1.	(a)	PQRS is a rectangle.

(i)	Calculate the area of PQRS.
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(ii)	Calculate the area of the triangle PSN.
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(iii)	Calculate the area of triangle SMN.
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(iv)	Calculate the area of trapezium NQRM.
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(4)

	
2.	A wire 18 m long runs from the top of a pole to the ground as shown in the diagram.
              The wire makes an angle of 35º with the ground.

	Calculate the height of the pole.
	Give your answer to a suitable degree of accuracy.
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(4)

3.	The diagram shows a running track.

	BA and DE are parallel and straight.  They are each of length 90 metres.
BCD and EFA are semi-circular. They each have a diameter of length 70 metres.
(a)	Calculate the perimeter of the track.
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(3)
(b)	Calculate the total area inside the track.
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 (4)

4.	

BDC is a straight line.
	
(a)	 Calculate the length of AC,
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(2)
(b)	Calculate the length of BD,
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(2)
(c)      show that angle BAC is a right angle.
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..................................................................................................................................
(2)

5.	Triangles ADE and ABC are similar.
DE is parallel to BC.
AD = 4 cm, DE = 6 cm and BC = 9 cm.

	Calculate the length of BD.
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
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Answer ........................................................... cm
(3)

6.	The diagram is a drawing of a triangular prism.

(a)	Calculate the area of triangle ABC.
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(2)
(b)	Calculate the volume of the prism.
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(2)

7.	Sally is trying to estimate the height of her school.  She measures the angle of elevation of the highest point as 35º.. She measures the distance from the bottom of the wall along level ground as 12.6 m.

(a)	Calculate the height of the school.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(b)	To what degree of accuracy should Sally give her answer?
Give a reason for your answer.
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.....................................................................................................................................
.....................................................................................................................................
(2)

8.	The diagram shows two shapes, a parallelogram and trapezium.
They both have the same area.

Not drawn to scale
	Find the height of the parallelogram, marked h on the diagram.
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...............................................................................................................................................
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(4)

9.	In the diagram AB is parallel to CD.
	AB = OC = 12 cm.  OB = 10 cm.

	Use similar triangles to calculate the length of CD.
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(3)

10.	CE = 7.5 cm

	Use Pythagoras’ theorem to calculate
(a)	the length of CD,
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.....................................................................................................................................
(2)
(b)	the length of CB.
.....................................................................................................................................
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.....................................................................................................................................
 (3)

(b)	Calculate angle BCA.
....................................................................................................................................
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Answer ...................................... degrees
(3)

11.	Use the information in the table to calculate the value of x.

...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
Answer ................................................................ cm
(3)
(Total 3 marks)

12.	The diagram shows a beam of uniform cross-section and length 4 metres.

	Calculate the volume of the beam.
Give your answer in cubic centimetres.
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...............................................................................................................................................
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Answer ................................................................ cm3
(Total 5 marks)

13.	The diagram shows part of a framework for a roof.

	Triangles ABC and CED are right angled. 
AC = 3.2 m      CE = 4.1 m
Angle ACB is 49°.     Angle EDC is 58°.
(a)	Calculate the length BC.
………………………………………………………………………………………
………………………………………………………………………………………
………………………………………………………………………………………
………………………………………………………………………………………
………………………………………………………………………………………
(3)
(b)	Calculate the length CD.
………………………………………………………………………………………
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………………………………………………………………………………………
………………………………………………………………………………………

 

14.	

(a)	Show clearly that these two triangles are similar.
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
 (2)
(b)	Calculate the value of x.
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
 (3)

15.	

	A ladder, 2.75 m long, leans against a wall.
The bottom of the ladder is 1.80 m from the wall, on level ground.
	Calculate how far the ladder reaches up the wall.
Give your answer to an appropriate degree of accuracy.
.....................................................………..........................................……………………
.....................................................………..........................................……………………
.....................................................………..........................................……………………
(4)

16.	This net will fold to make a three-dimensional shape.

(a)	Measure the size of the angle BPC.
....................................................................................................................................
(1)
(b)	Calculate the area of the net.
(Remember to state the units in your answer.)
....................................................................................................................................
....................................................................................................................................
....................................................................................................................................
....................................................................................................................................
(3)
(c)	(i)	Draw a sketch of the shape that the net makes when folded.

(1)

(ii)	What is the mathematical name of this shape?
..........................................................................................................................
(1)
(ii)	Calculate the volume of this shape.
(Remember to state the units in your answer.)
..........................................................................................................................
..........................................................................................................................
..........................................................................................................................
(3)

Content-type: application/msword; name="Heysham revision A.rtf"Content-transfer-encoding: QUOTED-PRINTABLEContent-Disposition: inline; Filename="Heysham revision A.rtf"1.	(a)	PQRS is a rectangle.

(i)	Calculate the area of PQRS.
........................................................................................................................
........................................................................................................................
(ii)	Calculate the area of the triangle PSN.
........................................................................................................................
........................................................................................................................
(iii)	Calculate the area of triangle SMN.
........................................................................................................................
........................................................................................................................
(iv)	Calculate the area of trapezium NQRM.
........................................................................................................................
........................................................................................................................
(4)

	
2.	A wire 18 m long runs from the top of a pole to the ground as shown in the diagram.
              The wire makes an angle of 35º with the ground.

	Calculate the height of the pole.
	Give your answer to a suitable degree of accuracy.
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
(4)

3.	The diagram shows a running track.

	BA and DE are parallel and straight.  They are each of length 90 metres.
BCD and EFA are semi-circular. They each have a diameter of length 70 metres.
(a)	Calculate the perimeter of the track.
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
(3)
(b)	Calculate the total area inside the track.
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
 (4)

4.	

BDC is a straight line.
	
(a)	 Calculate the length of AC,
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
(2)
(b)	Calculate the length of BD,
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
(2)
(c)      show that angle BAC is a right angle.
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
(2)

5.	Triangles ADE and ABC are similar.
DE is parallel to BC.
AD = 4 cm, DE = 6 cm and BC = 9 cm.

	Calculate the length of BD.
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
Answer ........................................................... cm
(3)

6.	The diagram is a drawing of a triangular prism.

(a)	Calculate the area of triangle ABC.
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
(2)
(b)	Calculate the volume of the prism.
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
(2)

7.	Sally is trying to estimate the height of her school.  She measures the angle of elevation of the highest point as 35º.. She measures the distance from the bottom of the wall along level ground as 12.6 m.

(a)	Calculate the height of the school.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(b)	To what degree of accuracy should Sally give her answer?
Give a reason for your answer.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)

8.	The diagram shows two shapes, a parallelogram and trapezium.
They both have the same area.

Not drawn to scale
	Find the height of the parallelogram, marked h on the diagram.
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
(4)

9.	In the diagram AB is parallel to CD.
	AB = OC = 12 cm.  OB = 10 cm.

	Use similar triangles to calculate the length of CD.
.....................................................………..........................................……………………
.....................................................………..........................................……………………
.....................................................………..........................................……………………
.....................................................………..........................................……………………
(3)

10.	CE = 7.5 cm

	Use Pythagoras’ theorem to calculate
(a)	the length of CD,
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(b)	the length of CB.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
 (3)

(b)	Calculate angle BCA.
....................................................................................................................................
....................................................................................................................................
....................................................................................................................................
....................................................................................................................................
Answer ...................................... degrees
(3)

11.	Use the information in the table to calculate the value of x.

...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
Answer ................................................................ cm
(3)
(Total 3 marks)

12.	The diagram shows a beam of uniform cross-section and length 4 metres.

	Calculate the volume of the beam.
Give your answer in cubic centimetres.
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
Answer ................................................................ cm3
(Total 5 marks)

13.	The diagram shows part of a framework for a roof.

	Triangles ABC and CED are right angled. 
AC = 3.2 m      CE = 4.1 m
Angle ACB is 49°.     Angle EDC is 58°.
(a)	Calculate the length BC.
………………………………………………………………………………………
………………………………………………………………………………………
………………………………………………………………………………………
………………………………………………………………………………………
………………………………………………………………………………………
(3)
(b)	Calculate the length CD.
………………………………………………………………………………………
………………………………………………………………………………………
………………………………………………………………………………………
………………………………………………………………………………………
………………………………………………………………………………………

 

14.	

(a)	Show clearly that these two triangles are similar.
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
 (2)
(b)	Calculate the value of x.
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
 (3)

15.	

	A ladder, 2.75 m long, leans against a wall.
The bottom of the ladder is 1.80 m from the wall, on level ground.
	Calculate how far the ladder reaches up the wall.
Give your answer to an appropriate degree of accuracy.
.....................................................………..........................................……………………
.....................................................………..........................................……………………
.....................................................………..........................................……………………
(4)

16.	This net will fold to make a three-dimensional shape.

(a)	Measure the size of the angle BPC.
....................................................................................................................................
(1)
(b)	Calculate the area of the net.
(Remember to state the units in your answer.)
....................................................................................................................................
....................................................................................................................................
....................................................................................................................................
....................................................................................................................................
(3)
(c)	(i)	Draw a sketch of the shape that the net makes when folded.

(1)

(ii)	What is the mathematical name of this shape?
..........................................................................................................................
(1)
(ii)	Calculate the volume of this shape.
(Remember to state the units in your answer.)
..........................................................................................................................
..........................................................................................................................
..........................................................................................................................
(3)