Edexcel (I)GCSE
Mathematics
Higher Tier
Geometry - Polygons
Total Marks: 55
You must have:
Ruler
Calculator
Instructions:
Use black ink or ball-point pen.
Answer All questions.
Answer the questions in the spaces provided there may be more space than you need
Show all the steps in any calculations and state the units.
Information:
The total mark for this paper is 55
The marks for each question are shown in brackets use this as a guide as to how much time to spend
on each question.
Advice:
Read each question carefully before you start to answer it.
Keep an eye on the time.
Write your answers neatly and in good English.
Try to answer every question.
Check your answers if you have time at the end.
2 1.
Diagram NOT
accurately drawn
127°
84°
114°
97°
Four of the angles of a pentagon are 97°, 114°, 127° and 84°.
Work out the size of the fifth angle.
. .. .. . .. . .. .. . .. . . .. . .. . . . .. . . . . .. . . . .. . . . . .. .
(Total for Question 12 is 4 marks)
°
13
2.
Diagram NOT
accurately drawn
P
A
The diagram shows two congruent regular pentagons and part of a regular n-sided
polygon A.
Two sides of each of the regular pentagons and two sides of A meet at the point P.
Calculate the value of n.
Show your working clearly.
n = . .. . .. .. . .. . .. .. . .. . .. . .. .. . . . . . .. . . . . .. . . . .. . . . .. . . . . .. . . . .. .
2 is 5 marks)
(Total for Question 13
4
D
3.
y°
E
142°
92°
F
C
Diagram NOT
accurately drawn
134°
123°
x°
G
H
107°
A
B
ABCDEF is a hexagon.
G is a point on AF.
H is a point on BC.
GH is parallel to AB.
(a) Give a reason why x = 107
.. ....... ..... .............. .. .. .. .. .. .. .. .. . .. .. .. .. .. . .... .... ... .... .... .... .... ... .... .... .... .... .... ... .... .... . .. .. . .. . .. .. . .. . .. .. . .. . .. .. . .. . .. . .. .. . .. . .. .. . .. . .. . .. .. . .. . .. .. . .. . .. . .. .. . .. . .. .. . .. . .. . .. .. . .. . .. .. . .. . .. . .. .. . .. . .. .. . ... . . . . .. . . .. . . . . .. . . . .. . . . . .. . . . .
(1)
(b) Work out the value of y.
y =.. .. . .. . .. . . .. . . . .. . . . . .. . . . .. . . . . .. . . . .. . .
(4)
(Total for Question 43 is 5 marks)
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'LDJUDP 127
DFFXUDWHO\ GUDZQ
7KH VL]H RI HDFK LQWHULRU DQJOH LV GHJUHHV JUHDWHU WKDQ WKH VL]H RI HDFK H[WHULRU DQJOH
:RUN RXW WKH QXPEHU RI VLGHV WKH UHJXODU SRO\JRQ KDV
( ( (( ( ( ( (( ( ( ( (( ( ( ( ( (( ( ( ( (( ( ( ( ( ((
7RWDO IRU 4XHVWLRQ 4 LV PDUNV
'R 127 ZULWH LQ WKLV VSDFH
22
5.
Diagram NOT
accurately drawn
The diagram shows a regular hexagon.
The perimeter of the hexagon is 42 cm.
Calculate the area of the hexagon.
Give your answer correct to 3 significant figures.
. . .. . . . . .. . .. . . . . .. . . . .. . . . . .. .
(Total for Question 22
5 is 5 marks)
cm2
3
6.
Diagram NOT
accurately drawn
x°
The diagram shows a regular 5-sided polygon.
(a) Work out the value of x.
x = .. ....... ....... ....... ....
(2)
Diagram NOT
accurately drawn
y°
The diagram shows a regular 6-sided polygon.
(b) Work out the value of y.
y = .. ....... ....... ....... ....
(2)
(Total for Question 63 is 4 marks)
19
7.
Diagram NOT
accurately drawn
The diagram shows part of a regular polygon.
The interior angle and the exterior angle at a vertex are marked.
The size of the interior angle is 7 times the size of the exterior angle.
Work out the number of sides of the polygon.
. ....... ....... ....... ......
(Total for Question 19
7 is 3 marks)
tt
20 Show that the recurring decimal 0.015 =
1
66
(Total for Question 20 is 2 marks)
21 There are 1300 sheets of paper, correct to the nearest 100 sheets, in a pile.
Each sheet is of equal thickness.
The height of the pile is 160 mm, correct to the nearest 10 mm.
Calculate the upper bound, in millimetres, for the thickness of one sheet of paper.
... ... . .... ....... ....... ...
(Total for Question 21 is 3 marks)
mm
99. 7KHGLDJUDPVKRZVDSDUDOOHORJUDPABCD.
,QWKHGLDJUDPDOOWKHDQJOHVDUHLQGHJUHHV
D
C
Diagram NOT
DFFXUDWHO\GUDZQ
4x – 30
x
xy
A
B
Work out the value of x DQGWKHYDOXHRIy.
x = ...... ....... ........ .......
y = ...... ....... ....... ....... .
(Total for Question 99 is 4 marks)
Do NOT write in this space.
910. (a) Find the sum of the interior angles of a polygon with 7 sides.
. .... ... .... ... .. .... ....... ....... ....... ....
q
(2)
Diagram NOT
accurately drawn
xq
The diagram shows a regular polygon with 7 sides.
(b) Work out the value of x.
Give your answer correct to 1 decimal place.
. ... .... ... ... ...... ....... ....... ....... .....
(2)
(Total for Question10
9 is 4 marks)
11.The size of each interior angle of a regular polygon with n sides is 140°
14
Work out the size of each interior angle of a regular polygon with 2n sides.
. .... ... .... .. ...... ........ ....... ......
°
11 is 5 marks)
(Total for Question 14
 3 
15 Simplify  2 x 2 y 


4
.... ... ...... ....... ....... ....... .......
(Total for Question 15 is 2 marks)
3
12.
B
A
Diagram NOT
accurately drawn
110°
D
X
C
ABCD is a parallelogram.
Angle DCB = 110°
X is the point on DC such that AX bisects the angle DAB.
Calculate the size of angle AXC.
.. . . .. . . . . .. . . . .. . . . .. . . . . .. . . .
(Total for Question12
3 is 4 marks)
Do NOT write in this space.
°
713. Here is a trapezium ABCD.
Diagram NOT
accurately drawn
D
C
20 cm
14 cm
A
8 cm
B
Angle DAB = angle ABC = 90°
AD = 20 cm
AB = 8 cm
BC = 14 cm
(a) Calculate the area of the trapezium ABCD.
.... ... .... ..... ....... ....... .
cm2
(2)
(b) Calculate the length of CD.
.. .... .. ....... ....... ....... ..
(4)
(Total for Question 13
7 is 6 marks)
cm