Exam Questions: Current Syllabus or New Syllabus?
N.B. Diagrams throughout are not accurately drawn.
1. The Venn diagram shows information about a coin collection.
ξ = 120 coins in the collection
T = coins from the 20th century
B = British coins
ξ
T
B
x ( x  15) x
x2
32
A coin is chosen at random.
It is British.
Work out the probability that it is from the 20th century.
2. The diagram shows a flower bed in the shape of a circle. The flower bed has a diameter
of 2.4m.
2.4m
Sue is going to put a plastic strip around the edge of the flower bed.
The plastic strip is sold in 2 metre rolls.
How many rolls of plastic strip does Sue need to buy?
You must show all of your working.
3. Triangle ABC has a right angle at C.
Angle BAC =48°
AB = 9.3cm
Calculate the length of BC.
P
4. PQR is a right-angled triangle.
PQ = 16cm.
8cm
PR = 8cm
Calculate the length of QR.
Give your answer correct to 2 decimal places.
R
16cm
5. The equation 𝑥 3 + 3𝑥 = 41
has a solution between 3 and 4.
Use a trial and improvement method to find this solution.
Give your answer correct to one decimal place.
You must show all of your working.
6. The diagram shows a rectangle inside a circle.
The centre of the rectangle and the centre of the circle are the same point.
The rectangle has dimensions 8cm by 6cm.
Work out the shaded area. Give your answer in terms of π.
7. The diagram shows quadrilateral OXYZ.
P, Q, R and S are the midpoints of OX, XY, YZ and OZ respectively.
Z
R
Y
S
Q
c
b
O
a
P
OP= a, XQ = b and OS = c.
Show that PQ is parallel to SR.
X
Q
8. Expand and simplify (𝑥 + 5)(𝑥 − 5)(3𝑥 + 2)
9. Angela drops a ball from a height of d metres onto the ground.
The time, t seconds, that the ball takes to reach the ground is given by
2𝑑
𝑡=√
𝑔
where g m/s2 is the acceleration due to gravity.
d = 35.6 correct to 3 significant figures.
g = 9.8 correct to 2 significant figures.
a) Write down the lower bound of d
b) Calculate the lower bound of t.
You must show all of your working.
10. a) Write down the exact value of tan 60°.
b) Find the exact area of this triangle.
60°
4√3
11. ABC is an arc of a circle centre O with radius 80m.
AC is a chord of the circle.
Angle AOC = 35°
A
80m
O
B
35°
80m
C
Calculate the area of the shaded region.
Give your answer correct to 3 significant figures.
12. A restaurant menu has 8 starters, 12 mains and 6 desserts.
A customer can choose from the following meals:
 A starter and a main,
 A main and a dessert,
 A starter, main and dessert.
Show that there are 744 different ways of choosing a meal at this restaurant.
13. The diagram shows a sequence of patterns made from grey tiles and white tiles.
Pattern 1
Pattern 2
Pattern 3
Pattern 4
The number of grey tiles in each pattern forms an arithmetic sequence.
a) Find an expression in terms of n, for the number of grey tiles in Pattern n.
The total number of tiles in each pattern is always the sum of the squares of two
consecutive whole numbers.
b) Find an expression in terms of n, for the total number of grey tiles and white tiles in
Pattern n. Give your answer in its simplest form.
c) Is there a pattern for which the total number of grey tiles and white tiles is 231? Give
a reason for your answer.
14. Two straight lines are shown.
B is the midpoint of AC.
TB : BS = 2 : 3
y
T
C (23,12)
B
A (15,6)
O
Work out the coordinates of T.
S (31,3)
x