Questions According to Examination Format
1.
In Diagram 1, PQRST is a regular pentagon, TQUR is a parallelogram and PQU is a straight line. The value x + y =A 36 C 108B 72 D 144
2.
In Diagram 2, PN = NM and PQK = KLN =. PNS and PMR are straight lines.
The value of y - x =A 8 C 53B 16 D 69
3.
In Diagram 3, PQVTU is a regular pentagon and QRSV is a parallelogram. The value of TSR A 36 C 72B 54 D 108
4.
In Diagram 4, the value of x + y =A 235 C 245B 240 D 250
5.
In Diagram 5, PQRUV is a regular pentagon and RSTU is a rhombus. The value of x + y =A 220 C 260B 240 D 280
6.
In Diagram 6, PQRU is a square and QRSV is a parallelogram. PVR is a straight line. The value of x =A 110 C 120B 115 D 125
7.
In Diagram 7, PWV, WUS, WQR, PQUT and RST is straight line. PWV and RST are parallel. The value of x + y =A 80 C 100B 90 D 110
Polygon 26
Diagram 1
Diagram 2
Diagram 3
Diagram 4
P
TV
Diagram 5
Diagram 6
Diagram 7
8.
In Diagram 8, PQRSWX is a regular hexagon. SV is parallel to TU. The value of x + y =A 184 C 204B 192 D 212
9.
In Diagram 9, RSTUVY is a regular hexagon. WVU is straight line. The value of x =A 120 C 220B 140 D 240
10.
In Diagram 10, PQRSTU is a regular hexagon. USW and WVQ are straight lines. The value of x + y =A 70 C 90B 80 D 100
11.
Diagram 11
In Diagram 11, QR = RS. The value of x + y =A 67.5 C 117.5B 80.5 D 147.5
12.
Diagram 12
In Diagram 12, E,F,G,H and I are some parts of a regular octagon vertices, EI is a straight line, the value of x + y =A 45 C 135B 100 D 150
13.
In Diagram 13, PQRST is a regular pentagon. PQV and SRV are straight lines. The value of x+ yA 72 C 108B 86 D 144
14.
In Diagram 14, SQRT is a straight line, PS = SR = RT, the value of x + y =A 120 C 180B 150 D 210
15.
In Diagram 15, PQRSTU is a regular hexagon. PQY is a straight line. The value of x + y =A 68 C 136B 90 D 180
Polygon 27
Diagram 8
Diagram 9
Diagram 10
Diagram 13
Diagram 14
Diagram 15
16.
In Diagram 16, QRSTUV is a regular hexagon. PQVWX are five continues vertices of a regular polygon with n sides. RVW is a straight line.A 15 C 10B 12 D 7
17.
In Diagram 17, PRT and QRS are straight lines. Find the value of x.A 45 C 65B 60 D 70
18.
In Diagram 18, PQRST is a regular pentagon. QPU and STUV are straight lines. Find the value of y.A 72 C 108D 100 D 144
Polygon 28
T U
S
R
W X
Diagram 16
Diagram 17
Diagram 18
Diagram 21
Diagram 22
P
T U
19.
Diagram 19 shows a hexagon, Find the value of x + y.A 130 C 160B 140 D 180
20.
In Diagram 20, ABCDE is a regular pentagon. AEF and GFDC are straight lines. Find the value of x.A 36 C 108D 72 D 118
21.
In Diagram 21, ABCDE is a regular pentagon. ABC and DCG are straight lines. Given BC is parallel to PQ. Find the value of x + y.A 100 C 114B 106 D 138
22.
Diagram 22 shows a regular hexagon, EL and HGL are straight lines. The value of y isA 15 C 60B 45 D 120
SPM Past Year Questions
November 2003
1.
In Diagram 1, PQRSTU is a regular hexagon. PUV and QPW are straight lines. The value of x + y =A 69 C 76
B 72 D 86
2.
In Diagram 2, PWQ is an isosceles triangle. PQR., PWV and STU are straight lines. The value of x + y =A 240 C 300B 280 D 380
July 2004
1.
In Diagram 1, PQSTU is a regular pentagon. PQR and TSR are straight lines. The value of x isA 36 C 60B 54 D 72
2.
Polygon 29
Diagram 19
Diagram 1
Diagram 2
S
T
U
P Q R
x
Diagram 1
220°
Diagram 20
A
R
Q
S
Diagram 2
Diagram 2 shows a regular polygon. The value of y isA 160 C 135B 140 D 120
November 2004
1.
In Diagram 1, GHJKL is a regular pentagon. FGH and FMJ are straight lines. The value of x + y =A 57 C 36B 42 D 21
November 2005
1.
Diagram 1 shows a pentagon PQRST. Straight line PQ is parallel to straight line UTS. Find the value of x + yA 216 C 250B 222 D 260
2.
Diagram 2 shows a rhombus PQRS. Find the value of z.A 15 C 60B 45 D 75
July 2005
Polygon 30
y°
Diagram 2
F G H
J
K
L
M
x°
15°
y°
Diagram 1
u
P
R
Diagram 1
UP
Q
R
S
Tmo
50o
In diagram 1, PQRTU is a regular pentagon and RST is a straight line.Find the value of m.A 36 B 58C 65 D 72
July 2006
1.
In Diagram 1, PQRST is a regular pentagon and TUVP is a quadrilateral. STU is a straight line. Find the value of y.A 72 B 73C 80 D 81
Nov 2006(N)
In Diagram I, PQRST is a regular pentagon and PSUV is a parallelogram, STU is a straight line.
Find the value of x
A 36 C 108
B 72 D 144
Nov 2007(1)
In Diagram 1, MNPQRSTU is a regular octagon and TUVW is a straight line.
Find the value of x
A 65 C 80
B 70 D 90
Nov 2007(2)
In Diagram 2, PQRW is a rhombus and VWP is a straight line.
Polygon 31
S T U
R
Q
P V
145o
100o
yo
P
QR
S
T
U
Vx
x 125
PQ
R
S
T U V W
M
N
P
QR
S
T
U
V120
40
110
120
y 2x
W
Calculate the value of x + y .
A 160 C 220
B 170 D 230
July 2007(1)
Diagram 1 shows two regular polygons, PQRSTUVW and JKLMNQ , which are joinedat Q .
Given that y = 2x , find the value of y
A 45 C 60
B 70 D 85
July 2007(2)
Diagram 2 shows a hexagon PQRSTU.
The value of x + y is
A 135 C 195
B 165 D 225
Nov 2008
Diagram 2 shows a regular pentagon PQRST and an equilateral triangle TUV. PUQ is a straight line.
Find the value of x.
A 47 C 60
B 49 D 71
Jun 2008(1)
In Diagram 2, PQRST is a regular polygon.PUT is a straight line. VP = VU.
Polygon 32
PW
V
U
T S
R
Q
N M
L
KJ
x
y
Q
P
R
S
T
U120 150
xy
yx
Q
R
ST
P
25
x
x
Q
R
ST
UV
P
120
Q
R
S
T
U
V
P110
y
X W
Find the value of x .
A 36 C 60
B 54 D 72
Jun 2008(2)
In Diagram 3, PQRTX is a pentagon which is symmetrical about the straight line QWV. RTV is a straight line. SRVU is a part of a regular hexagon.
Find the value of y.
A 130 C 144
B 132 D 145
ANSWERS1.11. x° = 180° - 43° - 60° = 77°
2. x° = 180° - 90° - 50° = 40°
3. y° = 60°
x° = 180° - 60° - 50° = 70°
4. y° = 40° x° = 180° - 40° - 30° = 110°
5. y° = 180° - 130° = 50°
x° = 180° - 40° - 50° = 90°
6. x° = 180° - 100° = 80°
z° = 180° - 120° = 60°
y° = 180° - 80° - 60° = 40°1.2
1. x° = 180° - 60° = 120°
2. x° = 60° 3. x° = 60°
4. x° = 60°
1.3
1. x° =
= 45°
2. y° = 65°x° = 180° - 65° - 65°
= 50°3. y° = 60° z° = 180° - 60° = 120°
x° =
= 30°
4. x° =
= 65°
1. x° = 70° + 50° = 120°
2. x° = 132° - 90° = 42°
3. x° = 42°y° = 70° + 42°
Polygon 33
= 112°
4. y° = 180° - 101° = 79°x° = 79° + 55°
= 134°
5. x° = 70° + 45° = 115°
1.5
1. x° = 360° - 54° - 137° - 62° = 107°
2. y° = 180° - 72° = 108°x° = 360° - 108° - 90° - 83° = 79°
3. y° = 180° - 135° = 45°x° = 360° - 120° - 95° - 45° = 100°z° = 180° - 100° = 80°
4. x° = 64°z° = 360° - 79° - 64° - 118° = 99°
1.6
1. x° = 180° - 40° = 140°y° = 140°
2. x° = 50°
y° =
= 130°
3. x° = 180° - 47° - 52° = 81°
x° = 81°
4. x° =
= 65°y° = 65° + 50° = 115°
1.7
1. Sum of interior angles= (4 – 2) 180°= 360°
2. Sum of interior angles= (6 – 2) 180°= 720°
3. x° = 720–145 – 68 – 162 – 150- 120 = 75°
4. x° = 540 – 240 – 40 – 100 - 110 = 50°
1.8
1. Sum of the exterior angles= a + b + c + d + e + f= 360°
2. Sum of the exterior angles= a + b + c= 360°
1.91. Size of the interior angles
=
=
= 108°
2. Size of the interior angles
=
=
= 135°
3. Size of the interior angles
=
=
= 144°
Questions According To ExaminationFormat 1. B 2. B3. B4. C5. B6. B
Polygon 34
7. A8. A9. D10. B11. C12. C13. D14. B15. B16. B17. B18. D19. C20. A21. C22. ASPM Past Year QuestionsNovember 20031. C 2. CJuly 20041. A 2. CNovember 20041. BNovember 20051. D 2. D July 2005 July 20061. B 1. DNov 2006
1. D
Nov 2007
1. C 2. A
Jun 2007
1. B 2. B
Jun 2008
1. A 2. D
Nov 20081. D
Polygon 35