1.	(a)	Write down the metric unit you would use to measure
(i)	the weight of a man,	…………………..
(ii)	the length of a classroom.	…………………..
(2)
(b)	(i)	Change 300 millimetres to centimetres
……………….. cm
(ii)	Change 4 litres to millilitres.
……………….. ml
(2)
(Total 4 marks)

2.	

The diagram shows a car park.
Mrs Roberts is selling the car park. She will accept any offer that is more than £28 per square metre.
	Mr Patel offers £194 700 for the car park..
Will Mrs Roberts accept Mr Patel’s offer for the car park?
	You must show how you reached your decision.

Decision ………………….(Total 6 marks)

3.	(a)	Factorise 3x + 6
……………………
(1)
Here is a right-angled triangle.

	The lengths of the three sides of the triangle are 3x + 6, 4x + 8 and 5x + 10.
All measurements are in centimetres.
(b)	Find an expression, in terms of x, for the perimeter of the triangle.
Give your answer in its simplest form.
…………………………….
(2)
	The perimeter of the triangle is 42 cm.
(c)	(i)	Find the value of x.
x = ……………………….
(1)
(ii)	Find the length of the shortest side of the triangle.
…………………………. cm
(4)
(Total 7 marks)

4.	The size of each exterior angle of a regular polygon is 40°.
	Work out the number of sides of the polygon.

………………………
(Total 2 marks)

5.	

	The diagram shows a solid cylinder.
The radius of the cylinder is 54 cm.
The height of the cylinder is 10 cm.
(a)	Calculate the curved surface area of the cylinder.
Give your answer correct to three significant figures.

……………….
(3)

	The diagrams show the circular top of the cylinder and a piece of plastic in the shape of a right-angled triangle. The two shorter sides of the triangle have lengths 76 cm and 77 cm.
(b)	Show that the triangular piece of plastic cannot completely fit on the top of the cylinder without overlapping.

(4)
(Total 7 marks)

6.	John weighs 88 kg and Sophie weighs 65 kg.
Both weights have been rounded to the nearest kg.

	Explain why their minimum combined weight is 152 kg.
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
(Total 1 mark)

7.	
Diagram NOT accurately drawn
	The diagram shows a sector of a circle, centre O, radius 10 cm.
The arc length of the sector is 15 cm.
	Calculate the area of the sector.
.......................... cm2
(Total 4 marks)

8.	

	AB is parallel to DC.
The lines AC and BD intersect at E.
AB = 8 cm	EC = 5 cm	DC = 6 cm
(a)	Explain why triangle ABE and triangle CDE are similar.
………………………………………………………………………………………………..
………………………………………………………………………………………………..
………………………………………………………………………………………………..
(2)
(b)	Calculate the length of AC.
…………………….. cm
(3)
(Total 5 marks)

9.	A car travels at 30 miles per hour.
Change 30 miles per hour to kilometres per hour.

…………………………… kilometres per hour
(Total 2 marks)

10.	Here is a solid cube.

	Write down
(i)	the number of faces of the cube,
…………………..
(ii)	the number of vertices of the cube,
…………………..
(iii)	the number of edges of the cube.
…………………..
(Total 3 marks)

11.	The length of a rectangle is 6.7 cm, correct to 2 significant figures.
(a)	For the length of the rectangle write down
(i)	the upper bound,
.....................................cm
(ii)	the lower bound.
.....................................cm
(2)
	The area of the rectangle is 26.9 cm2, correct to 3 significant figures.
(b)	(i)	Calculate the upper bound for the width of the rectangle.
Write down all the figures on your calculator display.
.....................................cm
(ii)	Calculate the lower bound for the width of the rectangle.
Write down all the figures on your calculator display.
.....................................cm
(3)
(c)	(i)	Write down the width of the rectangle to an appropriate degree of accuracy.
.....................................cm
(ii)	Give a reason for your answer.
...........................................................................................................................
(2)
(Total 7 marks)

12.	

	Calculate the area of a circle with diameter 12 cm.

………………………..
(Total 3 marks)

13.	
Diagram NOT accurately drawn

	PQR is a right-angled triangle.
	PR = 6 cm.
QR = 4 cm.
	Work out the length of PQ.
Give your answer correct to 3 significant figures.

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

14.	The length of a rectangle is 6.7 cm, correct to 2 significant figures.
	(a)	For the length of the rectangle write down
(i)	the upper bound,
…………………….cm
(ii)	the lower bound.
…………………….cm
(2)
	The area of the rectangle is 26.9 cm2, correct to 3 significant figures.
(b)	(i)	Calculate the upper bound for the width of the rectangle.
Write down all the figures on your calculator display.
…………………….cm
(ii)	Calculate the lower bound for the width of the rectangle.
Write down all the figures on your calculator display.
…………………….cm
(3)
(c)	Write down the width of the rectangle to an appropriate degree of accuracy.
…………………….cm
(1)
(Total 6 marks)

15.	A shaded shape is shown on the grid of centimetre squares.

(a)	Work out the perimeter of the shaded shape.

.......................cm
(1)
(b)	Work out the area of the shaded shape.
.....................cm2
(1)
(c)	Reflect the shaded shape in the mirror line.
(2)
(Total 4 marks)

16.	
	
	Work out the area of the shaded parallelogram in cm2

.…………… cm2
(Total 1 mark)

17.	Barry and Kath are studying a number pattern.
	The first three numbers in the number pattern are	1, 2, 4
	Barry says that the next number is 8.
	Kath says the next number is 7.
	Explain why both Barry and Kath could be right.
........................................................................................................................................
........................................................................................................................................
........................................................................................................................................
(Total 2 marks)

18.	The diameter of a circle is 12 centimetres.
(a)	Work out the circumference of the circle.
Give your answer, in centimetres, correct to 1 decimal place.

.............................. cm
(2)

	The length of each diagonal of a square is 20 cm.
(b)	Work out the area of the square.

.............................. cm2
(2)
(Total 4 marks)

19.	

	The diagram represents a large tank in the shape of a cuboid.
The tank has a base.
It does not have a top.
The width of the tank is 2.8 metres.
The length of the tank is 3.2 metres.
The height of the tank is 4.5 metres.
	The outside of the tank is going to be painted.
1 litre of paint will cover 2.5 m2 of the tank.
The cost of paint is £2.99 per litre.
	Calculate the cost of the paint needed to paint the outside of the tank.

£ ..................................
(Total 5 marks)

20.	The diagram shows a trapezium of height 3 m.

Find the area of this trapezium
State the units with our answer.
................................
(Total 3 marks)

21.	

	The diagram shows two shapes.
(a)	Write down the mathematical name for the shape A.
.................................
(1)
(b)	Write down the coordinates of the point P.
(...............,...............)
(1)
(c)	Write down the mathematical name of the triangle B.
.................................
(1)
	The coordinates of another point are (–2, –4).
(d)	Mark this point on the grid.
Label it Q.
(1)
(Total 4 marks)

22.	

	The diagram represents a garden in the shape of a rectangle.
All measurements are given in metres.
The garden has a flowerbed in one corner.
The flowerbed is a square of side x.
(a)	Write down an expression, in terms of x, for the shortest side of the garden.

.....................................
(1)
(b)	Find an expression, in terms of x, for the perimeter of the garden.
Give your answer in its simplest form.

.....................................
(2)
	The perimeter of the garden is 20 metres.
(c)	Find the value of x.
.....................................
(2)
(Total 5 marks)

23.	The table shows some rows of a number pattern.
Row 1	1	=		
Row 2	1 + 2	=		
Row 3	1 + 2 + 3	=		
Row 4	1 + 2 + 3 + 4			

				
Row 8				
(a)	In the table, complete row 4 of the number pattern.
(1)
(b)	In the table, complete row 8 of the number pattern.
(1)
(c)	Work out the sum of the first 100 whole numbers.

.....................................
(1)
(Total 3 marks)

24.	

	PQR is a triangle.
Angle PQR = 90°.
PQ = 12.5 cm.
QR = 5 cm.
	Calculate the value of x.
Give your answer correct to 1 decimal place.

.........................................
(Total 3 marks)

25.	

	Work out the value of a.

a = .............................
(Total 3 marks)

26.	Here are some patterns made up of dots.

(a)	In the space below, draw Pattern number 4.

(1)

(b)	Complete the table.
Pattern number	1	2	3	4	5	
Number of dots	10	14	18			
(1)
(c)	How many dots are used in Pattern number 10?

..........................
(1)
(Total 3 marks)

27.	

	The conversion graph above can be used for changing between kilograms and pounds.
(a)	Use the graph to change 22 pounds to kilograms.
............................. kg
(1)

(b)	Use the graph to change 2.5 kilograms to pounds.
..................... pounds
(1)
	Firoza weighs 110 pounds.
(c)	Change 110 pounds to kilograms.

............................. kg
(3)

28.	This is a map of part of Northern England.

Scale: 1 cm represents 10 km
	A plane flies in a straight line from Preston to Stoke-on-Trent.
(a)	How far does it fly?
Give your answer in kilometres.
..................... km(2)

(b)	Measure and write down the bearing of Preston from Manchester.

........................°
(1)
(Total 3 marks)

29.	

	This is part of the design of a pattern found at the theatre of Diana at Alexandria.
	It is made up of a regular hexagon, squares and equilateral triangles.
(a)	Write down the size of the angle marked x°.
.....................................°
(1)
(b)	Work out the size of the angle marked y°.

.....................................°
(2)

	The area of each equilateral triangle is 2 cm2.
(c)	Work out the area of the regular hexagon.

.....................................cm2
(2)
(Total 5 marks)

30.	

	An ice hockey puck is in the shape of a cylinder with a radius of 3.8 cm, and a thickness of 2.5 cm.
	It is made out of rubber with a density of 1.5 grams per cm3.	
	Work out the mass of the ice hockey puck.
Give your answer correct to 3 significant figures.

............... grams
(Total 4 marks)

31.	

	The diagram shows a semi-circle.
The diameter of the semi-circle is 15 cm.
	Calculate the area of the semi-circle.
Give your answer correct to 3 significant figures.
............................
(Total 3 marks)
32.	Daniel leaves his house at 07 00.
	He drives 87 miles to work.
He drives at an average speed of 36 miles per hour.
	At what time does Daniel arrive at work?…………………………
(Total 3 marks)

33.	

	BE is parallel to CD.
AE = 6 cm, ED = 4 cm, AB = 4.5 cm, BE = 4.8 cm.
(a)	Calculate the length of CD.
.......................cm
(2)
(b)	Calculate the perimeter of the trapezium EBCD.
.......................cm
(2)
(Total 4 marks)

34.	A can of drink is in the shape of a cylinder.
The can has a radius of 4 cm and a height of 15 cm.

	Calculate the volume of the cylinder.
Give your answer correct to 3 significant figures.

…………………………
(Total 3 marks)

35.	

	Triangle ABC is isosceles, with AC = BC.
	Angle ACD = 62°.
	BCD is a straight line.
(a)	Work out the size of angle x.

x = ………………°
(2)

	The diagram shows part of a regular octagon.
(b)	Work out the size of angle x.

x = ………………°
(3)
(Total 5 marks)