How do you work out the angles for a pie chart?

Divide the frequency of the category by the total frequency and multiply by 360. In an exam it is faster to find the angle for one item first, which is 360 divided by the total: with 45 people that is 8 degrees each, so a category of 6 people takes 48 degrees. Check the angles add to 360 before you draw or write anything down.

Are pie charts on the Higher paper or only Foundation?

Both. Pie charts are spec ref S2 on Edexcel 1MA1 and they are crossover content, so the same question can sit near the end of a Foundation paper and in the first third of a Higher one. At Higher tier you are more likely to be asked to interpret a chart, or to judge a claim about two charts, than to draw one with a protractor.

Is the pie chart formula on the Edexcel formulae sheet?

No. The Exam Aid sheet issued with 1MA1 papers carries the quadratic formula, the sine and cosine rules, the area of a triangle, the trapezium and prism formulae, the circle formulae, compound interest and the two probability rules. Pie chart angles are recall, but there is nothing much to recall beyond a full circle being 360 degrees.

Why can two pie charts not be compared just by looking at the sectors?

Because each sector is a share of its own total, and the two totals are usually different. A 90 degree sector of a survey of 120 people is 30 people, while a 60 degree sector of a survey of 300 people is 50 people. Work out both frequencies and compare those, then state which is larger and why the claim about the sector sizes fails.

Pie Charts - Edexcel GCSE Higher Maths

Typically 2-4 marks when it appears, and it does not appear on every paper · Spec 1MA1

A pie chart shows category totals as shares of one circle, so $360^\circ$ stands for the whole data set and each sector is that total scaled down. Find the angle for one item, $360 \div \text{total frequency}$ , and every sector angle is a multiple of it. On Edexcel 1MA1 this is spec ref S2, and it is crossover content shared with Foundation, which is why it turns up in the first third of a Higher paper rather than near the end. Nobody is going to miss a grade 7 over pie charts. The marks are quick, and they are usually lost to carelessness rather than to difficulty.

Edexcel writes it in two shapes. One gives a short frequency table and asks for the angles, or for the chart to be drawn accurately; the angles are where the method marks sit, and the drawing is worth one mark for a correct construction. The other describes a chart and gives the total, then asks for a frequency, a percentage or, working the other way, for the total itself from a single sector. Any of the three papers can carry it. On Paper 1 the totals are picked so they divide 360 exactly, so 30 people means $12^\circ$ each and 45 people means $8^\circ$ each; on Papers 2 and 3 a total of 35 is fair game and the angle comes out as a decimal.

The part that actually separates candidates is the last one, usually 2 marks and phrased as somebody's claim: two pie charts, two different totals, and a statement that the larger sector must mean the larger number of people. An angle is a proportion of its own total, so a $90^\circ$ sector of 120 people is 30 people while a $60^\circ$ sector of 300 people is 50. Work out both frequencies, put both numbers on the page, then answer the claim. A response saying only that the totals are different scores nothing; a response containing 30 and 50 and a conclusion scores both marks.

Worked example

Two pie charts show how students at two schools travel to school. At Kelsall School 180 students were asked, and the sector for bus is 100 degrees. At Marden School 300 students were asked, and the sector for bus is 72 degrees. Tom says, "The bus sector is bigger at Kelsall, so more Kelsall students travel by bus." Is Tom right? You must show your working.

[4 marks]

Kelsall: $360^\circ$ represents 180 students, so the bus sector represents $\frac{100}{360} \times 180 = 50$ students.
M1: a correct method for one of the two frequencies, angle over 360 multiplied by that school's own total
Marden: $360^\circ$ represents 300 students, so the bus sector represents $\frac{72}{360} \times 300 = 60$ students.
M1: the same method applied with the second total, not with the first
So 50 students at Kelsall and 60 students at Marden travel by bus.
A1: both frequencies correct
Tom is wrong. 60 is greater than 50, so more students travel by bus at Marden. The Kelsall sector is a larger slice of a smaller group.
C1: conclusion referring to both figures; a bare "no, the totals are different" earns nothing

Practice questions

These are original questions in Edexcel 1MA1 Higher style. There are no diagrams here, so every chart is given by listing its sectors in words, as in "the sector for football is 96 degrees". Almost every total divides 360 exactly, so the set works as non-calculator practice for Paper 1; where an angle does not come out as a whole number the stem says how to round it.

No account needed: the questions below are always free to check, plus 8 extra questions today. Your score so far updates as you go.

Question 1 Warm-up [2 marks]

40 students each chose one language to study. 7 of them chose Spanish. Work out the angle, in degrees, of the sector for Spanish.

Your answer (fractions like 1/2 are fine)
Question 2 Exam pace [2 marks]

A pie chart shows the pets owned by a group of people. The sector for cats is 84 degrees and it represents 14 cats. Work out the total number of pets.

Your answer (fractions like 1/2 are fine)
Question 3 Exam pace [3 marks]

A charity raised £900 in a week. £150 of it came from the online shop. A pie chart is drawn to show where the money came from. Work out the angle, in degrees, of the sector for the online shop.

Your answer (fractions like 1/2 are fine)
Question 4 Exam pace [3 marks]

A pie chart shows the hot drinks sold in a cafe. The sectors for tea and for coffee are in the ratio 5 : 4, and together they make 216 degrees. Work out the angle, in degrees, of the sector for tea.

Your answer (fractions like 1/2 are fine)
Question 5 Exam pace [3 marks]

A pie chart shows how 90 students travel to school. The sector for walking is 140 degrees. 15 of the students cycle. How many more students walk than cycle?

Your answer (fractions like 1/2 are fine)
Question 6 Stretch [4 marks]

A pie chart shows how 288 people travel to work. The angle of the sector for car is 45 degrees more than the angle of the sector for train. Together the car and train sectors make 215 degrees. Work out how many people travel by car.

Your answer (fractions like 1/2 are fine)

Common mistakes examiners see

Dividing 360 by the frequency of the category instead of using the total, so 9 walkers out of 24 pupils is written as $360 \div 9 = 40^\circ$ .

Work out the angle for one item first. With 24 pupils that is $360 \div 24 = 15^\circ$ each, so 9 walkers is $9 \times 15 = 135^\circ$ . Write the column total at the foot of the frequency table before you calculate anything.
Reading an angle as though it were a percentage, so a $54^\circ$ sector is reported as 54% of the group.

Divide by 360, not by 100: $\frac{54}{360} \times 100 = 15$ %. A sanity check that costs nothing is that a sector under $180^\circ$ has to be under half, so it cannot be 54%.
Comparing two pie charts by eye and concluding that the bigger sector means the bigger frequency, when the two charts were drawn from different totals.

Calculate both frequencies before you write a word. Only after you have two numbers can you say which group is larger, and the mark scheme wants those numbers quoted in the answer.
Given one sector's frequency and asked for another, treating the frequency you were handed as the total: 21 dogs at $126^\circ$ , then working out fish as $\frac{48}{360} \times 21$ .

Convert to degrees per item. $126 \div 21 = 6^\circ$ per pet, so the total is $360 \div 6 = 60$ pets and a $48^\circ$ sector is $48 \div 6 = 8$ fish. That one figure answers both halves of the question.
Rounding every angle to the nearest degree and ending with a set that totals 359 or 361, then drawing it anyway and leaving a visible gap.

Calculate all but one of the angles, then get the last one by subtracting from 360. Add your list up as the final line of working; an examiner reading a total of 360 knows the angles are consistent.

Frequently asked questions

How do you work out the angles for a pie chart?: Divide the frequency of the category by the total frequency and multiply by 360. In an exam it is faster to find the angle for one item first, which is 360 divided by the total: with 45 people that is 8 degrees each, so a category of 6 people takes 48 degrees. Check the angles add to 360 before you draw or write anything down.
Are pie charts on the Higher paper or only Foundation?: Both. Pie charts are spec ref S2 on Edexcel 1MA1 and they are crossover content, so the same question can sit near the end of a Foundation paper and in the first third of a Higher one. At Higher tier you are more likely to be asked to interpret a chart, or to judge a claim about two charts, than to draw one with a protractor.
Is the pie chart formula on the Edexcel formulae sheet?: No. The Exam Aid sheet issued with 1MA1 papers carries the quadratic formula, the sine and cosine rules, the area of a triangle, the trapezium and prism formulae, the circle formulae, compound interest and the two probability rules. Pie chart angles are recall, but there is nothing much to recall beyond a full circle being 360 degrees.
Why can two pie charts not be compared just by looking at the sectors?: Because each sector is a share of its own total, and the two totals are usually different. A 90 degree sector of a survey of 120 people is 30 people, while a 60 degree sector of a survey of 300 people is 50 people. Work out both frequencies and compare those, then state which is larger and why the claim about the sector sizes fails.

Pie Charts - Edexcel GCSE Higher Maths

Worked example

Practice questions

Common mistakes examiners see

Frequently asked questions

Related topics