1. ppr maths nbk
Plans & Elevations
Diagnostic Test
1 (a) Diagram 1(i) shows a solid right prism with rectangular base FGPN on a horizontal
table. EFGHJK is the uniform cross-section of the prism. Rectangle EKLM is an
inclined plane. Rectangle JHQR is a horizontal plane. EF, KJ and HG are vertical
edges.
L
M
5 cm
E K
5 cm
R
2 cm Q
N
2 cm
F J P
H
7 cm 5 cm
G
Diagram 1(i)
Draw a full scale plan of the solid. [ 3 marks]
Answer:

2. ppr maths nbk
(b) A solid cuboid is joined to the prism in diagram 1(i) at the vertical plane
PQRLMN. The combined solid is as shown in diagram 1(ii). The square base
FGSW is horizontal.
U
2 cm 7 cm
V
T
L
M X
7 cm
E K
W R
5 cm
N Q
S
F J
P
H
7 cm 5 cm
G
D
C
Draw full scale
(i) the elevation of the combined solid on a vertical plane parallel to FG as
view from C. [ 4 marks]
(ii) The elevation the combined solid on a vertical plane parallel to FG as view
from D. [5 marks]

3. ppr maths nbk
2. (a) Diagram 2(i) show a solid consisting of a cuboid and a half-cylinder which
are joined at the plane HJMN. The base GDEF is on a horizontal plane and
HJ = 3 cm.
N
M
H L
F J
3 cm
K
G E
6 cm 4 cm
X D
DIAGRAM 2(i)
Draw to full scale the elevation of the solid on a vertical plane parallel to DG as
viewed from X.
Answer :

4. ppr maths nbk
(b) A solid right prism is joined to the solid in diagram 2(i) at the vertical plane
ELMW. The combined solid is as shown in Diagram 2(ii). Trapezium PMWU
is the uniform cross-section of the prism and PQRM is an inclined plane. The
base DEUTSWFG is on a horizontal plane and EU = 2 cm.
P Q
N
M
R 5 cm
H L
F J
3 cm K S
W T
G 2 cm
E
U
6 cm 4 cm
D Y
Draw to full scale
(i) the plan of the combined solid, [ 4 marks]
(ii) the elevation of the combined solid on a vertical plane parallel to UT as viewd
from Y. [5 marks ]
Answer: (i)
(ii)

5. ppr maths nbk
3. Diagram 1 shows a solid consisting of a right prism and a half cylinder. ABQRS is
the uniform cross-section of the prism. Rectangle RSTU is an inclined plane while
rectangles ABCD and PQRU are horizontal planes. The edges AS, DT, CG and BQ
are vertical. CD is the diameter of the half cylinder.
T H
F
S E
S G
U
P
7cm Q
R
Q
D
4cm C
A 4cm
8cm X
B
Y
DIAGRAM 1
Given that CG = DE = 5 cm, PU = QR = 6 cm and both R and U are 4 cm
vertically above the base ABCD. Draw to full scale,
(a) the plan of the solid,
(b) the elevation of the solid on a vertical plane parallel to BC as viewed from X,
(c) the elevation of the solid on a vertical plane parallel to AB as viewed from Y.

6. ppr maths nbk
4. (a) Diagram 2(i) shows a solid right prism with a rectangular base ABCD on a
horizontal plane. The surface ABFE is the uniform cross-section of the solid.
The rectangle EFGH is an inclined plane. The edges AE, BF, CG and DH are
vertical. Draw to full scale, the elevation of the solid on a vertical parallel to AB
as viewed from X.
G
H
H F
D
C
4cm
E
6cm
2cm
A
8cm B
DIAGRAM 2(i)
X

7. ppr maths nbk
(b) A solid cuboid is joined to the solid in Diagram 2(i) at the vertical plane BCQP
to form the combined solid in Diagram 2(ii). The base ABJKSCD is resting on a
horizontal plane. DCS is a straight line.
G
Q R
Q
H
F
D
P C S
E M L
8cm
3cm Y
A B
J K
3cm
DIAGRAM 2(ii)
Draw to full scale,
(i) the plan of the combined solid,
(ii) the elevation of the combined solid on a vertical plane parallel to KS as
viewed from Y.

8. ppr maths nbk
5. (a) Diagram 3(i) shows a solid tin ingot in the shape of a right prism where the
trapezium BCHG is the uniform cross-section. The rectangular base ABCD rests
on a horizontal plane. The rectangle EFGH is a horizontal plane. The rectangles
ABGF and CDEH are inclined planes where ∠ BGH = ∠ CHG.
E
11cm
H
F
8cm
D G
A
C
11cm 2cm
B
X
DIAGRAM 3(i)
4
It is given that BC is 4 cm directly below GH and tan ∠ BGH = .
3
Draw to full scale, the elevation of the solid on a vertical plane parallel to AB as
viewed from X.

9. ppr maths nbk
(b) A solid cuboid is joined to the ingot in Diagram 3(i) at the vertical plane BCWV
to form the combined solid shown in Diagram 3(ii). The base ABPQCD is
resting on a horizontal plane. The edges DCQ and ABP are straight lines.
T
2cm
R
U
E
8cm S
H
F W 6cm
G V
D
D
A
C Q
11cm
B 3cm
P
Y
Draw to full scale, DIAGRAM 3(ii)
(i) the plan of the combined solid,
(ii) the elevation of the combined solid on a vertical plane parallel to PQ as
viewed from Y.

10. ppr maths nbk
Answer to Plan & elevation Diagnostic test:
5 cm 2 cm
1 (a) (b) (i) (ii)
2 cm
5 cm 7 cm
3 cm
5 cm
2 cm 5 cm 2 cm 2 cm
5 cm 2 cm
7 cm
2. (a) (b) (i) (ii)
2 cm
3 cm
2 cm 2 cm
3 cm
3 cm 3 cm
5 cm
6 cm 4 cm
4 cm
2 cm

11. ppr maths nbk
3 (a)
4cm
2cm 6cm
1 (b) (c)
3cm
1cm
5cm 7cm 6cm
4cm
4cm
4cm
4cm 4cm
8cm
6cm
4 (a) (b)(ii)
2cm 1cm
1cm
4cm
2cm
2cm
8cm

12. ppr maths nbk
4 (b)(i)
6cm
8cm
8cm
3cm
5 (a)
4cm
11cm
(b)(i)
11cm
3cm
2cm
3cm
3cm

13. ppr maths nbk
(b)(ii) 2cm
3cm 3cm
4cm
2cm