Solihull School Paper 1

$\rtqMathsColumnarArithmeticStyle \begin{array}{cccccccccccccc} & 5 & 8 & 5 & 9 \\ {}+ & 7 & 3 & 9 & 4 \\ \hline \end{array}$

$\rtqMathsColumnarArithmeticStyle \begin{array}{cccccccccccccc} & 7 & 6 & 5 \\ {}- & 3 & 8 & 9 \\ \hline \end{array}$

$\rtqMathsColumnarArithmeticStyle \begin{array}{cccccccccccccc} & 6 & 7 & 4 \\ {}\times & & & 7 \\ \hline \end{array}$

$\dfrac {2536} {4}$

How many seconds are there in $8 \rtqMathsUnit{minutes}$?

All these fractions are the same:

$\dfrac {2} {3}, \rtqMathsListSeparator \dfrac {10} {15}, \rtqMathsListSeparator \dfrac {60} {90}, \rtqMathsListSeparator \dfrac {x} {24}, \rtqMathsListSeparator \dfrac {50} {y}$

Here are some numbers:

$0.9, \rtqMathsListSeparator 0.899, \rtqMathsListSeparator 0.0999, \rtqMathsListSeparator 0.909, \rtqMathsListSeparator 0.09, \rtqMathsListSeparator 0.9009$

Mark has $400$ football stickers. He sticks $70 \%$ into his football sticker book, swaps $25 \%$ with his friend Peter and gives the rest away.

There are $329$ days until my birthday. How many weeks is this?

Write the number two hundred and $4$ million, thirty five thousand and eighty two in figures.

What is the next number in each of these sequences?

I think of a number, multiply it by $6$ and subtract $7$ to get an answer.

If you buy $8$ second class stamps costing $44 \rtqMathsUnitCurrencyPence$ each, how much change would you receive from $\rtqMathsSymbolPound 5$?

A train leaves Solihull at $6.35 \rtqMathsTimeAm$ and arrives at Liverpool at $10.22 \rtqMathsTimeAm$.

How many minutes does it take?

Mia cycles at $12 \rtqMathsUnit{mph}$. How far does she travel in:

A hockey tournament has $32$ teams competing, each with $11$ players.

Amy gets in a muddle with her arithmetic.

When it says add she always takes away.

When it says take away she always adds.

When it says multiply she always divides.

When it says divide she always multiplies.

What does she give as the answer to:

A test to find whether a number is divisible by $9$ is to add up the digits. If the result is divisible by $9$ so is the original number.

For example, in the number $576$, the sum of the digits is $5 + 7 + 6 = 18$.

Since $18$ is exactly divisible by $9$, the number $576$ is also divisible by $9$.

On the other hand, in the number $1357$, the sum of the digits is $1 + 3 + 5 + 7 = 16$.

Since $16$ is not divisible by $9$, the number $1357$ is not divisible by $9$.

If you go on holiday to Canada and change your Pounds into Canadian Dollars, you receive Dollars at the rate of $5$ Dollars for every $3$ Pounds.

In this question the shapes are NOT drawn to scale.

James starts a journey at $10.00 \rtqMathsTimeAm$ and drives at $60 \rtqMathsUnit{mph}$ until $1.00 \rtqMathsTimePm$.

Here is a sum with some signs missing

$2 \rtqMathsSpaceQuarterEm \rtqMathsBinaryOperatorBoxedEmptyUnknown \rtqMathsSpaceQuarterEm 3 \rtqMathsSpaceQuarterEm \rtqMathsBinaryOperatorBoxedEmptyUnknown \rtqMathsSpaceQuarterEm 4 = 10$

You can make it correct by putting in the correct signs:

$2 \times 3 + 4 = 10$

Fill in the gaps below to make the sums correct.

You may use any of the signs $+, -, \times, \div$ and you can use brackets if you wish.

The rule $a \rtqMathsBinaryOperatorAsterisk b$ means $a \times a + b \times b$.

That is, you multiply the first number by itself, multiply the second number by itself and then add the answers together.

For example,

$\begin{aligned} 2 \rtqMathsBinaryOperatorAsterisk 3 &= 2 \times 2 + 3 \times 3 \\\\ &= 4 + 9 \\\\ &= 13 \end{aligned}$

And:

$\begin{aligned} 1 \rtqMathsBinaryOperatorAsterisk 2 &= 1 \times 1 + 2 \times 2 \\\\ &= 1 + 4 \\\\ &= 5 \end{aligned}$

A rule for numbers is to add $12$ and divide the answer by $2$.

For example if you start with $10$ you add $12$ and get $22$ and then you divide by $2$ to get $11$.

So applying the rule to the number $10$ you get the answer $11$.

Some numbers read the same forwards and backwards, like $343$ and $1221$. We call these numbers “mirror numbers”.

The three digit number $452$ has a digit sum of $11$ because $4 + 5 + 2 = 11$.

The three digit number $584$ has a digit sum of $17$ because $5 + 8 + 4 = 17$.

Write down in the space below all $3$ digit numbers that have a digit sum equal to $25$.

There is a number of coins on a table. One quarter of them are showing heads. If I turn over two more coins to show heads then one third of the coins now show heads.

How many coins are on the table?

I want to draw a square in which the perimeter (total length around the outside) is equal in size to the area.

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the circles).

In the multiplication $6 \times 2 = 3$ all the digits are correct, but they are in the wrong places. The sum should be $2 \times 3 = 6$ or $(3 \times 2 = 6)$.

Another example is $3 \times 16 = 8$. This is wrong. It should be $3 \times 6 = 18$.

In the multiplications below the digits are also correct but in the wrong places. Write them again in the correct way:

Some of the digits are missing in the multiplications below. Find the missing digits and write out the multiplications in the answer box. You may use the same digit more than once.