Video: GCSE Mathematics Foundation Tier Pack 1 • Paper 3 • Question 6

GCSE Mathematics Foundation Tier Pack 1 • Paper 3 • Question 6

04:24

Video Transcript

The bar chart gives information about the number of students studying A-level mathematics, history, English, and chemistry at a particular school. What fraction of the mathematics students are boys?

To find the fraction of the mathematics students who are boys, we will need to calculate two amounts. We’ll need to find the number of mathematics students who are boys and then divide that by the total number of mathematics students.

Let’s begin by checking the scale on the vertical or the 𝑦-axis. We can see that two little squares represents four students. Dividing through by two tells us that one little square represents two students. Halving again, we can see that half a square represents one student.

We also have a key, and the key tells us that the number of students who are boys are represented by the transparent bars, whereas the number of students who are girls are represented by the grey bars.

The height of the bar representing the number of students who study mathematics who are boys is one square — that’s two students — more than 24. That’s 26. There are 26 boys who study mathematics. The height of the bar representing the number of students who study mathematics who are girls is half a square — that’s one student — more than 28. That means there are 29 girls who study mathematics. The total number of students who study maths can be found by adding 29 and 26. 29 plus 26 is 57, so the fraction of students who study mathematics who are boys is 26 over 57.

Trevor says, “There are more chemistry and history students than English students.” Is Trevor correct? You must justify your answer.

Let’s begin by calculating the number of students who study each of these subjects. The height of the bar representing the number of students who study history who are boys is half a square — that’s one student — under 20. There are 19 boys then who study history. We can see that there are 20 girls who study history. The total number of students who study history can be found by adding these two numbers. 19 plus 20 is equal to 39.

The height of the bar representing the number of students who study chemistry who are boys is half a square — that’s one student — above eight. There are nine boys who study chemistry. The height of the bar representing the number of girls who study chemistry is half a square below the number 12. So there are 11 girls who study chemistry. Nine plus 11 is 20, so there are 20 students who study chemistry in total.

Let’s repeat this process for the number of students who study English. There are 32 boys who study English and 27 girls. 32 plus 27 is 59, so there are a total of 59 students who study English.

We now need to compare the total number of students who study history and chemistry against the number who study English. The number of students who study history and chemistry is found by adding 39 to 20, which is 59. This means that Trevor is incorrect. There are the same number of students that study English as there are that study chemistry and history combined.

The pie chart gives information about the same 173 students studying these four A-level subjects. Ronald says, “It is easier to find out the number of students that study each subject from the pie chart than the bar chart.” Is Ronald correct? You must justify your answer.

Pie charts can be really helpful when you’re trying to compare parts of a whole. For example, we can see from this pie chart that a large proportion of the students are boys who study English. However, if we wanted to work out the exact number of boys who study English from the pie chart, we would first have to measure this angle. We would then write it as a fraction of 360 and find this fraction of 173.

To find the number of students who study each subject, we would have to repeat this process a whole load of times. So no, Ronald is incorrect. It’s much easier to read information off the bar chart as before than to measure lots of angles and perform calculations with them.

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