The Manchester Grammar School 2019 · Section A

Work out $463 + 327$.

Express $\dfrac {18} {25}$ as a decimal.

Work out $547 \times 3000$.

Work out $3.19 - 1.72$.

Add the product of $5$ and $13$ to the sum of $5$ and $13$.

What is the missing number in this list?

$101, \rtqMathsListSeparator 86, \rtqMathsListSeparator 74, \rtqMathsListSeparator 65, \rtqMathsListSeparator \rtqMathsSequenceEllipsis, \rtqMathsListSeparator 56$

Work out $3 \dfrac{3}{4} \div 2 \dfrac{1}{2}$, giving your answer in its simplest form.

What is $30 \%$ of $550 \rtqMathsUnit{cm}^3$?

Express $42 \rtqMathsUnit{minutes}$ as a fraction of one hour, giving your answer in its simplest form.

What is the missing number in the following sum?

$4{,}060{,}800 = 4{,}000{,}000 + \rtqMathsUnderlineEmptyValueMedium + 800$

John thinks of a number. He multiplies that number by four and then adds three to the result. If the answer he obtains is $35$,

What is the number he first thought of?

In a triangle, the largest angle is two times the middle angle and the middle angle is three times the smallest angle.

What is the size of the largest angle?

Alison has $6$ yellow discs, $5$ blue discs and $9$ red discs which she places in a bag.

When she draws one disc out, what is the probability that the disc is NOT red?

A shopkeeper buys a box of $60$ apples for $\rtqMathsSymbolPound 12$. If he finds that $\dfrac{1}{10}$ of the apples are bad and can't be sold, at what price must he sell each of the good apples so that he makes a total profit of $\rtqMathsSymbolPound 15$?

In the picture below is the net of a cube.

What would be the total surface area of the outside of the cube when the net is made into the cube?

Two bottles of water and three small bags of fruit cost a total of $\rtqMathsSymbolPound 2.55$.

If a bottle of water costs $15 \rtqMathsUnitCurrencyPence$ more than a bag of fruit, what is the cost of a bag of fruit?

Bilal has made a box in the shape of a cuboid with sides $4 \rtqMathsUnit{cm}, 5 \rtqMathsUnit{cm}$ and $32 \rtqMathsUnit{cm}$. He wants to make another different shaped box but with the same volume. This box will have a height of $10 \rtqMathsUnit{cm}$ and a square base. What will be the length of the base?

A large number of buses stop at the bus stop at the end of Old Hall Lane. The $42$ bus stops there every $6 \rtqMathsUnit{minutes}$, the $43$ bus stops there every $8 \rtqMathsUnit{minutes}$ and the $45$ bus stops every $15 \rtqMathsUnit{minutes}$. If all the buses stop at the Old Hall Lane stop at $4.00 \rtqMathsTimePm$:

Write down the total number of buses that will call at the stop between $4.20$ and $4.50 \rtqMathsTimePm$.

In a school table-tennis league each team plays each of the other teams twice during the year, once at home and once away.

If there are $30$ matches in total during the season, how many teams are there in the table-tennis league?

Chen writes down a two digit number. He finds that if he swaps the digits of the number round, the new number he creates is three more than one third of the original number.

What was the original number?