BMAT 2010-S1

The height and weight of three children were measured and the table below used to determine their BMI. Unfortunately some of the data have been lost. We know that Alex is 162cm tall, Jay is 150cm tall and has a BMI of 22, and Charlie is 156cm tall and has a BMI of 24. The combined weight of the children is 172kg.

Societies with a flourishing arts sector (including visual art, theatre, music and dance) tend to be more democratic, more egalitarian, economically more robust and to have more fulfilled, healthier citizens. So, if we want to live in the most democratic, egalitarian and economically robust society, we should demand that the Government subsidises the arts to a level which enables them to flourish.

The pupils in a class took two tests. The results and the teacher’s scatter graph are shown below:

62 trillion spam emails are sent every year, amounting to emissions of more than 17 million tons of carbon dioxide, one of the main contributors to global warming. More effective spam filtering could reduce the amount by 75%, which would be the equivalent of taking 2.3 million cars off the road. This would not deal with the extra energy being used to send out the messages in the first place, however. A better strategy would be to fight spam at the source. When one global web hosting firm was taken offline after it was found to have ties to spammers, global spam volume fell briefly by 70%.

I need to make 72 cakes for when my guests visit tomorrow. I make the cakes in batches of 12. It takes me 40 minutes to prepare each batch and then they need to be in the oven for 25 minutes (during which time I can be working on the next batch). Once they have finished baking, I need to spend 5 minutes putting the cakes out to cool before the oven is ready for the next batch. It is now 1pm.

Scientists have created a model to show how the climate would be affected if, in fifty years’ time, the world suddenly stopped the burning of fossil fuels which produces CO2 emissions. The model assumed that by then CO2 concentrations in the atmosphere would be double preindustrial levels. The scientists calculated that although levels of CO2 would fall as the oceans absorbed it, only one quarter of the CO2 in the atmosphere would have been absorbed in this way by the time the oceans had reached saturation point. The result would be a very small reduction in average global temperatures over the next 1000 years, there would be regular droughts, and sea levels would rise by up to a metre. So if the calculations as to the amount of CO2 that the oceans can absorb are correct, we cannot avoid the disastrous consequences of climate change.

1. It will be impossible suddenly to stop the burning of fossil fuels throughout the world.

2. It may be possible to reduce carbon dioxide levels significantly during the next fifty years.

3. Some predictions made in the past about climate change have not turned out to be accurate.

On a darts scoreboard, each number is made up by some of the lights in a 5 x 3 grid being lit. The correct appearance of each number is shown below:

Darts scores consist of three digits and the score can be anything between 002 and 501.

One night, for one player’s score, the first of the three digits was faulty and three of the lights were permanently on. All other lights were working normally. The score showed 805.

Throughout the world, boys and girls prefer to play with different types of toys. Boys typically like to play with cars and trucks, while girls typically choose to play with dolls. Why is this? A traditional sociological explanation is that boys and girls are socialised and encouraged to play with different types of toys by their parents, peers, and “society”. Growing scientific evidence suggests, however, that boys’ and girls’ toy preferences may have a biological origin.

In 2002, Gerianne M. Alexander of Texas A&M University and Melissa Hines of City University in London stunned the scientific world by showing that vervet monkeys showed the same sex typical toy preferences as humans. In an incredibly ingenious study, published in Evolution and Human Behaviour, Alexander and Hines gave two stereotypically masculine toys (a ball and a police car), two stereotypically feminine toys (a soft doll and a cooking pot), and two neutral toys (a picture book and a stuffed dog) to 44 male and 44 female vervet monkeys. They then assessed the monkeys’ preference for each toy by measuring how much time they spent with each. Their data demonstrated that the male vervet monkeys showed significantly greater interest in the masculine toys, and the female vervet monkeys showed significantly greater interest in the feminine toys. The two sexes did not differ in their preference for the neutral toys.

Throughout the world, boys and girls prefer to play with different types of toys. Boys typically like to play with cars and trucks, while girls typically choose to play with dolls. Why is this? A traditional sociological explanation is that boys and girls are socialised and encouraged to play with different types of toys by their parents, peers, and “society”. Growing scientific evidence suggests, however, that boys’ and girls’ toy preferences may have a biological origin.

In 2002, Gerianne M. Alexander of Texas A&M University and Melissa Hines of City University in London stunned the scientific world by showing that vervet monkeys showed the same sex typical toy preferences as humans. In an incredibly ingenious study, published in Evolution and Human Behaviour, Alexander and Hines gave two stereotypically masculine toys (a ball and a police car), two stereotypically feminine toys (a soft doll and a cooking pot), and two neutral toys (a picture book and a stuffed dog) to 44 male and 44 female vervet monkeys. They then assessed the monkeys’ preference for each toy by measuring how much time they spent with each. Their data demonstrated that the male vervet monkeys showed significantly greater interest in the masculine toys, and the female vervet monkeys showed significantly greater interest in the feminine toys. The two sexes did not differ in their preference for the neutral toys.

Throughout the world, boys and girls prefer to play with different types of toys. Boys typically like to play with cars and trucks, while girls typically choose to play with dolls. Why is this? A traditional sociological explanation is that boys and girls are socialised and encouraged to play with different types of toys by their parents, peers, and “society”. Growing scientific evidence suggests, however, that boys’ and girls’ toy preferences may have a biological origin.

In 2002, Gerianne M. Alexander of Texas A&M University and Melissa Hines of City University in London stunned the scientific world by showing that vervet monkeys showed the same sex typical toy preferences as humans. In an incredibly ingenious study, published in Evolution and Human Behaviour, Alexander and Hines gave two stereotypically masculine toys (a ball and a police car), two stereotypically feminine toys (a soft doll and a cooking pot), and two neutral toys (a picture book and a stuffed dog) to 44 male and 44 female vervet monkeys. They then assessed the monkeys’ preference for each toy by measuring how much time they spent with each. Their data demonstrated that the male vervet monkeys showed significantly greater interest in the masculine toys, and the female vervet monkeys showed significantly greater interest in the feminine toys. The two sexes did not differ in their preference for the neutral toys.

Throughout the world, boys and girls prefer to play with different types of toys. Boys typically like to play with cars and trucks, while girls typically choose to play with dolls. Why is this? A traditional sociological explanation is that boys and girls are socialised and encouraged to play with different types of toys by their parents, peers, and “society”. Growing scientific evidence suggests, however, that boys’ and girls’ toy preferences may have a biological origin.

In 2002, Gerianne M. Alexander of Texas A&M University and Melissa Hines of City University in London stunned the scientific world by showing that vervet monkeys showed the same sex typical toy preferences as humans. In an incredibly ingenious study, published in Evolution and Human Behaviour, Alexander and Hines gave two stereotypically masculine toys (a ball and a police car), two stereotypically feminine toys (a soft doll and a cooking pot), and two neutral toys (a picture book and a stuffed dog) to 44 male and 44 female vervet monkeys. They then assessed the monkeys’ preference for each toy by measuring how much time they spent with each. Their data demonstrated that the male vervet monkeys showed significantly greater interest in the masculine toys, and the female vervet monkeys showed significantly greater interest in the feminine toys. The two sexes did not differ in their preference for the neutral toys.

1 Vervet monkeys respond to toys in the same way as humans.

2 Some monkeys show the preferences alleged by Alexander and Hines.

I am planning to tile my floor. Each tile is square and has a design which is a 3×3 grid of squares. I want to use a combination of 4 different types of tile and when I have finished I want to have used the same number of each tile. I also want the proportion of squares of each colour to be equal.

As examination results come out again there will undoubtedly be concerns about the state ofthe education system. If the results are good then we will hear that the examinations are becoming too easy. On the other hand, if the results are poor, then we will hear about the poor state of funding for the education sector. Since there will be negative stories in the press either way, we should ignore these stories and not worry about them.

These are the most common versions of the digits that appear on digital displays, and are to be assumed in this question.

• top left changes from off to on.

• top right changes from on to off.

Although child road deaths and serious injuries have fallen by 52% in the past ten years, we should not assume that lessons in road safety are no longer vital for school pupils. A Government study reports that in 2006 almost 1,300 boy pedestrians and 700 girl pedestrians were killed or seriously injured in road traffic accidents, and that 500 child cyclists were killed or seriously injured, more than 400 of whom were male.

The image below shows a view of a conventional six sided die with opposite sides adding up to 7 (so the 1 is opposite the 6 etc).

From the position shown the die is rotated 90° in one direction and then 90° in a different direction.

When defending the British Museum’s stance on holding on to important historical artefacts that were taken from other countries, the tale of the Standard of Ur offers a huge case in support of the policy. Had Britain returned it to Iraq, it would have been lost along with so much of the country’s history when the national museum was looted. Consequently, it would have been lost to all of us. By keeping these treasures at the British Museum, their safety is ensured for the whole world.

The Rimmer Club is named after the character from the cult TV series “Red Dwarf” who has the letter H on his forehead.

Tonight is the Rimmer Club’s annual dinner. Rory has been given the task of making place cards. He has decided to make the cards in the form of a letter H, with dimensions as shown below:

He has a number of rectangular sheets of white card, measuring 33cm by 24cm from which to make the cards.

In 2005, the total number of passengers at UK airports rose to 228 million, compared to 5 million in 1955.

The numbers of passengers fell in the recession year of 1974, and in 1991, the year of the Gulf War, before continuing upward. There was also a marked flattening of the upward trend in 2001, the result of the Foot and Mouth outbreak and the September 11 attacks in New York. But these blips were temporary.

The number of passenger kilometres flown by UK airlines increased significantly over the past twenty years, from 80 billion kilometres in 1985 to 287 billion in 2005. Around 97% of the 2005 total was accounted for by international travel.

Nine in ten air passengers at UK airports in 2005 were travelling internationally. The country with which the UK exchanges the most air traffic is Spain. There were 34 million passenger movements between the two countries in 2005.

Heathrow was the busiest airport in the UK, with 68 million passengers in 2005. Gatwick was the second busiest (33 million passengers).

Demand for air travel is projected to continue growing well into the 21st century. Mid-range estimates from the Department for Transport suggest that the number of passengers at UK airports will grow to 500 million in 2030.

Notes:
Passengers on internal flights (domestic) are counted both at airport of departure and arrival.

Domestic passengers are counted both at airport of departure and airport of arrival. Suppose that domestic passengers were counted once per flight instead of both on departure and arrival, and the figures were adjusted accordingly.

In 2005, the total number of passengers at UK airports rose to 228 million, compared to 5 million in 1955.

The numbers of passengers fell in the recession year of 1974, and in 1991, the year of the Gulf War, before continuing upward. There was also a marked flattening of the upward trend in 2001, the result of the Foot and Mouth outbreak and the September 11 attacks in New York.
But these blips were temporary.

The number of passenger kilometres flown by UK airlines increased significantly over the past twenty years, from 80 billion kilometres in 1985 to 287 billion in 2005. Around 97% of the 2005 total was accounted for by international travel.

Nine in ten air passengers at UK airports in 2005 were travelling internationally. The country with which the UK exchanges the most air traffic is Spain. There were 34 million passenger movements between the two countries in 2005.

Heathrow was the busiest airport in the UK, with 68 million passengers in 2005. Gatwick was the second busiest (33 million passengers).

Demand for air travel is projected to continue growing well into the 21st century. Mid-range estimates from the Department for Transport suggest that the number of passengers at UK airports will grow to 500 million in 2030.

Notes:
Passengers on internal flights (domestic) are counted both at airport of departure and arrival.

In 2005, the total number of passengers at UK airports rose to 228 million, compared to 5 million in 1955.

The numbers of passengers fell in the recession year of 1974, and in 1991, the year of the Gulf War, before continuing upward. There was also a marked flattening of the upward trend in 2001, the result of the Foot and Mouth outbreak and the September 11 attacks in New York. But these blips were temporary.

The number of passenger kilometres flown by UK airlines increased significantly over the past twenty years, from 80 billion kilometres in 1985 to 287 billion in 2005. Around 97% of the 2005 total was accounted for by international travel.

Nine in ten air passengers at UK airports in 2005 were travelling internationally. The country with which the UK exchanges the most air traffic is Spain. There were 34 million passenger movements between the two countries in 2005.

Heathrow was the busiest airport in the UK, with 68 million passengers in 2005. Gatwick was the second busiest (33 million passengers).

Demand for air travel is projected to continue growing well into the 21st century. Mid-range estimates from the Department for Transport suggest that the number of passengers at UK airports will grow to 500 million in 2030.

Notes:
Passengers on internal flights (domestic) are counted both at airport of departure and arrival.

1 Between 1980 and 2005 the average increase per annum in the number of passengers more than trebled compared with the previous 25 years.

2 Heathrow and Gatwick between them account for more than 4 out of every 10 passengers passing through UK terminals.

3 To achieve the Department of Transport prediction for 2030, the average increase in the number of passengers going through UK terminals will have to exceed 10 million per annum.

In 2005, the total number of passengers at UK airports rose to 228 million, compared to 5 million in 1955.

The numbers of passengers fell in the recession year of 1974, and in 1991, the year of the Gulf War, before continuing upward. There was also a marked flattening of the upward trend in 2001, the result of the Foot and Mouth outbreak and the September 11 attacks in New York. But these blips were temporary.

The number of passenger kilometres flown by UK airlines increased significantly over the past twenty years, from 80 billion kilometres in 1985 to 287 billion in 2005. Around 97% of the 2005 total was accounted for by international travel.

Nine in ten air passengers at UK airports in 2005 were travelling internationally. The country with which the UK exchanges the most air traffic is Spain. There were 34 million passenger movements between the two countries in 2005.

Heathrow was the busiest airport in the UK, with 68 million passengers in 2005. Gatwick was the second busiest (33 million passengers).

Demand for air travel is projected to continue growing well into the 21st century. Mid-range estimates from the Department for Transport suggest that the number of passengers at UK airports will grow to 500 million in 2030.

Notes:
Passengers on internal flights (domestic) are counted both at airport of departure and arrival.

After the first Gulf War in the early 1990s and the flattening effects of Foot and Mouth and the September 11 attacks in 2001, passenger numbers at least recovered their previous trends. Therefore the recession of 2009, although it has brought a sharp fall in passenger numbers, will not necessarily prevent the Department of Transport’s prediction – that 500 million passengers will use UK terminals by 2030 – from being realised.

One fund-raising activity of a particular sports club is a weekly draw. Participants choose two different numbers between 1 and 15 inclusive. When the draw is made, two numbers between 1 and 15 inclusive are selected at random. The prize money is shared by anyone who has chosen these two numbers. If there are no winners, the prize fund rolls over to the following week.

When last week’s winning numbers were announced as 3 and 10, someone pointed out that it was the fifth successive week that the two numbers consisted of a total of three digits, all different.

Scientists have argued over whether the extinction of the dinosaurs was caused by a space impact or by super-volcanic activity which lasted for 1.5 million years. The space impact would have caused sudden large-scale fires and earthquakes. Volcanic activity would have caused a cooling of the atmosphere and acid rain which would be seen in changes to marine and land ecosystems over the 500,000 years before the extinction. As no such changes were identified during this period, the space impact is the only plausible explanation.

I am playing a card game with three friends. Each of us has two cards which are placed face up on the table. The score for a hand is calculated by adding up the value of the two cards and then doubling the total if the cards are the same suit (denoted by the symbols ♥, ♦, ♣ or ♠).

The highest score wins. My two cards are the 2♠ and 7♥. The other hands are:

• 4♦ and 7♦

• 5♣ and 8♠

• 2♥ and 9♣

I am the last person to play. I can exchange one of my cards with a card from another hand and I want to finish in the highest position possible.

The behaviour of the general public has contributed to the reluctance of doctors to do out-ofhours work. When doctors only ever had to deal with genuine medical emergencies out-ofhours then the workload was manageable. Unfortunately, the Government has helped stoke public expectations so that now people think they should be entitled to full medical care 24 hours a day, no matter how trivial the problem is. However, minor problems should be dealt with at day surgeries.

A target at a fair has twelve sections, marked as shown above. Participants throw four darts at the target. They win a prize if all four darts land in different sections of the target and the total score is at least 30.

Phil has thrown two of his four darts, scoring 12 and 8. He is confident that whenever he throws he will hit the target and, whatever section he aims at, the dart will never land further away than one of the two neighbouring sections. With this in mind, he realises that if he aims his third dart at 5 or 6 he can be confident of winning a prize.

During the trial of a 10 year old accused of frequent violent crimes, privacy laws meant that he could only be referred to in the media as ‘Child B’. One newspaper, however, continually referred to the boy as the ‘Devil Child’. Despite many media sources reporting the difficult and violent upbringing the boy himself had had, calling for understanding and leniency, many letters sent to newspapers and comments posted on internet forums showed strong public anger and calls for the harshest possible sentence. Almost all of those calling for tough measures used the term ‘Devil Child’. This shows that the name alone had influenced public opinion and prevented members of the public having sympathy for the child.

1. The newspaper that used the term ‘Devil Child’ reported the case and the child’s upbringing accurately.

2. The editors of the newspaper that used the term ‘Devil Child’ also called for the harshest possible punishment.

3. The newspaper that used the term ‘Devil Child’ had also continually referred to his victims as ‘innocent’ and ‘defenceless’.

Paul, who works in the fruit and vegetable section of a supermarket was given the job of making up packs of three apples from the contents of a large box of loose apples. Each pack had to weigh 600g, with an allowance of no more than 3g heavier or lighter.

When there were just seven apples left in the box he feared that he might not be able to make up any more packs, but after weighing them he found that he was able to make up two more.

The seven apples weighed 173g, 182g, 188g, 197g, 207g, 219g and 224g

Reducing class sizes in UK primary schools to 20 pupils would be very expensive and would produce little improvement in children’s education. This is confirmed by evidence from the USA. In the 1990s class sizes were reduced in California because the state had been ranked 49th out of 50 states in the reading ability of 9 to 10 year olds. Ten years and $50 billion later, California had risen only to 48th out of 50. If class sizes are reduced, more teachers are needed. Thus, in the UK, candidates with lower qualifications would have to be recruited, since there are already only 1.2 applicants for each teaching post. What is important is not whether there are 20 or 30 children in a classroom, but whether there is one good teacher. Countries whose children do well at school are those that recruit their teachers from the brightest graduates.

The net shown can be folded up to make a cube.

Vitelo Pareto observed that in Italy in 1906 that 80% of the wealth was owned by 20% of the people. The ‘Pareto Principle’ has since been applied to a wide range of other areas. For example in the USA it has been found that 20% of the population use 80% of the health care resources. Although most developed countries have a somewhat more even distribution of wealth in modern times, on a global scale it has been estimated that currently 20% of the world’s population have 82.7% of the world’s income.

Various parameters are used to give a measure of inequality of income within a society. One of the simplest of these is the ratio of the average income of the best paid 20% of the population to that of the lowest paid 20%. Among countries this ratio varies from 4.5 for Japan to 168 for Bolivia. It is clearly very high for some developing countries because a significant part of the population has no measurable income at all.

In the fictional country of Capitalia, the income distribution is as follows:

Vitelo Pareto observed that in Italy in 1906 that 80% of the wealth was owned by 20% of the people. The ‘Pareto Principle’ has since been applied to a wide range of other areas. For example in the USA it has been found that 20% of the population use 80% of the health care resources. Although most developed countries have a somewhat more even distribution of wealth in modern times, on a global scale it has been estimated that currently 20% of the world’s population have 82.7% of the world’s income.

Various parameters are used to give a measure of inequality of income within a society. One of the simplest of these is the ratio of the average income of the best paid 20% of the population to that of the lowest paid 20%. Among countries this ratio varies from 4.5 for Japan to 168 for Bolivia. It is clearly very high for some developing countries because a significant part of the population has no measurable income at all.

In the fictional country of Capitalia, the income distribution is as follows:

Vitelo Pareto observed that in Italy in 1906 that 80% of the wealth was owned by 20% of the people. The ‘Pareto Principle’ has since been applied to a wide range of other areas. For example in the USA it has been found that 20% of the population use 80% of the health care resources. Although most developed countries have a somewhat more even distribution of wealth in modern times, on a global scale it has been estimated that currently 20% of the world’s population have 82.7% of the world’s income.

Various parameters are used to give a measure of inequality of income within a society. One of the simplest of these is the ratio of the average income of the best paid 20% of the population to that of the lowest paid 20%. Among countries this ratio varies from 4.5 for Japan to 168 for Bolivia. It is clearly very high for some developing countries because a significant part of the population has no measurable income at all.

In the fictional country of Capitalia, the income distribution is as follows:

Vitelo Pareto observed that in Italy in 1906 that 80% of the wealth was owned by 20% of the people. The ‘Pareto Principle’ has since been applied to a wide range of other areas. For example in the USA it has been found that 20% of the population use 80% of the health care resources. Although most developed countries have a somewhat more even distribution of wealth in modern times, on a global scale it has been estimated that currently 20% of the world’s population have 82.7% of the world’s income.

Various parameters are used to give a measure of inequality of income within a society. One of the simplest of these is the ratio of the average income of the best paid 20% of the population to that of the lowest paid 20%. Among countries this ratio varies from 4.5 for Japan to 168 for Bolivia. It is clearly very high for some developing countries because a significant part of the population has no measurable income at all.

In the fictional country of Capitalia, the income distribution is as follows:

The graphs below show an index of health as a function of both inequality and wealth for a range of countries (the same group of developed countries is shown in both graphs).

1 Within any given country, the richer people are no healthier than the poor.

2 Countries with less variability of income generally have healthier people.