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Questions Sheets - Teacher Resources ©DCG SolutionsOrthographic & Auxiliary Projection

1) The 3D graphic below shows a house with solar panels mounted on the roof. The plan and incomplete elevation of the house are also shown to the right. (a) Complete the elevation of the house with the position of the solar panels shown on the roof.(b) Draw an auxiliary view of the house on the given X1Y1, which will show thetrue angles of inclination of the solar panels to the horizontal plane. Exam Craft Mocks 2012 OL A(Slide No 3)

2) The 3D graphic below shows a typical coal bunker. The drawing to the right shows the plan and incomplete elevation of the coal bunker.(a) Complete the elevation of the bunker. (b) Determine the dihedral angle between surfaces A and B.Exam Craft Mocks 2013 OL A(Slide No 4)

3) The 3D graphic below shows a lectern used in a lecture hall. (a) Determine the true angle between the inclined surface A and the horizontal plane.(b) Determine the true length of the edge PQindicated in the diagram.Exam Craft Mocks 2014 OL A(Slide No 5)

X Y

X Y

A

B

P

A

Q

X Y

Questions Sheets - Teacher Resources ©DCG Solutions

5) The 3D graphic below shows tetrahedron. The drawing on the left shows the plan of a regular tetrahedron.

(a) Draw the elevation of the tetrahedron on the given XY line.(b) Draw the projections of a sphere that will circumscribe the tetrahedron.Exam Craft Mocks 2012 HL A(Slide No 7)

6) The 3D graphic below shows a camera tripod which is in the form of a regular tetrahedron.The drawing on the right shows the plan and elevation of a tetrahedron.(a) Determine the dihedral anglebetween the surfaces ABC and ABD.(b) Draw the projections of a sphere which is tangential to all surfaces of the tetrahedron.Exam Craft Mocks 2014 HL A(Slide No 8)

4) The 3-D graphic below shows a toaster. The incomplete elevation of the toaster is shown on the drawing on the right.(a) Complete the elevation showing the correct position for the rectangular slots shown in plan.(b) Determine the true angle between surface Aand the horizontal plane.Exam Craft Mocks 2015 OL A (Slide No 6)

Orthographic & Auxiliary Projection

a

b

c d

X Y

AB

C

D

D,CB

A

X Y

A

X Y

7) The 3D graphic on the right shows a memory key.Fig. B-7 shows an isometric view of the device.a) Draw an elevation of the device looking in the direction of the arrow.b) Draw a plan projected from the elevation.c) Draw an auxiliary elevation of the memory key projected from the plan

which will include the true shape of surface A.Scale 1:1Exam Craft Mocks 2013 OL B(Slide No 9)

Questions Sheets - Teacher Resources ©DCG SolutionsOrthographic & Auxiliary Projection

8) The 3D graphic on the right shows a golf trophy for achieving a hole in one.Fig. B-8 below shows an isometric view of the trophy.a) Draw an elevation of the trophy looking in the direction of the arrow.

(Ignore the circular hole shown).b) Draw a plan projected from the elevation.c) Draw an auxiliary elevation of the trophy projected from the plan which will

include the true shape of surface A.Scale 1:1Exam Craft Mocks 2014 OL B(Slide No 10)

A

Fig B-7

Fig B-8

A


9) The 3-D graphic on the right shows a traffic bollard. Fig B-9 below shows an isometric view of the traffic bollard mounted on a concrete pedestal. The concrete pedestal is in the form of a regular octagon.a) Draw an elevation of the bollard in the direction of the arrow shown.b) Draw a plan projected from the elevation.c) Draw an auxiliary elevation of the concrete pedestal and bollard projected

from the plan which will include the true shape of surface A.Scale 1:1Exam Craft Mocks 2015 OL B(Slide No 11)

Orthographic & Auxiliary Projection

A

Fig B-9

Questions Sheets - Teacher Resources ©DCG SolutionsAxonometric Projection

1) The 3D graphic shows a letter box.A set of isometric axes and a partially completed drawing of the box are shown on the right. The elevation and plan of the box have been positioned relative to the axes as shown.Complete the axonometric projection.Exam Craft Mocks 2012 OL A (Slide No 13)

2) The 3D graphic below shows a letter box.A set of isometric axes and a partially completed drawing of the box are shown on the left. The elevation and plan of the box have beenPositioned relative to the axes as shown.Complete the axonometric projection.Exam Craft Mocks 2013 OL A(Slide No 14)

3) The 3D graphic below shows a letter box. A set of isometric axes and a partially completed drawing of the box are shown on the right.The elevation and plan of the box have been positioned relative to the axes as shown.Complete the axonometric projection.Exam Craft Mocks 2014 OL A(Slide No 15)

y

xz

xz

y

y

xz

400

80o 80o

180

4) The 3D graphic below shows a measuring tape.Fig B-4 shows an incomplete isometric projection of the tape.The elevation and plan of the tape are also shown in their required positions.a) Draw the given equilateral triangle abc and the axonometric axes X, Y and Z.a) Draw the elevation and plan positioned as shown.b) Draw the axonometric projection of the tape.Scale 1:1Exam Craft Mocks 2015 OL B (Slide No 16)

XZ

Yc

a b

Fig. B-4

45°

100

°30

10×10

5) The 3D graphic on the right shows a typical swing bin found in many homes.The figure below shows the elevation and end view of the lid of the bin. The

trimetric axes are also shown.a) Draw the trimetric axes at the given angles and position the plan and

elevation in their position to the axes.b) Complete the axonometric projection of the lid.Scale 1:5Exam Craft Mocks 2012 HL B (Slide No 17)

XY

Z


6) The 3D graphic on the right shows a letter box.Fig. B-6 shows the elevation and end view of the letter box.a) Draw the trimetric axes X, Y and Z at the given angles.b) Position the plan and elevation in their correct position relative to the axes.c) Complete the axonometric projection of the letter box.Scale 1:5Exam Craft Mocks 2013 HL B(Slide No 18) 350

125

X Y

7) Fig. B-7 shows an incomplete trimetric projection,using the axonometric method, of a toaster, based on the 3D graphic below. The elevation and plan are shown in their required positions.

a) Draw the trimetric axes X, Y and Z and the scalene triangle abc.

b) Draw the elevation and plan orientated as shown and complete the trimetric projection.

Scale 1:1Exam Craft Mocks 2015 HL B(Slide No 19)

Fig. B-6

Fig. B-7

XY

Z


Questions Sheets - Teacher Resources ©DCG SolutionsPerspective Projection

2) The 3D graphic shows a bus shelter.The drawing on the left is a partially completed perspective view of the structure.Complete the perspective drawing using auxiliary vanishing points to determine the 20o degree roof. Exam Craft Mocks 2012 HL A(Slide No 22)

3) The 3D graphic shows a coal bunker. The drawing on the right is a partially completed perspective view of the bunker.Complete the perspective drawing using auxiliary vanishing points for the sloping lid surface, which has a true inclination of 40° to the horizontal plane.Exam Craft Mocks 2013 HL A(Slide No 23)

1) The image below shows a try square which can be found in most workshops. The drawing on the right is a partially completed perspective viewof the try square.Complete the perspective drawing of the try square.Exam Craft Mocks 2015 OL A(Slide No 21)

4) The 3D graphic shows a toaster. The drawing on the right is a partially completed perspective view of the toaster.Complete the perspective drawing using auxiliary vanishing points for the sloping lid surface which has a true inclination of 25° to the horizontal plane.Exam Craft Mocks 2014 HL A(Slide No 24)

5) The 3-D graphic shows an obelisk, a stone pillar tapering to a pyramid on top.The drawing on the right shows the partially completed perspective projection of an obelisk.(a) One of the vanishing points, VP1 is shown. Locate the other vanishing point.(b) Complete the perspective projection of the obelisk.(c) Determine the true height of the structure.Exam Craft Mocks 2015 HL A(Slide No 25)

S


6) The 3D graphic above shows a typical coal bunker.Fig. B-6 shows the plan and elevation of a model of the coal bunker.a) Draw the given plan.b) Make a perspective drawing of the bunker given the following information:

• The spectator point is 75 mm from corner A• The picture plane is touching corner A• The horizon line is 30 mm above the ground line.

Scale 1:1Exam Craft Mocks 2012 OL B(Slide No 26)

30°

S

A

7) The 3D graphic below shows a speaker for a sound system.Fig B-7 shows the plan and elevation of a speaker. a) Draw the given plan.b) Make a perspective drawing of the speaker given the

following information:• The spectator is 90 mm from corner A• The picture plane is touching corner A• The horizon line is 50 mm above the ground line.


Fig. B-7

30°

S

X

A

Y

Fig. B-6


5

8) The 3D graphic above shows a toaster. Fig. B-8 below shows the plan and elevation of a toaster. a) Draw the given plan. b) Make a perspective drawing of the toaster given the

following information:• The spectator is 90mm from corner A• The picture plane is touching corner A• The horizon line is 50mm above the ground line.


X Y

Fig. B-8

A30o

Fig. B-9

9) The 3D graphic above shows a house with a solar panel on the roof.

Fig. B-9 to the right shows the plan and elevation of the house.

a) Draw the given plan. b) Make a perspective drawing of the house and solar

panels given the following information:• The spectator is 70mm from corner A and in the

direction of the arrow shown.• The picture plane passes through point B.• The horizon line is 40mm above the ground line.• The roof has a true inclination of 40o.

Scale 1:1DCG Solutions Sample HL B(Slide No 29)

BA


1) The 3D graphic below shows an arrangement of geometric solids which are in contact. All three solids rest on the horizontal plane.The drawing on the right shows the elevation andincomplete plan of cone A and cylinder B.(a) Complete the plan.(b) Show the projections of a sphere C of diameter 32 mm in contact with both solids and resting on the horizontal plane.(c) Show all points of contact.Exam Craft Mocks 2012 OL A(Slide No 31)

Questions Sheets - Teacher Resources

2) The 3D graphic below shows an inverted cone A and a sphere B resting on the horizontal plane. (a) Draw the elevation of sphere B.(b) Draw the plan and elevation of thesecond sphere, C (shown in red),when it has been moved to position C1and is in contact with cone A andsphere B.Exam Craft Mocks 2013 OL A(Slide No 32)

Solids In Contact

A B

A B

A

B

A

Y

CC1

X

©DCG Solutions

3) The 3D graphic shows an arrangement of spheres. Also shown is the front elevation and plan of two of the spheres.Draw the plan and elevation of the third sphere, C (shown in blue) when it has been moved to position C1 and is in contact with the other two spheres.Exam Craft Mocks 2014 OL A(Slide No 33)

4) The 3-D graphic shows an arrangement of geometric solids including spheres and a cone. Also shown is the incomplete front elevation and plan of a cone A and a sphere B resting on the horizontal plane.(a) Draw the elevation of sphere B. (b) Draw the plan and elevation of the second sphereC (shown in blue) when it has been moved to position C1 and is in contact with cone A and sphere B.Exam Craft Mocks 2015 OL A(Slide No 34)

X Y

A

B

C1

C

X Y

A

C1

A

C1

B

C

Questions Sheets - Teacher ResourcesSolids In Contact ©DCG Solutions

6) The 3D graphic shows a cone A and sphere B in contact and resting on the horizontal plane.Fig. B-6 shows the elevation of the cone and sphere.a) Draw the elevation and plan of the cone and sphere.b) Draw the projections of a second sphere C resting on the horizontal plane and is in contact with the given sphere at a point 18mm above the horizontal plane.c) Draw the traces of a tangent plane to cone A and sphere C.Scale 1:1Exam Craft Mocks 2012 HL B(Slide No 36)

X Y

90

A

B

5) Fig B-5 shows the plan of a cone of altitude of 95 mm and a diameter of 90 mm resting on the horizontal plane. The position of a point P is also shown in plan.a) Draw the plan and elevation of the cone and locate point P in the plan and elevation.b) Draw the projections of a sphere which rests on the horizontal plane and is in contact with the given cone at point P.c) Determine the traces of a tangent plane to the cone and sphere.Scale 1:1Exam Craft Mocks 2012 HL B(Slide No 35)

Fig. B-5

X Y

P

Questions Sheets - Teacher ResourcesSolids In Contact ©DCG Solutions

Fig. B-6

©DCG SolutionsConic Sections

1) The 3D graphic below shows a tennis racket which is in the shape of an ellipse.the drawing on the right shows the directrix, line of eccentricity, the position of the major axis of an ellipse and the position of one of the focal points.(a) Locate the position of the focal point and determine the minor axis.(b) Draw the upper portion of the ellipse.Exam Craft Mocks 2012 OL A(Slide No 38)

2) The 3D graphic below shows a digital radio which is in the shape of a parabola.The drawing on the left shows the directrix, the axis and the position of the focal point of a parabola.(a) Locate the position of the vertex. (b) Draw the projections of the parabola.Exam Craft Mocks 2013 OL A(Slide No 39)

3) The 3D graphic shows an elliptical orbit of the moon around the earth.The drawing below shows the directrix, line of eccentricity, the position of the major axis of an ellipse, one of the vertices and the position of one of the focal points.(a) Locate the position of the other vertex and determine the minor axis.(b) Draw the upper portion of the ellipse.Exam Craft Mocks 2014 OL A(Slide No 40)

D

D

V V

E

F

DD

D

D

V F

5) The suspension bridge shown in the diagram shows a parabola suspending the road from the supporting columns.The drawing on the right shows a triangle where the line AC is a tangent to a parabola with point A on the directrix and point B is the focal point.Determine the directrix and draw a portion of the curve.Exam Craft Mocks 2012 HL A(Slide No 42)

6) A digital radio in the shape of a parabola is shown. The drawing on the right shows the directrix (DD) and a point (P) on the curve of a parabola.(a) Locate the exact position of the focus, vertex and draw the curve.(b) Determine the centre of curvature for the point P on the parabola.Exam Craft Mocks 2013 HL A(Slide No 43)

4) The graphic below shows a diver as he falls towards the water. The path created by the diver is a parabola.The drawing shows the directrix, the axis and the position of the focal point of a parabola. (a) Locate the position of the vertex.(b) Draw the projections of the parabola.Exam Craft Mocks 2015 OL A(Slide No 41)

F

DD

A

B

C

DD

P

©DCG SolutionsConic Sections Questions Sheets - Teacher Resources

7) The 3D graphic below shows a tennis racket which is in the shape of an ellipse.The drawing on the right shows a line L which is a tangent to an ellipse. Also shown is the axis of an ellipse with one focal point F shown.(a) Find the second focal point. (b) Determine the length of the major axis and draw a portion of the curve.Exam Craft Mocks 2014 HL A(Slide No 44)

8) The 3-D graphic below shows a coal bucket which has been constructed in the form of a cone. The top section has been truncated as shown.The drawing on the right shows the elevation of the cone.(a) Draw the elevation of the focal sphere. (b) Determine the major and minor axes for the elliptical cut.(c) Draw a portion of the elliptical curve.Exam Craft Mocks 2015 HL A(Slide No 45)

F

PL

©DCG SolutionsConic Sections Questions Sheets - Teacher Resources


2) The plan and elevation of a triangular plane ABC is shown below.(a) Determine the traces of the oblique plane containing the plane ABC.(b) Determine, and indicate in degrees, the true angle between the traces of the oblique plane.Exam Craft Mocks 2013 HL A(Slide No 48)

1) The 3-D graphic above shows a lean to shed, with a sloping roof as shown.The drawing on the left shows the incomplete projections a similar shed with a skylight window on the roof.(a) Determine the traces of the oblique plane containing the roof surface.(b) Complete the projections of the windows in elevation.(c) Determine the true angle of inclination the roof makes with the horizontal plane.DCG Solutions Sample Question A (Slide No 47)

A

B

C

BA

C

X Y

Oblique Plane

4) The 3-D graphic below shows a building in the form of a cylinder. The building has a sloping roof as shown.The drawing on the right shows the incomplete projections a truncated cylinder which has been cut by the oblique plane VTH.An auxiliary elevation is also given.(a) Complete the plan and elevation of the cut cylinder.(b) Determine the true shape of the cut surface.Exam Craft Mocks 2015 HL A(Slide No 50)

A

A

B

B

3) The 3-D graphic shows an obelisk.The drawing on the right shows the plan and elevation of the obelisk.(a) Determine the traces of the oblique plane containing the surface B.(b) Determine the true shape of surface B.(c) Determine the traces of the oblique plane containing the surface A.

DCG Solutions Sample Question A(Slide No 49)

X YT

H

V

Questions Sheets - Teacher Resources ©DCG SolutionsOblique Plane

5) The 3D graphic shows a sports trophy with the base in the shape of an equilateral triangular prism supporting a triangular based pyramid.Fig. B-5 shows the plan and elevation of the trophy which has been cut by the oblique plane VTH.•Draw the given plan and elevation.•Draw the projections of the solid when it has beencut by the oblique plane VTH.Scale 1:1Exam Craft Mocks 2012 OL B(Slide No 51) X Y

T

V

H

42

60°

6) The 3-D graphic below shows an award trophy in the form of a truncated pentagon prism. The trophy has a sloping top as shown.The drawing on the right shows the projections a truncated prism which has been cut by the oblique plane VTH with is inclined at 45o

to the horizontal plane.The plan of the prism is a regular pentagon positioned as shown.(a) Complete the plan and elevation of the cut cylinder.(b) Construct a true shape of the cut surface.(c) Determine the true length of a line drawn from a to b.Exam Craft Mocks 2015 HL B(Slide No 52)

1174

b

a

Fig. B-5

Questions Sheets - Teacher Resources ©DCG SolutionsOblique Plane

Questions Sheets - Teacher Resources ©DCG SolutionsIntersecting Planes & Skew Lines

1) The projections of two skew lines AB and CD are shown. Determine the shortest distance between the two lines.Exam Craft Mocks 2013 HL A (Side No 54)

2) Light sabres are often a feature of futuristic sci-fi movies. The projections of two skew lines ABand CD are shown.(a) Determine the shortest distance between the two lines.(b) Determine the true length of both light sabres and identify, which if any, is longer than the other.Exam Craft Mocks 2014 HL A(Slide No 55)

A

D

BC

A

BD

C

X Y

A

BC

D

A

D

BC

3) The flight paths of two aircraft are shown by the two skew lines AB and CD. Determine the projections of the shortest distance between the two lines.Exam Craft Mocks 2015 HL A(Slide No 56)

X Y

A

A

C

C

D

D

B

B


A C

D

B

C

D

A

B

A

B

D

C

X Y

B

DA

C

4) The projections of two skew lines AB and CD are shown. Determine the shortest horizontal distance between the two lines.Exam Craft Mocks 2013 HL A(Side No 57)

5) The path of two tracks on a roller-coaster are shown by the two skew lines AB and CD. A platform must be added between the tracks for maintenance.Locate the shortest horizontal distance betweenthe tracks to determine the location of the platform.DCG Solutions Sample HL A (Slide No 58)


A B

D

C

B

D

A C

6) The projections of two skew lines AB and CD are shown. Determine the shortest horizontal distance between the two lines.Exam Craft Mocks 2012 HL A (Slide No 59)

A

B D

C

X Y

A

C

B

D

7) The projections of two skew lines AB and CD are shown. Determine the shortest perpendicular distance between the two lines.DCG Solutions Sample HL A(Slide No 60)


a) Draw the plan and elevation of the intersecting planes.b) Determine the dihedral angle between the planes.c) Determine the traces of the plane that contains the triangle ABC.d) Determine the true shape of the triangle ABC.

Exam Craft Mocks 2013 HL B (Slide No 61)

10) The 3D graphic on the right shows a military aeroplane comprising of a series of intersecting surfaces.The horizontal and vertical coordinates for the planes ABD, BCE and ECD are given below:

a) Draw the plan and elevation of the intersecting planes.b) Identify the true angle of inclination between the plane ABD and the horizontal plane.c) Determine the dihedral angle between the planes ABD and BCE.

Scale 1:1DCG Solutions Sample Question HL B(Slide No 63)

8) The light shades shown on the right incorporate planar faces which intersect as shown.The horizontal and vertical coordinates for the outer points of two intersecting triangular planes ABC and BCD are given below

9) The 3-D graphic on the right shows a piece of sculpture incorporating geometric shapes.The horizontal and vertical coordinates for of the surfaces ABCD and BEC are given below:

a) Draw the plan and elevation of the plane BEC.b) Determine the position for the point D in plan and complete the plan and elevation

for the plane ABCD.c) Determine the dihedral angle between the planes.d) Determine the true shape of the plane ABCD.

Scale 1:1 Exam Craft Mocks 2015 HL B (Some dimensions have been edited)(Slide No 62)

A = 105 - 80 - 10

B = 155 - 80 - 50

C = 135 - 15 - 90

D = 95 - 45 - 85

A = 200 - 90 - 30

B = 150 - 0 - 80

C = 150 - 60 - X

D = 250 - 0 - 80

E = 200 - 0 - 125

A = 100 - 65 - 55

B = 165 - 80 - 75

C = 150 - 10 - 20

D = 115 - 30 - X

E = 210 - 35 - 60


1) The 3D below shows a square based prism, which has been pierced by an equilateral triangle of side 64 mm.Fig. B-1 to the right shows the plan and elevation of the solid.a) Draw the given plan and elevation of the prism.a) Project an end elevation of the solid.Scale 1:1Exam Craft Mocks 2012 OL B(Slide No 65)


X Y60o

30o

2) The 3D graphic below shows a shaped solid which has been penetrated by an equilateral triangular prism.Fig. B-2 shows the incomplete plan and elevation of the solids.a) Draw the given plan and elevation of the solids

showing all lines of interpenetration.b) Project an end elevation of the solids.Scale 1:1Exam Craft Mocks 2013 OL B(Slide No 66)

6010 18

40 30

Intersection Solids

Fig. B-1

Fig. B-2

3) The 3D graphic below shows an equilateral triangular based prism which has been penetrated by a square basedprism of side 50mm.Fig. B-3 shows the incomplete plan and elevation of the solids.

a) Draw the given plan and elevation of the solids showing all lines of interpenetration.b) Project an end elevation of the solids.


15 15

45o

45o

4) The 3-D graphic above shows the intersection of a wall and a pillar.Fig B-4 shows the plan and incomplete elevation of the structure.

a) Draw the given plan and elevation of the structure showing all lines of interpenetration.

b) Draw an end view of the structure.Scale 1:1Exam Craft Mocks 2015 OL B(Slide No 68)

20

50

15 15

X Y

45o 45o

Fig. B-3

Fig. B-4

Questions Sheets - Teacher Resources ©DCG SolutionsIntersection Solids

(a) Complete the plan, showing all lines ofinterpenetration.Hint; Use a section plane to find theintersection points.

DCG Solutions Sample HL A(Slide No 69)

5) The 3D graphic shows a solid intersected by a triangular prism.The given drawing shows the incomplete elevation and plan ofthe solids which penetrate each other.

6) The 3D graphic of two intersecting solids is shown below. The prism which intersect the solid is an equilateral triangular prism.

The drawing to the left shows the incomplete projections of the solids.

Complete the drawing, showing all lines of interpenetration. DCG Solutions Sample HL A (Slide No 70)


8) The 3D graphic of two intersecting solids is shown below.Fig. B-8 shows the incomplete projections of the solids, which penetrate each other.

a) In the diagram a truncated equilateral triangular prism of 80mm side is resting on one face. Draw the outlineplan and elevation of this triangular prism.

b) Another equilateral triangular prism of side 60mm penetrates the pyramid as shown. Draw the outline elevation and plan of this triangular prism.

a) Complete the drawing, showing all lines of interpenetration.

Scale 1:1Exam Craft Mocks 2013 HL B(Slide No 73, 74)

145

25

60o

35

60o

15o

10

X Y

7) The image on the right shows two intersecting solids. Fig. B-7 shows the incomplete projections of the solids which penetrate each other.

a) Draw the plan and elevation of the pentagonal based pyramid.b) An equilateral triangular prism of side 55mm penetrates the pyramid as

shown. Draw the outline elevation and plan of this triangular prism.c) Complete the drawing showing all lines of interpenetration.Scale 1:1Exam Craft Mocks 2015 HL B(Slide No 71, 72)

X Y

2510o

10o

Fig. B-8

Fig. B-7


9) The 3D graphic of two intersecting solids is shown on the right.Fig. B-9 shows the incomplete projections of the solids which penetrate each other.

a) In the diagram, a truncated pyramid stands on the horizontal plane. Draw the plan and elevation of this pyramid.

b) A square based prism of side 45mm penetrates the pyramid as shown. Draw the outline plan and elevation of this prism

c) Complete the drawing showing all lines of interpenetration.

Scale 1:1Exam Craft Mocks 2014 HL B(Slide No 75, 76)

Fig. B-9

30o

45

11

30o


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