The table shows the probabilities that a biased dice will land on 2, on 3, on 4, on 5 and on 6
| Number on dice | 1 | 2 | 3 | 4 | 5 | 6 |
| Probability | 0.17 | 0.18 | 0.09 | 0.15 | 0.1 |
Neymar rolls the biased dice 200 times.
Work out an estimate for the total number of times the dice will land on 1 or on 3
(3)
On Saturday, some adults and some children were in a theatre. The ratio of the number of adults to the number of children was 5: 2
Each person had a seat in the Circle or had a seat in the Stalls. 
of the children had seats in the Stalls. 117 children had seats in the Circle.
There are exactly 2600 seats in the theatre.
On this Saturday, were there people on more than 60% of the seats? You must show how you get your answer.
(5)
The diagram shows a prism with a cross section in the shape of a trapezium.
On the centimetre grid below, draw the front elevation and the side elevation of the prism. Use a scale of 2 cm to 1 m.
(4)
Olly drove 56 km from Liverpool to Manchester. He then drove 61 km from Manchester to Sheffield.
Olly’s average speed from Liverpool to Manchester was 70 km/h. Olly took 75 minutes to drive from Manchester to Sheffield.
Work out Olly’s average speed for his total drive from Liverpool to Sheffield.
(4)
Janie drove from Barnsley to York.
Janie’s average speed from Barnsley to Leeds was 80 km/h. Her average speed from Leeds to York was 60 km/h.
Janie says that the average speed from Barnsley to York can be found by working out the mean of 80 km/h and 60 km/h.
If Janie is correct, what does this tell you about the two parts of Janie’s journey?
(1)
ABC and EDC are straight lines. EA is parallel to DB.
EC = 8.1 cm. DC = 5.4 cm. DB = 2.6 cm.
Work out the length of AE.
(2)
AC = 6.15 cm.
Work out the length of AB.
(2)
A number, n, is rounded to 2 decimal places. The result is 4.76
Using inequalities, write down the error interval for n.
(2)
The cumulative frequency graph shows some information about the heights, in cm, of 60 students.
Work out an estimate for the number of these students with a height greater than 160 cm.
(2)
The diagram shows triangle A drawn on a grid.
Kyle reflects triangle A in the x-axis to get triangle B. He then reflects triangle B in the line y = x to get triangle C.
Amy reflects triangle A in the line y = x to get triangle D. She is then going to reflect triangle D in the x-axis to get triangle E.
Amy says that triangle E should be in the same position as triangle C.
Is Amy correct? You must show how you get your answer.
(3)
The table shows some information about eight planets.
| Planet | Distance from Earth (km) | Mass (kg) |
| Earth | 0 | 5.97  1024 |
| Jupiter | 6.29  108 | 1.898  1027 |
| Mars | 7.83 107 | 6.42 1023 |
| Mercury | 9.17  107 | 3.302  1023 |
| Neptune | 4.35 109 | 1.024 1026 |
| Saturn | 1.28  109 | 5.68 1026 |
| Uranus | 2.72 109 | 8.683 1025 |
| Venus | 4.14 107 | 4.869 1024 |
Write down the name of the planet with the greatest mass.
(1)
Find the difference between the mass of Venus and the mass of Mercury.
(1)
Nishat says that Neptune is over a hundred times further away from Earth than Venus is.
Is Nishat right? You must show how you get your answer.
(2)
There are 30 students in Mr Lear’s class. 16 of the students are boys.
Two students from the class are chosen at random.
Mr Lear draws this probability tree diagram for this information.
Write down one thing that is wrong with the probabilities in the probability tree diagram.
(1)
Owen and Wasim play for the school football team.
The probability that Owen will score a goal in the next match is 0.4 The probability that Wasim will score a goal in the next match is 0.25
Mr Slater says,
“The probability that both boys will score a goal in the next match is 0.4 + 0.25”
Is Mr Slater right? Give a reason for your answer.
(1)
The histogram shows some information about the ages of the 134 members of a sports club.
20% of the members of the sports club who are over 50 years of age are female.
Work out an estimate for the number of female members who are over 50 years of age.
(3)
Here are some graphs.
In the table below, match each equation with the letter of its graph.
(3)
A, B, C and D are four points on the circumference of a circle.
AEC and BED are straight lines.
Prove that triangle ABE and triangle DCE are similar. You must give reasons for each stage of your working.
(3)
ONQ is a sector of a circle with centre O and radius 11 cm.
A is the point on ON and B is the point on OQ such that AOB is an equilateral triangle of side 7 cm.
Calculate the area of the shaded region as a percentage of the area of the sector ONQ. Give your answer correct to 1 decimal place.
(5)
2 − 
− 
can be written as a single fraction in the form 
where a and b are integers.
Work out the value of a and the value of b.
(4)
The diagram shows part of the graph of y = x2 – 2x + 3
By drawing a suitable straight line, use your graph to find estimates for the solutions of x2 – 3x – 1 = 0
(2)
P is the point on the graph of y = x2 – 2x + 3 where x = 2
Calculate an estimate for the gradient of the graph at the point P.
(3)
The diagram shows 3 identical circles inside a rectangle. Each circle touches the other two circles and the sides of the rectangle, as shown in the diagram.
The radius of each circle is 24 mm.
Work out the area of the rectangle. Give your answer correct to 3 significant figures.
(4)
Here are the first five terms of a sequence.
4 11 22 37 56
Find an expression, in terms of n, for the n th term of this sequence.
(3)
L is the circle with equation x2 + y2 = 4
Find an equation of the tangent to L at the point P.
(3)
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