A fair four-sided dice is numbered 3, 4, 5 and 6. The dice is rolled twice and the two scores are multiplied together.
Complete the table to show all the possible outcomes.
[1]
Find the probability that the outcome is a multiple of 8.
[2]
Triangle T is drawn on a coordinate grid.
Translate triangle T by vector 
-32
.
[2]
The price of a laptop is reduced in a January sale from £450 to £382.50.
Work out the percentage reduction in the price of the laptop.
[3]
The graph shows the price of the laptop in the months before the January sale.
Explain why this graph is misleading.
[1]
The diagram shows a prism of length 8 cm. The cross-section of the prism is a right-angled triangle.
Draw an accurate plan view of the prism on the one-centimetre grid below.
[2]
A teacher asks their class which of the following values is the smallest.
2-1 4-3 10-2
One student says
2-1 is the smallest because 2 is smaller than 4 and 10.
Explain the error made by the student in their reasoning and write down the smallest value.
........ The smallest value is........
[2]
A kitchen has space for a fridge.
The width, w, of the space is 70 cm, correct to the nearest centimetre.
Complete the error interval for the width, w.
[2]
A fridge is advertised as having a width of 69.5 cm, correct to 1 decimal place.
Show that this fridge may not fit in the space.
[2]
Each member of a tennis club is classed as a junior, an adult or a senior.
• 16% of the members are seniors.
• The ratio of the number of juniors to the number of adults is 9: 5.
• There are 95 more juniors than seniors.
Work out the total number of members of the tennis club. You must show your working.
[6]
Construct the perpendicular from the point P to the line AB. Show all of your construction lines.
[2]
Solve by factorising.
x2 + 15x - 16 = 0
[3]
The diagram shows a sphere with radius 3 cm and a cube with side length x cm.
The surface area of the sphere is equal to the surface area of the cube.
Work out the side length, x cm, of the cube. You must show your working.
[The surface area, A, of a sphere with radius r is A = 4πr2.]
[5]
Amit invests some money at a rate of 4% per year compound interest. After 2 years the value of Amit’s investment is £1352.
Work out how much money Amit invested.
[4]
You may use these kinematics formulae to answer this question.
v = u + at
where a is the constant acceleration, u is the initial velocity, v is the final velocity, s is the displacement and t is the time taken.
A particle has an initial velocity of 2 m/s. After 6 seconds the particle has a velocity of 11 m/s. The particle had constant acceleration.
Work out the distance the particle has travelled in the 6 seconds.
[4]
The diagram shows two similar triangles, AEB and ADC.
AB = 8 cm, BE = 5 cm and CD = 17.5 cm
Work out the length of BC.
[3]
16 807 = 75.
Write 16 807 000 000 as a product of its prime factors.
[3]
A packet of 6 pens contains 4 red pens and 2 blue pens.
A pen is taken at random from the packet and is not replaced. A second pen is then taken at random from the packet.
Complete the tree diagram.
First pen
Second pen
[2]
Find the probability of taking two pens of the same colour.
[3]
On the axes below, sketch the graph y =-x2.
[2]
Write down a possible equation for the graph sketched below.
[1]
Two Year 11 classes, 11G and 11K, record their times for a race. The box plots show the distribution of the times, in seconds, for each class.
Write down the percentage of students in 11G who took longer than 14.6 seconds.
[1]
Which class, 11G or 11K, was fastest on average? Include values to support your decision.
[2]
Sasha creates a four-digit passcode.
They use four digits from 0 to 9. They do not use any digit more than once.
Work out how many of the possible four-digit passcodes are even.
[4]
Shape L is drawn on the grid.
Enlarge shape L with scale factor - 2 and centre of enlargement at (- 1, 2).
[3]
A container takes 8 minutes to be filled with water.
The graph shows the rate of flow, in litres per minute, of the water into the container during the 8 minutes.
Show that 126 litres of water flows into the container between 0.5 minutes and 7.5 minutes.
[1]
Work out the average rate of flow, in litres per minute, of water into the container during the 8 minutes.
(b)........ litres per minute
[4]
The graph of y =-3x intersects the graph of x2 + y2 = 70 at two points.
Work out the exact coordinates of the two points. You must show your working.
(........,........) and (........,........)
[5]
The diagram shows a square-based pyramid ABCDE. O is the centre of the base.
The length of the base is 10.7 cm. Angle EAO is 67°.
Calculate the length of AE. You must show your working.
[6]
A pot of tea is made using boiling water and left to cool. The temperature, T °C, of the pot of tea after n minutes is given by the formula
T = abn.
The graph shows some information about the temperature of the pot of tea.
Find the value of a and the value of b.
[3]
Show that the equation x4 + 3x2 - 2x - 5 = 0 has a solution between x = 1 and x = 2.
[3]
Find this solution correct to 1 decimal place. You must show calculations to support your answer.
[4]
A bag contains only round tiles and square tiles. Each tile is either black or white.
The ratio of round tiles to square tiles is 3: 1. 45% of all the tiles are round black tiles. 9% of all the tiles are square white tiles.
Show that the proportion of round tiles that are black is less than the proportion of square tiles
that are black.
[6]
The paper as printed
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