Edexcel (I)GCSE
Mathematics
Higher Tier
Geometry - Mensuration of 2-D shapes
Total Marks: 99
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 99
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 (a) Here is a shape made from a rectangle and a semicircle.
15
Diagram NOT
accurately drawn
2.7 cm
7.1 cm
The length of the rectangle is 7.1 cm.
The radius of the semicircle is 2.7 cm.
Work out the area of the shape.
Give your answer correct to 3 significant figures.
.. . .. . .. .. . .. . .. .. . . . . . .. . . . . .. . . . .. . . . ..
(4)
cm2
(b) Here is another shape made from a rectangle and a semicircle.
Diagram NOT
accurately drawn
r cm
L cm
The length of the rectangle is L cm.
The radius of the semicircle is r cm.
The perimeter, P cm, of the shape is given by the formula
P = ʌr + 2L + 2r
Make r the subject of the formula P = ʌr + 2L + 2r.
r = . .. . .. . .. .. . .. . . .. . . . . .. . . . .. . . . .. . . . . .. . . . .. . .
(3)
(Total for Question 15
2 is 7 marks)
63 The diagram shows a trapezium PQRS.
Q
6cm
R
Diagram NOT
accurately drawn
5cm
P
8cm
S
(a) Calculate the area of the trapezium PQRS.
. . .. . .. .. . .. . . .. . . . .. . . . . .. . . . .
cm2
(2)
(b) Calculate the length PQ.
Give your answer correct to 3 significant figures.
. .. . .. . . . . . .. . . . .. . . . . .. . . . .. . .
(4)
(Total for Question 36 is 6 marks)
cm
184
C
Diagram NOT
accurately drawn
B
9 cm
35°
A
D
9 cm
O
AOD is a diameter of a circle, with centre O and radius 9 cm.
ABC is an arc of the circle.
AC is a chord.
Angle ADC = 35°
Calculate the area of the shaded segment.
Give your answer correct to 3 significant figures.
. .. .. . .. . .. .. . .. . .. . .. .. . .. . .. .. . .. . .. . .. . . . . .. . . . . .. . . . .. . . . .
4 is 6 marks)
(Total for Question 18
cm2
95
B
Diagram NOT
accurately drawn
4 cm
C
6 cm
6 cm
A
E
4 cm
D
ABCD is a rhombus.
The diagonals AC and BD cross at the point E.
AE CE FP
BE DE FP
Angle AEB ƒ
(a) Work out the area of the rhombus.
..........................................................
cm2
(3)
(b) Work out the length of AB.
Give your answer correct to 3 significant figures.
..........................................................
(3)
(Total for Question 59 is 6 marks)
cm
76
C
D
Diagram NOT
accurately drawn
9 cm
5 cm
A
B
N
The shape ABCD is made from a rectangle ANCD
and the right-angled triangle NBC.
ANB is a straight line.
AN = 9 cm.
NB = 5 cm.
The area of rectangle ANCD is 36 cm2
Work out the area of shape ABCD.
.. . .. . .. . .. .. . .. . .. .. . .. . .. . .. .. . .. . .. .. . .. . .. . .. . . . . . . . .. . . . .. . . . . .. . .
(Total for Question 67 is 4 marks)
Do NOT write in this space.
cm2
7
8
16 cm
Diagram NOT
accurately drawn
10 cm
4 cm
9 cm
The diagram shows a shape.
Work out the area of the shape.
. .. . .. .. . . . . . .. . . . .. . . . . .. . . . .. .
cm2
(Total for Question 87 is 4 marks)
8 (a) Factorise n2 + 8n
.. . .. .. . .. . .. .. . .. . .. .. . .. . .. . .. .. . . . . . .. . . . . .. . . . .. . . . .. . . . . .. . . . .
(2)
(b) Expand and simplify 3(2xííx + 3)
.. . .. .. . .. . .. . .. .. . .. . .. .. . .. . .. .. . . . . . .. . . . . .. . . . .. . . . . .. . . . .. . . . .
(2)
(c) Expand and simplify (y + 7)(y + 2)
. .. . .. . .. . .. .. . .. . .. .. . .. . .. . .. .. . .. . . .. . . . .. . . . . .. . . . .. . . . . .. . . . ..
(2)
(Total for Question 8 is 6 marks)
219 Here is a shape.
Diagram NOT
accurately drawn
C
7 cm
7 cm
&>X
A
9 cm
B
The shape is made from triangle ABC and a sector of a circle, centre C and radius CA.
CA = 7 cm.
CB = 16 cm.
Angle ACB&>X
Calculate the area of the shape.
Give your answer correct to 3 significant figures.
. .. .. . .. . .. . .. .. . .. . . .. . . . .. . . . . .. . . . .. . . . .
9 is 6 marks)
(Total for Question 21
cm2
10 The diagram shows the path of an athlete on a running track.
10
85 m
Diagram NOT
accurately drawn
36.6 m
The path consists of two straight lengths and a semicircle at each end.
Each straight length is 85 metres.
Each semicircle has a radius of 36.6 metres.
Calculate the area enclosed by the path.
Give your answer correct to 3 significant figures.
. ... .... ... .... ... .... ... .... . .. ...... ....... ....... ..
(Total for Question 10
10 is 4 marks)
Do NOT write in this space.
m2
12 11
C
Diagram NOT
accurately drawn
9.5 cm
A
7.6 cm
B
The diagram shows a shape made from triangle ABC and a semicircle with diameter BC.
Triangle ABC is right-angled at B.
AB = 7.6 cm and AC = 9.5 cm.
Calculate the area of the shape.
Give your answer correct to 3 significant figures.
.... ... .... ... .... ... .. ....... ....... ...
(Total for Question 11
12 is 5 marks)
cm2
713 A square hole is cut from a circular piece of card.
Diagram NOT
accurately drawn
3.2 cm
3.2 cm
10 cm
The square has sides of length 3.2 cm.
The diameter of the circular piece of card is 10 cm.
Work out the area of the shaded region.
Give your answer correct to 3 significant figures.
... ... . ..... ....... ....... ..
cm2
(Total for Question 13
7 is 4 marks)
8
Express 825 as a product of its prime factors.
.. .... ... .... ... .... ... . ... ..... ....... ....... ....... ...
(Total for Question 8 is 3 marks)
1314
D
C
Diagram NOT
accurately drawn
O
10 cm
10 cm
A
B
The diagram shows a square ABCD drawn inside a circle, centre O.
A, B, C and D are points on the circle.
The lengths of the sides of the square are 10 cm.
AC is a diameter of the circle.
Calculate the circumference of the circle.
Give your answer correct to 3 significant figures.
.. .. . .. . .. . .. . . . . . . . .. . . . .. . . . . .. . . . ..
(Total for Question 14
13 is 4 marks)
cm
315 The diagram shows a rectangle PQRS.
PQ = 14 cm and QR = 9 cm.
The point A lies on PS so that PA = 5 cm.
The point B lies on SR so that BR = 8 cm.
8 cm
S
B
R
Diagram NOT
accurately drawn
9 cm
A
5 cm
P
14 cm
Q
(a) Work out the area of triangle AQB.
. .. .. . .. . .. . .. .. . .. . . . . . .. . . . .. . . . . .. . . . .. . . .
cm2
(4)
(b) Work out the length of AQ.
Give your answer correct to 3 significant figures.
.. . .. . .. .. . .. . .. .. . . . . . .. . . . . .. . . . .. . . . . .. . . . .
(3)
(Total for Question 15
3 is 7 marks)
cm
3
16
Diagram NOT
accurately drawn
7.6 cm
(a) A circle has a radius of 7.6 cm.
Work out the area of the circle.
Give your answer correct to 3 significant figures.
... .... .. ...... ....... ......
cm2
(2)
The radius, 7.6 cm, is correct to 1 decimal place.
(b) (i) Write down the upper bound of the radius.
. .... ..... ....... ....... ....
cm
.... ... .. ....... ....... .....
cm
(ii) Write down the lower bound of the radius.
(2)
(Total for Question 16
3 is 4 marks)
Do NOT write in this space.
5
17
Diagram NOT
DFFXUDWHO\GUDZQ
FP
6 cm
6 cm
FP
7KHGLDJUDPVKRZVDPHWDOSODWHLQWKHVKDSHRIDUHFWDQJOH
7KHUHFWDQJOHKDVOHQJWKFPDQGZLGWKFP
7ZRLGHQWLFDOFLUFOHVHDFKRIGLDPHWHUFPKDYHEHHQFXWRXWRIWKHSODWH
:RUNRXWWKHDUHDRIWKHVKDGHGUHJLRQRIWKHPHWDOSODWH
Give your answer correct to the nearest cm.
. ... .... .. ....... ....... ....
(Total for Question 17
5 is 4 marks)
Do NOT write in this space.
cm
418 The diagram shows a shape with one line of symmetry.
10 cm
Diagram NOT
accurately drawn
12 cm
4 cm
15 cm
Work out the area of the shape.
... .... ... .... ... .... .... .. ...... ....... ......
(Total for Question 18
4 is 4 marks)
cm2
Diagram NOT
accurately drawn
2 19
8 cm
17 cm
32 cm
The diagram shows a circle inside a rectangle.
Work out the area of the shaded region.
Give your answer correct to 3 significant figures.
... .... . ....... ........ .....
cm2
(Total for Question 19
2 is 3 marks)
3
A bag contains only red counters, blue counters and yellow counters.
The number of red counters in the bag is the same as the number of blue counters.
Mikhail takes at random a counter from the bag.
The probability that the counter is yellow is 0.3
Work out the probability that the counter Mikhail takes is red.
....... ....... ....... .......
(Total for Question 3 is 3 marks)
1720
Diagram NOT
accurately drawn
x cm
2x cm
(x + 7) cm
The diagram shows a trapezium.
The trapezium has an area of 17 cm2
(a) Show that 2x2 + 7x – 17 = 0
(3)
(b) Work out the value of x.
Give your answer correct to 3 significant figures.
Show your working clearly.
x = ... ....... ....... ........ ...
(3)
20 is 6 marks)
(Total for Question 17
2 21 The wheel of the Singapore Flyer is a circle with a diameter of
150 metres.
(a) Calculate the circumference of the wheel.
Give your answer correct to the nearest metre.
... .... ... .... .. ... ....... .....
metres
(2)
The wheel takes 30 minutes to rotate once.
(b) Work out the average speed of a point on the circumference of the wheel as it
rotates once.
Give your answer in metres per second correct to 3 significant figures.
. .... .... ... .... ... .... ... .... .
metres per second
(3)
The diagram shows a giant wheel above horizontal ground.
Diagram NOT
accurately drawn
D
x
h
The wheel is a circle of diameter D metres.
The lowest point of the wheel is h metres above the ground.
The centre of the wheel is x metres above the ground.
(c) Express h in terms of D and x
.. .... ... .... ... .... .... ... ... ... ...... ........ ....... ....... .
(2)
(Total for Question 21
2 is 7 marks)
Do NOT write in this space.