IGCSEMaths: ExtendedCIEExam QuestionsPythagoras & TrigonometryRight-Angled Triangles - Pythagoras & Trigonometry

Syllabus Edition

First teaching 2023

First exams 2025

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Right-Angled Triangles - Pythagoras & Trigonometry (CIE IGCSE Maths: Extended)

Exam Questions

3 hours45 questions

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Right-Angled Triangles - Pythagoras & Trigonometry

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Right-Angled Triangles - Pythagoras & Trigonometry

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1
Sme Calculator5 marks

Here is a rectangle.

q2-medium-4-10-right-angled-triangle-edexcel-gcse-maths

The 8-sided shape below is made from 4 of these rectangles and 4 congruent right-angled triangles.

q2-2-medium-4-10-right-angled-triangle-edexcel-gcse-maths

Work out the perimeter of the 8-sided shape.
You must show all your working.

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2
Sme Calculator4 marks

Trianglespace A B C spacehas perimeter 20 cm.

A B space= 7 cm.
B C space= 4 cm.

By calculation, deduce whether triangle space A B C spaceis a right-angled triangle.

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3
Sme Calculator3 marks

q4-easy-4-10-right-angled-triangle-edexcel-gcse-maths

Calculate the value of x.
Give your answer as an exact value.

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1
Sme Calculator4 marks

q22-paper2-spec2025-cie-igcse-further-maths

Find the exact value of x.

x = ...........................

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2
Sme Calculator3 marks

The length of one side of a rectangle is 12cm.
The length of the diagonal of the rectangle is 13cm.

Calculate the area of the rectangle.

.......................................... cm2

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3
Sme Calculator4 marks

Calculate the area of this trapezium.

cie-igcse-q17-area-trapeziumGive your answer as an exact value.

......................................... cm2

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1
Sme Calculator4 marks

q2-veryhard-4-10-right-angled-triangle-edexcel-gcse-maths

A B C D is a rectangle.
C D E is a straight line.

A B = 12 cm
Angle A C B= 60°
Angle E A C = 90°

Calculate the length of C E.
You must show all your working.

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2
Sme Calculator4 marks

The table shows some values of x and y that satisfy the equation y space equals space a space cos space x degree space plus space b

x 0 30 60 90 120 150 180
y 3 1 plus square root of 3 2 1 0 1 minus square root of 3 negative 1

Find the value of y when x = 45

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3
Sme Calculator4 marks

Simplify   fraction numerator 2 space sin space 45 degree minus tan space 45 degree over denominator 4 space tan space 60 degree end fraction

Give your answer in the form  fraction numerator square root of a minus square root of b over denominator c end fraction where a comma space b and c are integers.

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4
Sme Calculator6 marks

ADB and BCD are right-angled triangles.
BC = CD.
AD equals 10 square root of 6 space mm

Angle BAD = 30°.

tan space 30 degree equals fraction numerator 1 over denominator square root of 3 end fraction

q19b-paper5-nov2019-ocr-gcse-maths

Work out the length of BC.

...........................mm

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