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