Is Pythagoras' theorem given to you in the Edexcel GCSE maths exam?

Yes, for the 2025 to 2027 assessment windows. Every 1MA1 paper comes with an Exam Aid sheet, and a^2 + b^2 = c^2 is on both tiers' versions, alongside the right-angled sine, cosine and tangent ratios; the Higher sheet adds the sine rule, the cosine rule and the area rule. Knowing the formula is still not the same as knowing which side is c, and that is what the questions test.

Is Pythagoras' theorem on the Foundation paper as well as Higher?

Yes. G20 is a crossover spec point, so a plain two-mark Pythagoras question can sit on either tier. Higher takes it further with surd answers on the non-calculator paper, the distance between two coordinates, and Pythagoras applied twice inside a solid, which G20 carries too: the reference ends with the words 'in two and three dimensional figures', and the three dimensional half of that is Higher only.

How many marks is a Pythagoras question worth on Edexcel Higher?

A standalone one is usually 2-3 marks, and on Higher it tends to sit early, where the demand is lowest. When Pythagoras is one stage of a bigger problem, such as finding a radius before a circumference or a height before an area, the question tends to be worth 4-5 marks with Pythagoras earning the first process mark.

When do you add and when do you subtract in Pythagoras' theorem?

Add the squares when the side you are looking for is the hypotenuse, the side opposite the right angle. Subtract when the hypotenuse is already given and you want one of the shorter sides. The check is quick: the hypotenuse has to end up longer than both of the other sides.

Pythagoras' Theorem - Edexcel GCSE Higher Maths

Typically 2-5 marks per paper, often as the first step of a longer problem · Spec 1MA1

Pythagoras' theorem ties the three sides of a right-angled triangle together: square the two shorter sides, add them, and you have the square of the hypotenuse. On Edexcel's 1MA1 specification it is reference G20, a crossover point that both tiers are assessed on, but the Higher versions go further than Foundation ones: exact answers left in surd form, the distance between two coordinates, chords and isosceles triangles split down the middle, and the step into three dimensions where the diagonal of a base becomes a side of the next triangle.

Edexcel can set it on any of the three papers. On Papers 2 and 3 you have a calculator and the question usually finishes with 'give your answer correct to 3 significant figures' or 'correct to 1 decimal place', so the rounding instruction is part of what is being marked. Paper 1 is non-calculator, which is why the numbers there tend to be Pythagorean triples (3-4-5, 5-12-13, 8-15-17, 7-24-25) or why the answer is meant to stay as a surd such as $2\sqrt{5}$ . The theorem itself is printed on the Exam Aid sheet that comes with the paper, so nothing here rests on recalling $a^2 + b^2 = c^2$ ; it rests on knowing which side $c$ is.

A short Pythagoras question carries 2-3 marks: a method mark for squaring and then correctly adding or subtracting, an accuracy mark for the length. If you add when the hypotenuse is one of the numbers you were given, the method mark goes too, because the wrong operation is not partial credit for the right one. The other regular loss is writing down the squared value, 56.25 rather than 7.5, and never taking the root. Longer questions hide Pythagoras inside something else, an area, a perimeter, a circumference, a bearing, so practise spotting a right angle nobody has pointed at, and finish by checking that the side you called the hypotenuse really is the longest one you have written.

Worked example

In triangle PQR, PQ = PR = 13 cm and QR = 10 cm. M is the midpoint of QR, and angle PMQ is a right angle. Work out the area of triangle PQR. Give your answer in square centimetres.

[4 marks]

M is the midpoint of QR, so $QM = 10 \div 2 = 5$ cm. Triangle PQM is right angled at M.
M1: halving the base of the isosceles triangle to create a right-angled triangle
The right angle is at M, so PQ is the hypotenuse of triangle PQM: $PM^2 = 13^2 - 5^2 = 169 - 25 = 144$ .
M1: subtracting the squares, since the 13 cm side is the hypotenuse
$PM = \sqrt{144} = 12$ cm.
A1: root taken; 144 on the answer line would lose this mark
Area of triangle PQR $= \frac{1}{2} \times 10 \times 12 = 60$ square centimetres.
A1: full base of 10 cm with the perpendicular height of 12 cm, not 5 cm

Practice questions

These are original questions written in Edexcel 1MA1 Higher style. Pythagoras turns up on all three papers, so some of these have exact surd answers for Paper 1 practice while the rest state a rounding your answer has to match. Every triangle is described in words, so read the right angle first: it tells you which side is the hypotenuse before you touch a number.

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]

In triangle ABC, angle B is a right angle, AB = 8 cm and BC = 15 cm. Work out the length of AC, in cm.

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

A rectangular field measures 80 m by 60 m. A straight path runs from one corner to the opposite corner. Work out the length of the path, in metres.

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

A television screen is a rectangle 96 cm wide and 54 cm high. Work out the length of the diagonal of the screen, in cm, correct to 1 decimal place.

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

A cuboid measures 3 cm by 4 cm by 12 cm. Work out the length of the diagonal running from one corner of the cuboid to the corner furthest from it, in cm.

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

A cuboid measures 4 cm by 5 cm by 8 cm. Work out the length of the diagonal running from one corner of the cuboid to the corner furthest from it, in cm, correct to 1 decimal place.

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

PQRS is a trapezium in which PS is parallel to QR. Angle SPQ and angle PQR are both right angles. PQ = 5 cm, PS = 8 cm and QR = 20 cm. Work out the length of SR, in cm.

Your answer (fractions like 1/2 are fine)

Common mistakes examiners see

Adding the squares when the hypotenuse is one of the lengths you were given. From a hypotenuse of 8.5 cm and a shorter side of 4 cm, $8.5^2 + 4^2 = 88.25$ gives 9.4 cm, a 'shorter' side longer than the hypotenuse.

Find the side opposite the right angle before you write any numbers. If that side is given, subtract; if it is the one you want, add. Then sanity-check: the hypotenuse must be the longest of the three.
Stopping at the squared value. Writing $8.5^2 - 4^2 = 56.25$ and putting 56.25 cm on the answer line earns the method mark and drops the accuracy mark.

Give the square root its own line: $x^2 = 56.25$ , then $x = \sqrt{56.25} = 7.5$ . If your length is larger than both numbers in the question, you have skipped the root.
Rounding the first length to 1 decimal place and feeding the rounded value into a second calculation, so a perimeter or an area lands just outside the accepted range.

Keep the unrounded value on the calculator, using the answer key or a memory store, and round only the figure you write on the answer line.
Testing whether a triangle is right angled by adding the two shorter sides: for 9 cm, 12 cm and 15 cm, arguing that $9 + 12 \ne 15$ so it cannot be right angled.

Compare $a^2 + b^2$ with $c^2$ , where c is the longest side, and write both values down: $81 + 144 = 225$ and $15^2 = 225$ . Finish with a sentence saying the triangle is right angled, because Edexcel awards a mark for the conclusion.
On Paper 1, turning $\sqrt{20}$ into a guessed decimal, or leaving $\sqrt{20}$ alone when the question asks for the form $a\sqrt{b}$ .

With no calculator, keep the exact value and take out the largest square factor: $\sqrt{20} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}$ .

Frequently asked questions

Is Pythagoras' theorem given to you in the Edexcel GCSE maths exam?: Yes, for the 2025 to 2027 assessment windows. Every 1MA1 paper comes with an Exam Aid sheet, and $a^2 + b^2 = c^2$ is on both tiers' versions, alongside the right-angled sine, cosine and tangent ratios; the Higher sheet adds the sine rule, the cosine rule and the area rule. Knowing the formula is still not the same as knowing which side is $c$ , and that is what the questions test.
Is Pythagoras' theorem on the Foundation paper as well as Higher?: Yes. G20 is a crossover spec point, so a plain two-mark Pythagoras question can sit on either tier. Higher takes it further with surd answers on the non-calculator paper, the distance between two coordinates, and Pythagoras applied twice inside a solid, which G20 carries too: the reference ends with the words 'in two and three dimensional figures', and the three dimensional half of that is Higher only.
How many marks is a Pythagoras question worth on Edexcel Higher?: A standalone one is usually 2-3 marks, and on Higher it tends to sit early, where the demand is lowest. When Pythagoras is one stage of a bigger problem, such as finding a radius before a circumference or a height before an area, the question tends to be worth 4-5 marks with Pythagoras earning the first process mark.
When do you add and when do you subtract in Pythagoras' theorem?: Add the squares when the side you are looking for is the hypotenuse, the side opposite the right angle. Subtract when the hypotenuse is already given and you want one of the shorter sides. The check is quick: the hypotenuse has to end up longer than both of the other sides.

Pythagoras' Theorem - Edexcel GCSE Higher Maths

Worked example

Practice questions

Common mistakes examiners see

Frequently asked questions

Related topics