A group of 100 pupils attended their school sports day.
13 pupils did not compete in either Track or Field events. The expressions in the following Venn diagram represent the number of pupils in each category. The universal set, ε, contains all the pupils.
One pupil is chosen at random from the group.
What is the probability that this pupil competed only in Track events?
[2]
The table below shows some of the values of y = 2x2 − 6 for values of x from –3 to 2.
| x | – 3 | – 2 | – 1 | 0 | 1 | 2 |
| y = 2x2 − 6 | 2 | – 4 | – 6 | 2 |
On the graph paper opposite, draw the graph of y = 2x2 − 6 for values of x
from –3 to 2.
[2]
In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
A mass is shared in the ratio 3: 5. The larger share is 44 lb (pounds).
Calculate the total mass.
Give your answer in kilograms (kg).
You must show all your working.
[6]
The mean of five whole numbers is 20.
The mean of three of these numbers is 22. The other two numbers have a difference of 6.
Find the other two numbers.
[4]
The diagram below shows the graph of a straight line for values of x from –2 to 2.
Write down the gradient of the straight line in the diagram.
[1]
Write down the equation of the straight line in the form y = mx + c, where m and c are
whole numbers.
[1]
Write down the equation of a different straight line that is parallel to the straight line in
the diagram.
[1]
Grey tiles are used to make patterns as follows.
Pattern 1 Pattern 2 Pattern 3 Pattern 4
How many grey tiles would you need to make Pattern n?
[2]
The length of each side of a square is 15 cm, correct to the nearest 1 cm.
Calculate the greatest possible perimeter of this square.
[2]
In the diagram below, ABCD and ABCE are cyclic quadrilaterals.
Calculate the size of angle y.
State the circle theorem that you have used to find your answer.
Circle Theorem:........
[2]
Express 
− 
as a single fraction in its simplest form.
[4]
Using the axes below, find the region that satisfies the following inequalities.
Make sure that you clearly indicate the region that represents your answer.
[3]
The diagram below shows a solid cone.
The cone has: • base radius = rcm
• total surface area = 144πcm2. Calculate the value of r.
In your working, express any areas in terms of π.
[3]
Factorise 2x2 + 3x − 20.
Hence solve the equation 2x2 + 3x − 20 = 0.
[3]
The following diagram shows a sketch of y = tan x for values of x from 0° to 360°.
Given that tan 23° = 0·4245, correct to 4 decimal places, write down all the solutions of the equation
tan x = – 0·4245
for values of x from 0° to 360°.
[2]
Two similar solids have surface areas of 3 cm2 and 75 cm2.
The volume of the smaller solid is 0·4 cm3.
Calculate the volume of the larger solid.
[4]
Mathew has six cards.
He chooses three of the cards at random.
He does not replace any of the cards.
Calculate the probability that the first card is a 7, the second card is a 5 and the third
card is a 6.
[2]
Calculate the probability that the product of the numbers on Mathew’s three cards is a
cube number.
[2]
The paper as printed
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