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Name : __________________________________________ Form : 5 _______
1 Calculate the angle between plane HEL and plane HJKL
2. Calculate the angle between plane LCD with plane HJKL
1
L
MN
K
J
E
10
8
L
H
K
J
10
8
4
CDD
H
6
AB
CD
A B
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Questions Base On SPM Format
1. Diagram 1 shows a pyramid with a
rectangular base PQRS. V is vertically
above P.
Calculate the angle between the line VR
and the plane PQRS.
2. Diagram 2 shows a cuboid with horizontal
base KLMN.
Calculate the angle between the line SL and the
base NKLM.
3. Diagram 3 shows a cuboid.
ACBDEFGH. Given EH = FG = 8 cm.
Calculate the angle between the plane EHD
and the plane FEHG.
4. Diagram 4 shows a right prism with a
horizontal plane ABCD. It is a uniform prism
and its cross section is an isosceles triangle of
sides 4 cm. The thickness of the prism, EA = 4
cm.
Calculate the angle between the plane ABH and
the plane ABE.
2
DIAGRAM 1
DIAGRAM 2
DIAGRAM 3
A B
C
H
E D
DIAGRAM 4
KL
MN
RS
P Q
12 cm
4 cm
5 cm
P Q
RS
V
8 cm
6 cm
11 cm
F E
HB
CD
A
G
7 cm
5 cm
6 cm
4 cm4
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5) Diagram 5 shows a pyramid with the
horizontal plane, TRS. The rectangle PQRS
is vertical plane.
Calculate the angle between the plane PTS
and the plane TQR.
6) Diagram 6 shows a cuboid. Z is the
midpoint of TW .
Calculate the angle between plane YVZ and the
horizontal plane XYVW.
7) Diagram 7 shows a right prism with
base the rectangular plane ABCD. Right
triangle BCF is the uniform cross-section of
the prism. The rectangular surface DCFE is
vertical while the rectangular surface BAEF
is inclined.
Calculate the angle between the plane DB
and plane EDCF.
8) Diagram 8 shows a pyramid REFGH. The
base EFGH is a horizontal rectangle. R is the
midpoint of HG. The apex R is 9 cm vertically
above the point S.
Calculate the angle between line ER and the
plane EFGH.
3
YV
WX
TS
R U
10 cm
6 cm
4 cm4
Z
DIAGRAM 6
T
R
S
QP
12 cm
13 cm
10 cm
DIAGRAM 5
B
DIAGRAM 7DIAGRAM 8
EF
GH
R
5 cm
24 cm
S
A
CD
FE
8 cm
6 cm
6 cm
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9) Diagram 9 shows a cuboid. P is the
midpoint of line RQ.
Calculate the angle between the plane LQY
and the plane MQRN.
10) Diagram 10 shows a right prism. Right
angled triangle SUT is the uniform cross-
section of the prism.
Calvulate the angle between the plane PSR and
the plane PUTR..
11) Diagram 11 shows a prism . The base
PQRS is a horizontal rectangle . X is themidpoint of SR.
Calculate the angle between line PX and
the plane SRML.
12) Diagram 12 shows a right prism with
rectangle base EFGH. EFPQ and GHPQ arerectangle.
Calculate the angle between line LQ and the
base EFGH.
4
DIAGRAM 9 cm
LMM
QP
RS
KNN
Y
10 cm
6 cm
12 cm
U
Q
ST
P
R
5 cm12 cm
20 cm
DIAGRAM 10
PQ
RS
ML
X
12 cm
8 cm
5 cm
DIAGRAM 11 cm
F
G
E
P
H
MM
L
6 cm
5 cm
12 cm
DIAGRAM 12 cmD
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Name : __________________________________________ Form : 5 _______
a) Name the angle between the two planes.
Example 1: Plane EFGH and
plane GHDA
Angle :
DHE and AGF
1. a) Plane KLSP and plane
JKLM
b) Plane PSWV and plane
VUXW
Example 2 : Plane PQLK andplane SRLK
Angle :
QLR and PKS
2. a) Plane ABCD and planeADEF
b) Plane URST and planeXRSY
Example 3 : Plane TRQ and
plane SRQP
Angle : TRS
3. a) Plane ABCD and plane
ABV
b) Plane PQSR and plane
PQK
c) Plane JKLM and plane
PKL
d) Plane MHEL and plane
NHE
e) Plane ABCD and plane
BCE
5
AB
CD
V
J K
Q
M
RS
P
L
P Q
RS
X
W
V
U
GH
EF
DA
B C
BA
F
E
D C
R S
UT
YX
PQ
RS
LK
P
Q
RS
LK
T
RS
QP
J K
Q
M
RS
P
L
BA
F
E
D C
GH
EF
LK
N MM
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Example 4: Plane DEV and
DEFG
Angle : VMO
4a) Plane GCB and plane
ABCD
b) Plane KLMN and plane
KPN
c) Plane ABE and plane
ABCD
d) Plane RUQ and plane
SRUT
e) Plane SURP and plane
PTR
Exercise 1 : Name the angle between the two planes
a) Plane SRQP and plane QUTR b) Plane JQRM and plane JKLM
c) Plane RSYX and plane URST d) Plane BCF and plane ABCD
6
DE
FG
V
OOM A B
CD
G
OOL
BA
F
E
D C
L
K
R
U
S
P
TQQ
NN
M
J K
Q
M
RS
P
L
R S
UT
YX
BA
F
E
D C
T
LM
NKK
EE
F
P
WU
R
TT
V
S
P
T
Q
R
U
P
S
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e) Plane GMLF and plane GHEF f) Plane PQA and plane PQRS
C
Exercise 2 : Name the angle between the two planes
a) The diagram shows a pyramid with a
horizontal base DEFG. Name the anglebetween the plane VDE and the plane of
DEFG.
b) The diagram shows a cuboid with a
horizontal base JKLM .Name the anglebetween the plane SRKJ and the plane of
SRLM.
c) The diagram shows a prism. Name the
angle between the plane RSY and the plane
of RSTU.
d) The diagram shows a prism. Name the
angle between the plane ABE and the plane
of ABCD.
7
J K
Q
M
RS
P
L
R S
UT
YX
BA
F
E
D C
Q
P
GH
EF
LK
N M
P Q
RS
X
W
V
U
B
A
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e) The diagram shows a cuboid. Name the
angle between the plane HEK and the plane
of GHEF
f) The diagram shows a prism. Name the
angle between the plane UVWX and the
plane
of
PSWV.
8
GH
EF
LK
NMM
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Name : ________________________________ Form : 5 A1
Date : 30-07-2008 ( 11.10-11.50 12.30)Instruction : Circle the correct answer.
1. Diagram 1 shows a pyramid with a
rectangular base PQRS. V is vertically above
P.
Name the angle between the line VR and the
plane PQRS
A. PRV B. VRS
C. PVQ D. VQS
2. Diagram 2 shows a cuboid.
Name the angle between the line PM and the
plane SRMN.
A. PMK B. PMQ
C. PMR D. PMS
3. In the diagram 3, X and Y are the
midpoints of PW and SV respectively.
The angle between line RX and the plane
RSVU is
A. RXY B. XYR
C. XRY D. XQR
4. Diagram 4 shows a right prism.
Name the angle between line EK and plane
EFJH.
A. EKJ B. EKF
C. HEK D. JEK
9
KL
MN
RS
P Q
P Q
RS
V
DIAGRAM 1DIAGRAM 2
Q P
WS
VU
R TT
X
DIAGRAM 3D
Y
F G
K
H
E J
DIAGRAM 4D
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5. Diagram 5 shows a pyramid .PQRS is a
rectangle.
Name the angle between the line TQ and the
plane PQRS
A. QPT B. QST
C. RST D. SQT
6. Diagram 6 shows a cuboid.
The angle between the line SU and plane
PSWT is
A. USP B. USQ
C. UST D. USW
7. Diagram 7 shows a cuboid.
The angle between plane QPV and the plane
QPWT is
A. VQW B. UQT
C. VPW D. QPV
8. Diagram 8 shows a right prism.
Name the angle between the plane EGKH
and the plane FGKJ.
A. EGF B. EKF
C. HGJ D. GKE
10
TU
VW
RS
P Q
DIAGRAM 5
DIAGRAM 6
Q P
WS
VU
R T
DIAGRAM 7
F G
K
H
E J
DIAGRAM 8
T
RS
QPP
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9. Diagram 9 shows a right prism .
Name the angle between the plane ACS and
the plane SADR.
A. CAS B. SCD
C. ACD D. CAD
10. Diagram 10 shows a right pyramid
MABCD with its square base ABCD .
The angle between the line MC and plane
ABCD is
A. MCD B. MCA
C. AMC D. AMD
11. The diagram 11 shows a right prism on a
horizontal plane. Given that STU is an
equilateral triangle and PV = VR = SW =
WU .
The angle between the plane PRT and the
plane PRUS is
A. PQS B. RQU
C. TQW D. TVW
12. Diagram 12 shows a prism. A and B are
the mid-points of JK and ML, respectively.
JXK and MYL are isosceles triangle.
Name the angle between line AY and the
plane JKLM.
A. YBA B. AYB
C. YAB D. ABY
11
DIAGRAM 11
DIAGRAM 9
Q C
DR
AS
PB
Q
PP
WS
U
R
TT
V
J K
L
Y
XM
DIAGRAM 12D
AA
BB
DIAGRAM 10
A B
CD
M
O
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13. Diagram 13 shows a right prism .
Name the angle between line DM and the
plane ACFD.
A. CDM B. DCM
C. CMD D. DCB
14. Diagram 14 shows a pyramid.
The angle between the plane GHJK and plane
HJL is
A. GHL B. JHL
C. KJL D. KLJ
15. The diagram 15 shows a right prism on a
horizontal plane SRUT. Equilateral triangle
RUQ and STP are the uniform cross-section
of the prism. M and N are the mid-points of
ST and RU, respectively.
The angle between the plane PRN and the
plane RSTU is
A. PRS B. MRP
C. PNM D. NPM
16. Diagram 16 shows a cuboid with base
PQRS . .
Name the angle between the plane WXR and
the plane QRWV.
A. QRX B. RXQ
C. RWX D. SXU
12
DIAGRAM 14DIAGRAM 13
C
DD
MA
B
F
L
JK
HG
R
U
S
P
T
Q
DIAGRAM 15D
NN
M R
Q
U
W
T
S
P
VV
X
DIAGRAM 16D
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17. Diagram 17 shows a cuboid with
rectangular base EFGH .
Name the angle between the plane PSG and
the plane PSHE.
A. SGH B. PGE
C. GSH D. GPE
18. Diagram 18 shows a cuboid on a
horizontal plane EFGH. J is a mid-point of
GH.
The angle between the plane ABGJ and the
plane ABCD is
A. AJE B. AGE
C. GBC D. GAC
19. Diagram 19 shows a prism on a
horizontal plane QRP and vertical rectangular
QRST .
Name the angle between the plane PRS and
the plane QRST is
A. PSQ B. PST
C. PRT D. PRQ
20. Diagram 20 shows a prism with
rectangular base JKLM . LM is normal to
base JKLM .
Name the angle between line NK and base
JKLM.
A. NKM B. NMK
C. NMJ D. NKJ
13
DIAGRAM 17
E
H
R
P
Q
F
G
S
DIAGRAM 20
DIAGRAM 18
A
BC
D
E
F G
HJ
R
T
Q
P
S
DIAGRAM 19
J K
LM
NN
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PAST YEAR SPM QUESTIONS
Nov 2003, Q13
1. Diagram 6 shows a right prism with an isosceles triangle PQR as its horizontal base. M and
N are the mid-point of SU and RQ, respectively.
Name the angle between the plane PQR and the plane PUS.
A. UPT B. NPT
C. PNQ D. MPN
July 2004, Q16
2. Diagram 9 shows a cuboid with PQRS as its horizontal base.
Name the angle between the plane TQR and the plane TUVW.
A. TRW B. TQV
C. WTR D. VTQ
Nov 2004, Q14
3. Diagram 8 shows a cuboid with horizontal base PQRS.
14
T
R Q
USS MM
N
P
PQ
RS
WT
U V
PQ
RS
WT
U V
DIAGRAM 6
DIAGRAM 9
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Name the angle between the line QV and the plane QUR.
A. VUR B. VUQ
C. VQU D. VQR
July 2005, Q14
4. Diagram 6 shows a right pyramid NPQRS with square base PQRS.
The angle between the line NQ and the base PQRS is
A. PQN B. NQS
C. QNS D. QNR
Nov 2005, Q14
5. Diagram 7 shows a right pyramid with a quadrilateral base EFGH.
15
Q R
SP
N
DIAGRAM 8
DIAGRAM 6
E F
GH
V
DIAGRAM 7
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What is the angle between the line VF and the base EFGH ?
A. VFE B. FVH
C. VFH D. FVE
July 2006, Q14
6. Diagram 7 shows a cuboid with a horizontal base TUVW.
The angle between the line PW and the base TUVW is
A. PWV B. PUW
C. PTW D. PWU
Nov 2006, Q14
7. Diagram 7 shows a cuboid with a horizontal base TUVW.
Diagram 7
Name the angle between the plane PQWT and the plane SRWT.
A. QTR B. QWR
C. QTS D. QWS
16
VW
TU
SP
Q R
DIAGRAM 7