3D Pythagoras & Trigonometry (OCR GCSE Maths: Higher): Exam Questions

3 hours36 questions
1
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4 marks

The diagram shows a right-angled triangular prism ABCDEF.

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Length AD = 11 cm, length CD = 10 cm and length CF = 6 cm.

Calculate the exact length of AF.

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

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2
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3 marks

A B C D is a horizontal rectangular field.

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A vertical pole, A E, is placed at the corner A of the field.

A E equals 12 space straight m      A B equals 18 space straight m A D equals 8 space straight m

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

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3
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4 marks

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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4
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3 marks

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
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3 marks

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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6
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1 mark

Here is a cube with edge length space x spacecm

One diagonal is shown.

q16-paper-2h-nov-2021-aqa-gcse-maths

Circle the length, in centimetres, of the diagonal.

square root of 3 space x

cube root of 3 x squared end root

square root of x cubed end root

cube root of 3 x

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7
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3 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

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Work out the volume of the cuboid.

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

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8
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3 marks
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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9
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4 marks
cie-igcse-2020-oct-nov-p4-tz3-q6a

ABCDEFGH is a cuboid.
AB = 8 cm, BC = 5 cm and CG = 11 cm.

i) Calculate angle CAB.

 

Angle CAB = ................................................ [2]

ii) Calculate angle GAC.

 

Angle GAC = ................................................ [2]

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10
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4 marks
7nbfuCQj_cie-igcse-2018-may-jun-3-p4-q6b

The diagram shows a cuboid.
A B = 8 cm, B C = 4 cm and C R = 5 cm.

Calculate the angle between the diagonal A R and the plane B C R Q.

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1
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4 marks

A B C D E F G H space spaceis a cuboid.

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

A B space equals space 7.3 space cm
C H space equals space 8.1 space cm
Angle space B C A space equals space 48 degree

Find the size of the angle between A H and the plane A B C D.
Give your answer correct to 1 decimal place.

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2
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4 marks

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

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

A B space equals space 7 space cm comma space A F equals space 5 space cm space and space F C equals space 15 space cm.

Calculate the volume of the cuboid.
Give your answer correct to 3 significant figures.

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3a
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4 marks

The diagram shows a pyramid.

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B C D E spaceis a square with sides of length 10 cm.
The other faces of the pyramid are equilateral triangles with sides of length 10 cm.

Calculate the volume of the pyramid.
Give your answer correct to 3 significant figures.

3b
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2 marks

Find the size of angle D A B.

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4
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5 marks

The length of the longest diagonal of a cube is 25cm.
Calculate the total surface area of the cube.

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

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5
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6 marks

The diagram shows a right-angled triangular prism ABCDEF.

q20-paper4-nov2018-ocr-gcse-maths

Calculate angle AFB.

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6
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5 marks

The diagram shows a cuboid ABCDEFGH.

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Calculate angle BHF.

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7
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4 marks

A B C is an isosceles triangle in a horizontal plane.

The point T is vertically above B.

q22-4ma1-2hr-qp-jan21-paper2-igcse-maths

Angle A B C space equals space 140 degree
A B space equals space B C space equals space 8 c m
T B space equals space 10 space c m
M is the midpoint of A C.

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

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8
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5 marks

The diagram shows cuboid 

q18-paper2h-nov2020-edexcel-igcse-maths-1

table row cell A B space end cell equals cell space 5 space cm space end cell row cell A H space end cell equals cell space 4 space cm end cell end table

The size of the angle between C H and the plane A B C D is 35 degree

Calculate the volume of the cuboid.
Give your answer correct to 3 significant figures.

..............................................cm cubed

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9
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4 marks

Here is a cube A B C D E F G H.

q20-paper1hr-jan2019-edexcel-igcse-maths

M is the midpoint of the edge G H.

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

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10
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4 marks

The diagram shows a triangular prism A B C D E F with a horizontal base A B E F.

q22-4ma1-1h-qp-june21-paper1-igcse-maths

A C space equals space B C space equals space F D space equals space E D space equals space 12 space cm       A B space equals space 10 space cm           B E space equals space 15 space cm

Calculate the size of the angle between A D and the base A B E F.
Give your answer correct to 3 significant figures.

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11a
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3 marks

The diagram shows a prism A B C D E F G H with a horizontal base.

q17-paper1hr-nov2020-edexcel-igcse-maths

The base of the prism, E F G H, is a square of side 12 cm.
Trapezium A D E F is a cross section of the prism where A F and D E are vertical edges.

table row cell D E space end cell equals cell space C H space equals space 10 space cm space end cell row cell A D space end cell equals cell space B C space equals space 15 cm end cell end table

Work out the size of the angle between C F and the base E F G H.
Give your answer correct to one decimal place.