1
1
Find the highest common factor (HCF) of
and
.
...................................................
[2]
[Total: 2]
2
Find the value of y when x = 6.
Give your answer as a mixed number in its simplest form.
Answer y = ...................................................
[2]
[Total: 2]
3
A train journey starts at 23 40 and finishes at 06 50.
Work out the time taken for this journey.
........................ h ....................... min [1]
[Total: 1]
4
Write the recurring decimal
as a fraction.
...................................................
[1]
[Total: 1]
2
5
Find the value of x when
x = .................................. [1]
[Total: 1]
6
Find the value of p.
p = ...................................................
[1]
[Total: 1]
7
Solve.
x = ...................................................
[2]
[Total: 2]
3
8
Solve the equation.
x = ...................................................
[3]
[Total: 3]
9
Solve.
...................................................
[2]
[Total: 2]
10
Find the nth term of this sequence.
8, 17, 32, 53, 80, ...
...................................................
[2]
4
[Total: 2]
11
The sequence of diagrams above is made up of small lines and dots.
(a) Complete the table.
Diagram 1
Diagram 2
Diagram 3
Diagram 4
Number of
small lines
4
10
18
28
Number of
dots
4
8
13
19
Diagram 5
Diagram 6
[4]
(b) For Diagram n find an expression, in terms of n, for the number of small lines.
...................................................
[2]
r = ...................................................
[2]
(c) Diagram r has 10 300 small lines.
Find the value of r.
5
(d) The number of dots in Diagram n is
.
Find the value of a and the value of b.
a = ...................................................
b = ...................................................
[2]
[Total: 10]
12
Find the nth term of each sequence.
(a) –1, –3, –5, –7, –9, …
...................................................
[2]
6
(b) 2, 9, 28, 65, 126, …
...................................................
[2]
[Total: 4]
13
Find the value of
(a)
,
(b)
(c)
...................................................
[1]
...................................................
[1]
...................................................
[1]
,
.
[Total: 3]
14
The door to a museum has an 8-digit code to unlock it.
•
The next odd number after 35 gives digits 1 and 2.
•
The next prime number after 23 gives digits 3 and 4.
•
The square root of 225 gives digits 5 and 6.
•
The value of 26 gives digits 7 and 8.
Use this information to complete the door code.
Digits 1 and 2 have been completed for you.
Digit
1
2
Code
3
7
3
4
5
6
7
8
[3]
[Total: 3]
7
15
a°
NOT TO
SCALE
126°
c°
b°
63°
The diagram shows two straight lines intersecting two parallel lines.
Find the values of a, b and c.
a = ...................................................
b = ...................................................
c = ...................................................
[3]
[Total: 3]
8
16
In the triangle ABC, AB = AC and angle BAC = 38°.
BCD is a straight line.
Work out angle ACD.
Angle ACD = ...................................................
[3]
[Total: 3]
17
A student measures the angles in a triangle as 55°, 85° and 50°.
Explain why the student is incorrect.
....................................................................................................................................................................
[1]
[Total: 1]
9
18
Find all the positive integers which satisfy the inequality.
...................................................
[2]
[Total: 2]
19
Write as a single fraction in its simplest form.
...................................................
[3]
[Total: 3]
20
The summit of Mount Everest is 8848 metres above sea level.
Ayding Lake is 154 metres below sea level.
Work out the difference in height between these places.
................................................... m
[1]
[Total: 1]