Download Key Stage 4 Term 3 Puzzle Word document

Term 3 AGAT
Puzzle Booklet
Key Stage 4
Name & TG:
These puzzles are designed to be tackled without a
calculator.
Please show your workings and avoid merely
guessing.
Hand in by 15 February to Mr Cobb or your maths
teacher if you want your answers marked.
1.
2
4
and
. Each term after the second term is the
3
5
average (mean) of the two previous terms. What is the fifth term in the sequence?
The first two terms of a sequence are
A
2.
5
34
1
2
C
10
13
D
3
4
E
10
11
Which of these five expressions represents the largest number?
(9
A 9
Page | 1
B
9
)
B 999
C 999
D (99)9
E 999
3.
In the Soft Boulder Café each table has 3 legs, each chair has 4 legs and all the
customers and the three members of staff have two legs each. There are four chairs at
each table. At a certain time, three-quarters of the chairs are occupied by customers and
there are 206 legs altogether in the café.
How many chairs does the café have?
A 20
4.
Page | 2
C 28
D 32
E 36
Eight unit cubes are arranged to form an imaginary 2 by 2 by 2 cube. What is the largest
number of unit cubes one can remove from this arrangement if the resulting shape has to
have the same surface area as the original?
A 0
5.
B 24
B 1
C 2
D 3
ABCDE is a regular pentagon. FAB is a straight line and FA = AB.
E 4
What is the ratio x : y : z?
F
B
A
x
y
z
C
E
D
A 1:2:3
6.
B 2:2:3
C 2:3:4
D 3:4:5
E 3:4:6
The number 34 × 45 × 56 is written out in full.
How many zeros are there at the end of the number?
A none
Page | 3
B 4
C 5
D 6
E more than 6
7.
A pencil AB lying on a table is given a half-turn about the end B (so that A moves to A′)
and then a half-turn about A′ (so that B moves to B′). The point C on the pencil is one third
of the way from A to B.
What is the ratio of the total distances moved by A and by C?
A
A 3:1
8.
C
B 3:2
B
A'
C 1:1
D 2:3
E 1:3
( x – 1)( x 4 + 1)( x 2 + 1)( x + 1) equals
A x8 − 1
B x8 + x6 + x4 + x2 + 1
D x8 + x7 + x6 + x5 + x4 + x3 + x2 + x + 1
Page | 4
B'
C x8 + 1
E
x8 − x6 + x4 − 1
9.
A rectangular sheet of paper with sides 1 and 2 has been folded once as shown, so
that one corner just meets the opposite long edge.
What is the value of the length d?
1
d
2
A
10.
1
2
C
7
16
If a = b − c, b = c − d and c = d − a, then
A 1
Page | 5
2 –1
B
B
1
2
C 0
D
3– 2
E
2
3
a b c d
  
equals
b c d a
D –
1
2
E –1
11.
The following equation is true for all a, b and c:
a3 + b3 + c3 = (a + b + c)3 − 3 (a + b + c) (ab + bc + ca) + kabc
What is the value of k?
A −6
12.
B −3
C 0
D 3
E 6
Three people each think of a number which is the product of two different primes.
Which of the following could be the product of the three numbers which are thought of?
A 120
Page | 6
B 144
C 240
D 3000
E 12100