CIE IGCSE Maths: Extended

Topic Questions

IGCSEMaths: ExtendedCIETopic Questions3. Geometry3.11 3D Pythagoras & Trigonometry

Syllabus Edition

First teaching 2021

Last exams 2024

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3.11 3D Pythagoras & Trigonometry

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1
Sme Calculator5 marks

cie-igcse-2020-may-june-p2-tz1-q18

The diagram shows cuboid A B C D E F G H of length 20 cm and width 5.5 cm.
The volume of the cuboid is 495 cm3 .

Find the angle between the line A G and the base of the cuboid A B C D.

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2
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cie-igcse-2019-may-jun-p2-tz2-q24

A B C D E F G H is a cuboid.
A B equals 18 space text cm end text, B C equals 7 space text cm end text and C G equals 12 space text cm end text.

Calculate the angle that the diagonal A G makes with the base A B C D. 

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3
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cie-igcse-2020-mary-jun-p2-tz3-q20

The diagram shows a pyramid with a square base ABCD.
The diagonals AC and BD intersect at M.
The vertex V is vertically above M.
AB = 11 cm and AV = 18.6 cm.
 
Calculate the angle that AV makes with the base.

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4
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cie-igcse-2018-oct-nov-p2-tz2-q22

The diagram shows a cuboid with dimensions 5.5 cm, 8 cm and 16.2 cm.

Calculate the angle between the line AB and the horizontal base of the cuboid.

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5
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cie-igcse-2018-oct-nov-p2-tz3-q23

The diagram shows a triangular prism.
AB = 12 cm, BC = 6 cm, PC = 4 cm, angle BCP = 90° and angle QDC = 90°.
 
Calculate the angle between AP and the rectangular base ABCD.

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1
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cie-igcse-2020-oct-nov-p2-tz1-q21

The diagram shows a cuboid P Q R S T U V W.
P V space equals space 17.2 space cm
The angle between the line P V and the base T U V W of the cuboid is 43 degree.

Calculate P T.

P T space equals ........................................... cm

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2
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The diagram shows a cuboid A B C D E F G H.

q19-4ma1-1h-qp-jan20-paper1-igcse-maths

E H space equals space 9 space cm comma space space space space H G space equals space 5 space cm  and     G B space equals space 6 space cm.

Work out the size of the angle between space A H space and the plane E F G H.
Give your answer correct to 3 significant figures.

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3
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The diagram shows a triangular prism.

q19-paper2h-june2018-edexcel-igcse-maths

A F space equals space 10 space cm comma space space A B space equals space 24 space cm space andspace B C space equals space 8 space cm.
Anglespace F A B space = angle A D C = angle B C D equals 90 degree

Work out the size of the angle between the line B E and the plane A B C D.
Give your answer correct to 1 decimal place.

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4
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The diagram shows cuboid A B C D E F G H.

q21-paper2h-june2019-edexcel-igcse-maths

For this cuboid

the length of A B : the length of B C : the length of C F = 4 : 2 : 3

Calculate the size of the angle between A F and the plane A B C D.
Give your answer correct to one decimal place.

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5
Sme Calculator3 marks

The length of a diagonal of a cuboid is 20 cm

The diagonal makes an angle of 24° with the base.

The area of the base is 150 cm2

q24-paper-3h-june-2019-aqa-gcse-maths

Work out the volume of the cuboid.

...................................... cm3

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1
Sme Calculator4 marks

cie-igcse-2019-may-june-1-q21

The diagram shows a pyramid with a square base ABCD of side length 8cm.
The diagonals of the square, AC and BD, intersect at M.
V is vertically above M and VM = 10 cm.

Calculate the angle between VA and the base.

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2
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The diagram shows a triangular prism.

q1-veryhard-4-12-3d-pythogoras-and-trigonometry-edexcel-gcse-maths

The base, A B C D, of the prism is a square of side length 15 cm.
Angle space A B E spaceand angle space C B E spaceare right angles.
Angle space E A B space= 35°

M spaceis the point on space D A spacesuch that

D M colon M A space equals 2 colon 3


Calculate the size of the angle between space E M spaceand the base of the prism.
Give your answer correct to 1 decimal place.

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3
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V A B C D spaceis a solid pyramid.

q2-veryhard-4-12-3d-pythogoras-and-trigonometry-edexcel-gcse-maths

A B C D spaceis a square of side 20 cm.

The angle between any sloping edge and the plane space A B C D spaceis 55°

Calculate the surface area of the pyramid.
Give your answer correct to 2 significant figures.

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4
Sme Calculator6 marks

V A B C D is a square-based pyramid.

The horizontal base A B C D has side length 10 cm and centre M.

Angle V M A is 90°
Angle V A M spaceis 68°

q27-paper3h-nov2017-aqa-gcse-maths

Volume space of space pyramid space equals space 1 third cross times area space of space base space cross times space perpendicular space height

Work out the volume of the pyramid.

....................cm3

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5
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The diagram shows the prism A B C D E F with cross section triangle A B C.

q21-4ma1-1hr-qp-jan20-paper1-igcse-maths

Angle space B E C space= 40° and angle space A C B spaceis obtuse.
A C = 6 cm and space C E space= 13cm

The area of triangle space A B C spaceis 22 cm squared

Calculate the length of A B.
Give your answer correct to one decimal place.

..................cm

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