtqMathsSymbolPound 100$ for each computer she sells.
1. 11.a
  How much will she earn if she sells $15$ computers?
2. 11.b
  How many computers does she sell if she earns $\rtqMathsSymbolPound 12600$ ?
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12
Find:
1. 12.a
  $20\%$ of $\rtqMathsSymbolPound 840$
2. 12.b
  $12 \dfrac{1}{2}\%$ of $6.80 \rtqMathsUnit{metres}$ , giving your answer in centimetres.
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13

Find the size of the angle, in degrees, turned by the minute hand of a clock as it moves from the:
1. 13.a
  $12$ to the $1$
2. 13.b
  $3$ to the $7$
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14

The above diagram shows a solid box.
1. 14.a
  What is the area of the shaded face?
2. 14.b
  What is the total surface area of the box?
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15
Find $\dfrac{1}{3}$ of $2 \dfrac{1}{4}$ .
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16
1. 16.a
  On the graph plot the following points: $(-2, 4) , (1, 7)$ and $(4, 4)$ .
2. 16.b
  Plot one further point so that the shape made by joining up the four points has $4$ lines of symmetry and rotational symmetry order $4$ .
  
  Write down the co-ordinates of the point you have plotted.
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17
There are $27$ students in Mrs Din's class.

Mrs Din buys $4$ boxes of chocolates.

There are $36$ chocolates in each box.

She shares out the chocolates equally amongst her $27$ students.
1. 17.a
  Work out the number of chocolates each student receives.
2. 17.b
  Work out the number of chocolates left over.
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18

From the numbers in the ring write down all the:
1. 18.a
  square numbers
2. 18.b
  cube numbers
3. 18.c
  prime numbers
4. 18.d
  factors of $56$
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19
Given that $a = 2, b = -3$ and $c = 4$ , find the value of the following expressions:
1. 19.a
  $5a + 2c$
2. 19.b
  $\dfrac{1}{2} a^2 - b$
3. 19.c
  $\dfrac{3ac}{2b^3}$
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20
The number of insects in a colony doubles each week. If there were $100$ insects in the colony at the start of the first week,
1. 20.a
  how many would there be after $6 \rtqMathsUnit{weeks}$ ?
2. 20.b
  After how many weeks would there first be more than $100 \rtqMathsDigitGroupSeparator 000$ ?
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21
What are the length and width of a rectangle:
1. 21.a
  whose perimeter is $48 \rtqMathsUnit{cm}$ and whose width is one half of its length?
2. 21.b
  whose area is $48 \rtqMathsUnit{cm}^2$ , perimeter is $32 \rtqMathsUnit{cm}$ and length is greater than width?
3. 21.c
  whose area is $72 \rtqMathsUnit{cm}^2$ , and width is twice its length?
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22
Starting with the number $6$ , the operation $\rtqMathsSymbolWhiteDiamond \rtqMathsSpaceQuarterEm 3$ is applied followed by the operation $\rtqMathsSymbolWhiteUpTriangle \rtqMathsSpaceQuarterEm 1$ to give a final answer of $1$ , as in this example below:

$6 \rtqMathsBinaryOperatorWhiteDiamond 3 \rtqMathsBinaryOperatorWhiteUpTriangle 1 = 1$

Using the same operation for the diamond and triangle, find the missing numbers.
1. 22.a
  $15 \rtqMathsBinaryOperatorWhiteDiamond 3 \rtqMathsBinaryOperatorWhiteUpTriangle 1 = \rtqMathsQuestionMarkPlaceholder$
2. 22.b
  $\rtqMathsQuestionMarkPlaceholder \rtqMathsBinaryOperatorWhiteDiamond 3 \rtqMathsBinaryOperatorWhiteUpTriangle 1 = 8$
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23
John came home from his vacation at his grandmother's with $5$ books.

While he was away he bought $2$ books at the bookshop and got $1$ book as a present from his grandmother. During his stay at his grandmother's, he also gave his cousin $4$ books that he had finished.

How many books did he take with him when he left for his holiday?
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Runs	$0$	$25$	$15$	$40$	$52$	$15$	$6$	$8$	$25$	$35$	$10$

Here is a train timetable.

Place	Time of departure
Crewe	$08 \rtqMathsTimeSeparator 00$
Wolverhampton	$08 \rtqMathsTimeSeparator 40$
Birmingham	$09 \rtqMathsTimeSeparator 00$
Coventry	$09 \rtqMathsTimeSeparator 30$
Rugby	$09 \rtqMathsTimeSeparator 40$
Milton Keynes	$10 \rtqMathsTimeSeparator 10$
London	$10 \rtqMathsTimeSeparator 45$

24.a
How many minutes should it take the train to travel from Wolverhampton to Milton Keynes?
24.b
If the train is $35 \rtqMathsUnit{minutes}$ late leaving Crewe, what time should it arrive in London?

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25
List all the positive integers less than $20$ that have TWO different factors, other than $1$ and itself.
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26
Mark has a market stall.

He sells apples at $56 \rtqMathsUnitCurrencyPence$ for each kilogram.

Bianca buys $4 \rtqMathsUnit{kilograms}$ of apples. She pays for her apples with a $\rtqMathsSymbolPound 5$ note.
1. 26.a
  How much change should she get?
2. 26.b
  Mark bought $25$ melons for his stall. He paid $\rtqMathsSymbolPound 16$ for $25$ melons.
  
  Work out the price Mark paid for each melon, in pence.
3. 26.c
  Five of the melons were bad. Mark sold the other $20$ for $120 \rtqMathsUnitCurrencyPence$ each.
  
  Work out the total amount for which Mark sold the melons.
4. 26.d
  Work out what profit Mark made in selling the melons, giving your answer as a fraction of the cost of buying the melons.
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27
Find the angles marked in the diagram.

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28
At noon the temperature is $3 \rtqMathsSpaceQuarterEm \text{degrees Celsius}$ and it rises at a steady $1.5 \rtqMathsSpaceQuarterEm \text{degrees per hour}$ throughout the afternoon.
1. 28.a
  What will the temperature be at $1500 \rtqMathsUnit{hrs}$ ?
2. 28.b
  From $1800 \rtqMathsUnit{hrs}$ the temperature begins to fall at a steady rate so that by midnight it is $-3 \rtqMathsSpaceQuarterEm \text{degrees}$ and continues to fall at this same rate through the rest of the night.
  
  What will the temperature be by $0400 \rtqMathsUnit{hrs}$ ?
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29
Yesterday was one of those days. Not only did my watch break at $10.24 \rtqMathsTimeMeridiem{a.m.}$ but when I shook it the watch started going backwards at the correct rate. What is the real time if my watch shows:
1. 29.a
  $10.10 \rtqMathsTimeMeridiem{a.m.}$
2. 29.b
  $9.43 \rtqMathsTimeMeridiem{a.m.}$
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30
This mystery number has $4$ digits.

Every digit is an odd number.

None of the digits is a $9$ .

Every digit in the number is different.

The smallest digit is in the thousands place.

The greatest digit is in the ones place.

This describes two possible numbers. The mystery number is the greater of those two numbers.

What is the mystery number?
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31
$2$ packets of crisps and $2$ drinks costs $\rtqMathsSymbolPound 1.50$ . $2$ packets of crisps and $1$ drink costs $\rtqMathsSymbolPound 1.10$ .

What would it cost me if I buy $3$ packets of crisps and $4$ drinks?
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Runs	$0$	$25$	$15$	$40$	$52$	$15$	$6$	$8$	$25$	$35$	$10$

Place

Time of departure

Crewe

08 \rtqMathsTimeSeparator 00

Wolverhampton

08 \rtqMathsTimeSeparator 40

Birmingham

09 \rtqMathsTimeSeparator 00

Coventry

09 \rtqMathsTimeSeparator 30

Rugby

09 \rtqMathsTimeSeparator 40

Milton Keynes

10 \rtqMathsTimeSeparator 10

London

10 \rtqMathsTimeSeparator 45