E = {odd numbers less than 30} A = {3, 9, 15, 21, 27} B = {5, 15, 25}
Complete the Venn diagram to represent this information.
(4)
A number is chosen at random from the universal set, E.
What is the probability that the number is in the set A 
B?
(2)
Solve the simultaneous equations
3 x + y = –4 3 x – 4 y = 6
(3)
The table shows some information about the dress sizes of 25 women.
| Dress size | Number of women |
| 8 | 2 |
| 10 | 9 |
| 12 | 8 |
| 14 | 6 |
3 of the 25 women have a shoe size of 7
Zoe says that if you choose at random one of the 25 women, the probability that she has either a shoe size of 7 or a dress size of 14 is 
because
Is Zoe correct? You must give a reason for your answer.
(1)
Daniel bakes 420 cakes. He bakes only vanilla cakes, banana cakes, lemon cakes and chocolate cakes. 
of the cakes are vanilla cakes. 35% of the cakes are banana cakes. The ratio of the number of lemon cakes to the number of chocolate cakes is 4:5
Work out the number of lemon cakes Daniel bakes.
(5)
In the diagram, AB, BC and CD are three sides of a regular polygon P.
Show that polygon P is a hexagon. You must show your working.
(4)
The density of apple juice is 1.05 grams per cm3.
The density of fruit syrup is 1.4 grams per cm3.
The density of carbonated water is 0.99 grams per cm3.
25 cm3 of apple juice are mixed with 15 cm3 of fruit syrup and 280 cm3 of carbonated water to make a drink with a volume of 320 cm3.
Work out the density of the drink. Give your answer correct to 2 decimal places.
(4)
ABC is a right-angled triangle.
Calculate the length of AB. Give your answer correct to 3 significant figures.
(2)
A square, with sides of length x cm, is inside a circle. Each vertex of the square is on the circumference of the circle.
The area of the circle is 49 cm2.
Work out the value of x. Give your answer correct to 3 significant figures.
(4)
The box plot shows information about the distribution of the amounts of money spent by some male students on their holidays.
Work out the interquartile range for the amounts of money spent by these male students.
(2)
The table below shows information about the distribution of the amounts of money spent by some female students on their holidays.
| Smallest | Lower quartile | Median | Upper quartile | Largest | |
| Money spent (£) | 60 | 180 | 300 | 350 | 650 |
On the grid above, draw a box plot for the information in the table.
(2)
Chris says,
“The box plots show that the female students spent more money than the male students.”
Is Chris correct? Give a reason for your answer.
(1)
Naoby invests £6000 for 5 years. The investment gets compound interest of x % per annum.
At the end of 5 years the investment is worth £8029.35
Work out the value of x.
(3)
Jeff is choosing a shrub and a rose tree for his garden. At the garden centre there are 17 different types of shrubs and some rose trees.
Jeff says,
“There are 215 different ways to choose one shrub and one rose tree.”
Could Jeff be correct? You must show how you get your answer.
(2)
The points A, B, C and D lie in order on a straight line.
AB: BD = 1:5 AC: CD = 7:11
Work out AB: BC: CD
(3)
Write down the three inequalities that define the shaded region.
(4)
Calculate the value of x. Give your answer correct to 3 significant figures.
(5)
with x0 = 
2.5
Explain the relationship between the values of x1, x2 and x3 and the equation x3 + 2x2 + 4 = 0
(2)
A train travelled along a track in 110 minutes, correct to the nearest 5 minutes.
Jake finds out that the track is 270 km long. He assumes that the track has been measured correct to the nearest 10 km.
Could the average speed of the train have been greater than 160 km/h? You must show how you get your answer.
(4)
Jake’s assumption was wrong. The track was measured correct to the nearest 5 km.
Explain how this could affect your decision in part (a).
(1)
A, B and C are points on a circle of radius 5 cm, centre O. DA and DC are tangents to the circle. DO = 9 cm
Work out the length of arc ABC. Give your answer correct to 3 significant figures.
(5)
The equation of a curve is y = ax A is the point where the curve intersects the y-axis.
The equation of circle C is x2 + y2 = 16
Draw a sketch of circle B.
Label with coordinates the centre of circle B and any points of intersection with the x-axis.
(3)
The paper as printed
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