Forest School 2012 · Paper 1

Work out $57+26$.

Work out $34-18$.

Work out $324 \times 11$.

Work out $3138 \div 6$.

How many hours were there in the year $2011$?

Isaac has $\rtqMathsSymbolPound 148$ and he spends $\rtqMathsSymbolPound 97$. How much does he have left?

Find $\dfrac{3}{4}$ of $30$.

What number is exactly halfway between $1\dfrac{1}{2}$ and $3$?

Calculate $3.6 \div 0.4$.

The bus should leave my house at $3 \rtqMathsTimeSeparator 46 \rtqMathsTimePm$ and should take $12 \rtqMathsUnit{minutes}$ to get to the train station. The bus arrives $4 \rtqMathsUnit{minutes}$ late and then takes $6 \rtqMathsUnit{minutes}$ longer than usual to get to the station.

What time do I arrive at the station?

How many thirds are there in $2\dfrac{2}{3}$?

Using $7$, $6$, $5$, $4$ in order and addition and subtraction signs we can make $10$, as shown below.

$7 \rtqMathsSpaceQuarterEm - \rtqMathsSpaceQuarterEm 6 \rtqMathsSpaceQuarterEm + \rtqMathsSpaceQuarterEm 5 \rtqMathsSpaceQuarterEm + \rtqMathsSpaceQuarterEm 4 \rtqMathsSpaceQuarterEm = \rtqMathsSpaceQuarterEm 10$

Fill in the gaps below with either addition or subtraction signs to make $12$.

$7 \rtqMathsSpaceQuarterEm \rtqMathsSpaceQuarterEm \rtqMathsBinaryOperatorBoxedEmptyUnknown \rtqMathsSpaceQuarterEm \rtqMathsSpaceQuarterEm 6 \rtqMathsSpaceQuarterEm \rtqMathsSpaceQuarterEm \rtqMathsBinaryOperatorBoxedEmptyUnknown \rtqMathsSpaceQuarterEm \rtqMathsSpaceQuarterEm 5 \rtqMathsSpaceQuarterEm \rtqMathsSpaceQuarterEm \rtqMathsBinaryOperatorBoxedEmptyUnknown \rtqMathsSpaceQuarterEm \rtqMathsSpaceQuarterEm 4 \rtqMathsSpaceQuarterEm \rtqMathsSpaceQuarterEm = \rtqMathsSpaceQuarterEm \rtqMathsSpaceQuarterEm 12$

Theo bought a chocolate bar for $72 \rtqMathsUnitCurrencyPence$ and some balloons, each of which cost $20 \rtqMathsUnitCurrencyPence$. He paid with a $\rtqMathsSymbolPound 10$ note and received $\rtqMathsSymbolPound 3.88$ change.

How many balloons did he buy?

Four friends each sent good luck cards to each other. How many cards were sent altogether?

Write $0.32$ as a fraction in its lowest terms.

The $15^\text{th}$ of April was a Monday. What day was the $5^\text{th}$ of March of the same year?

A drawer contains $4$ red socks and $4$ blue socks. What is the smallest number of socks you need to take out in order to be sure that you have at least one matching pair?

What digits do the symbols represent in this subtraction?

$\rtqMathsColumnarArithmeticStyle \begin{array}{cccccccccccccc} & \rtqMathsSymbolBlackSquare & 7 & 2 \\ -& 3 & \rtqMathsSymbolBlackTriangle & 8 \\ \hline & 4 & 7 & \rtqMathsSymbolBlackHeartSuit \end{array}$

A coat cost $\rtqMathsSymbolPound 125$ and was then reduced by $20\%$ in a sale.

What is the new price?

What is the smallest positive whole number that is exactly divisible by $2,3,4,5$ and $6$?

Four $1 \rtqMathsUnit{cm}$ squares fit inside a $2 \rtqMathsUnit{cm}$ square as shown here.

How many $1 \rtqMathsUnit{cm}$ equilateral triangles would fit inside a $3 \rtqMathsUnit{cm}$ equilateral triangle?

What is a quarter of $398$?

The mass of a jar $\dfrac{1}{4}$ full of Marmite is $250 \rtqMathsUnit{g}$. It has a mass of $350 \rtqMathsUnit{g}$ when it is $\dfrac{3}{4}$ full.

What is the mass of the empty jar?

A palindromic number is the same when written backwards as forwards, e.g. $454$ is a palindromic number.

How many palindromic numbers are there between $100$ and $200$?

Rehema rolls a fair dice $30$ times. How many times should she expect to get a $5$?

Consecutive whole numbers are next to each other. For example, $4$ and $5$ are consecutive whole numbers. Another example would be $16$ and $17$.

$\sqrt{70}$ lies between two consecutive whole numbers. What are they?

Write, in words, the number $3 \rtqMathsDigitGroupSeparator 052 \rtqMathsDigitGroupSeparator 002$.

Amy thinks of a prime number that is greater than $10$.

She multiplies the number by three.

Maryam says: “Your answer is an odd number.”

Is Maryam correct? Explain your answer carefully.

A toy train of length $16 \rtqMathsUnit{cm}$ approaches a tunnel of length $59 \rtqMathsUnit{cm}$.

How many seconds will it take the train to pass completely through the tunnel at a speed of $5 \rtqMathsUnit{cm/second}$?

A clock is fast. It gains $2 \rtqMathsUnit{minutes}$ every hour. It is set correctly at $1 \rtqMathsTimePm$.

What time does the clock show when the correct time is $8 \rtqMathsTimeSeparator 30 \rtqMathsTimePm$?

In a football match the final score was $3 \text{\textendash} 1$. At half time the score was $1 \text{\textendash} 0$ and during the second half of the match the scores went $2 \text{\textendash} 0$, $2 \text{\textendash} 1$, $3 \text{\textendash} 1$.

In another match the full time score was $4 \text{\textendash} 3$. If the half time score was $2 \text{\textendash} 2$, list all the different possible scores that there could have been during the second half of the game (not including $2 \text{\textendash} 2$).

If:

$\begin{aligned} 5 \rtqMathsBinaryOperatorAsterisk 3 &= 5^2 + 3 \\\\ &= 25 + 3 \\\\ &= 28 \end{aligned}$

Find:

Graph to show the sales of “Mario Kart 37” at Bob's game shop last year

What is $5\%$ of $5 \rtqMathsUnit{kg}$? Give your answer in grams.

$512$ is a Dudeney number because:

$512 = 8 \times 8 \times 8$ and

$8 = 5 + 1 + 2$, the sum of the digits of $512$.

Similarly,

$17576 = 26 \times 26 \times 26$ and

$26 = 1 + 7 + 5 + 7 + 6$

Using the information given below, find two more Dudeney numbers.

$\begin{aligned} 14 \times 14 \times 14 &= 2744 \\\\ 15 \times 15 \times 15 &= 3375 \\\\ 16 \times 16 \times 16 &= 4096 \\\\ 17 \times 17 \times 17 &= 4913 \\\\ 18 \times 18 \times 18 &= 5832 \\\\ 19 \times 19 \times 19 &= 6859 \\\\ 20 \times 20 \times 20 &= 8000 \end{aligned}$

Find the next two numbers in each of these sequences:

What is the area of a square that has perimeter $28 \rtqMathsUnit{cm}$? Give the units with your answer.

In a group of $46$ children, $30$ like carrots, $23$ like bananas and $3$ do not like either.

A journey of $45 \rtqMathsUnit{miles}$ takes me an hour and a half travelling at the same speed throughout.

How far had I gone in $1 \rtqMathsUnit{hour}$?