The following formula can be used to change a temperature f degrees Fahrenheit to a temperature c degrees Celsius.
Sean and Kate measure the temperature of a heated iron bar.
Sean measures the temperature of the iron bar as x degrees Fahrenheit. Kate measures the temperature of the iron bar as y degrees Celsius.
Given that x = 2y,
find the temperature, in degrees Fahrenheit, of the iron bar.
(2)
The Earth is assumed to move around the Sun in a circular orbit of radius 1.5 × 108 km.
Assuming that the Earth takes 365 days to complete one orbit of the Sun,
calculate the average speed, in m/s to 3 significant figures, of the Earth as it orbits the Sun.
(4)
Figure 1 shows circle QRST with centre O.
SQ is a diameter of the circle.
QR = 60 mm RS = 40 mm ST = 50 mm
Without using a calculator, find the exact length, in mm, of QT.
(5)
Over the course of a week of seven days, Alan plays a series of games. He plays exactly one game each day.
On Sunday, the probability that Alan wins his game is 
On a day other than Sunday, the probability that Alan wins his game is 
The incomplete probability tree diagram below is to give information about Alan’s result on a randomly chosen day in a week of seven days.
Complete the probability tree diagram below.
(3)
Find the expected number of games Alan will win in a week of seven days.
(2)
E is the universal set and A, B and C are three sets.
Here is information about these sets.
n(A) = 45
n(B) = 48
n(C) = 55
n(A 
B) = 24 n(A 
C) = 25
n(B C) = 27
n(A B C) = x n(Aʹ Bʹ Cʹ) = y
Show all this information on the Venn diagram, giving the number of elements in each appropriate subset, in terms of x or y.
(3)
Given that n(E) = 100
find an expression for y in terms of x.
Give your answer in its simplest form.
(2)
Using your Venn diagram and your answer to part (b), find the greatest possible value of x.
Give reasons for your answer.
(3)
An element is selected at random from the 100 elements in the universal set.
Find the probability that this element is in the set (B 
Cʹ) 
(Bʹ 
C).
(2)
Represent your solution on the number line on the next page.
(1)
Represent your solution on the number line on the next page.
(1)
Write down the set of values for which
(a) (ii)
−7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
(b) (ii)
−7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
Only use this line if you need to redraw your solution.
−7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
(2)
Given that
complete the following table.
| a | c |
| 16 | 240 |
| 250 | |
| 135 |
(6)
Figure 2 shows a kite ABCD in which
AEC and BED are straight lines.
Calculate the area, in cm2, of ABCD.
(2)
Prove that triangle ABE is similar to triangle BCE.
(3)
The points with coordinates (1, 2), (1, 5) and (3, 2) are the vertices of triangle A.
On the grid, draw and label triangle A.
(1)
Triangle B is the image of triangle A under a reflection in the line with equation y = −x
On the grid, draw and label triangle B.
(2)
Triangle C is the image of triangle A under the transformation with the matrix M where
(2)
Hence, on the grid, draw and label triangle C.
(1)
Describe fully the single transformation that maps triangle B onto triangle C.
(2)
The single transformation that maps triangle B onto triangle C is represented by the matrix N
State, giving a reason, the matrix N2
Turn over for a spare grid if you need to redraw your triangles.
Only use this grid if you need to redraw your triangles.
(2)
Figure 3 shows the triangle OAB where OA
= 12a and OB
= 6b M is the midpoint of OA and N is the midpoint of AB.
The point P on BM is such that BP: BM = 2: 3
Simplifying your answer, find, in terms of a and b
(i) BM
(ii) OP
(3)
Hence show that O, P and N are collinear.
(4)
Given that | a| = | b | = 1 cm and that 
AOB = 70°
find the length, in cm to 3 significant figures, of OP.
[ Cosine rule: a2 = b2 + c2 − 2bc cosA ]
(3)
The equation of a curve is y = f (x) where f (x) = x3 − 10x2 + 20
Complete the table of values for y = x3 − 10x2 + 20
Give your values of y to one decimal place where necessary.
| x | −2 | −1.5 | −1 | −0.5 | 0 | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 |
| y | −28 | −5.9 | 17.4 | 20 | 11 | 0.9 | −12 | −43 |
(3)
On the grid opposite, plot the points from your completed table and join them to form a smooth curve.
(3)
A curve C has equation y = g (x) where B = g (x) and 
= f (x)
The curve C has two turning points in −2 
x 
3
Using your graph, find the x coordinates of these two turning points on the curve C.
(3)
Referring to your graph, determine which of these two turning points is a maximum and which is a minimum.
You should explain your reasoning clearly.
Turn over for a spare grid if you need to redraw your curve.
Only use this grid if you need to redraw your curve.
(4)
Indre buys 1000 Hungarian dolls in Budapest to sell in Austria.
She pays in Hungarian forints.
Indre pays 1900 forints for each small doll she buys.
She pays 10 300 forints for each large doll she buys.
The number of small dolls that Indre buys is 4 times the number of large dolls that she buys.
Calculate the total cost, in forints, of the 1000 dolls that Indre buys.
(3)
Indre has to pay 100 euros to transport the dolls from Hungary so that she can sell them in Austria.
Initially the price of each small doll that Indre sells is 8 euros and the price of each large doll that Indre sells is 40 euros.
She sells 80% of the small dolls and 
of the large dolls at these prices. Indre then reduces the price of each of her remaining dolls by 40%
She sells all of the remaining dolls.
When Indre bought the dolls, the exchange rate was 1 euro = 327.6 forints.
Calculate the total profit, in euros to 2 decimal places, that Indre made by selling all 1000 dolls.
(8)
Calculate the percentage profit, to 3 significant figures, that Indre made.
(2)
State how the percentage profit in part (c) (i) would be affected if the total profit calculated in part (b) had been in forints.
(1)
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