数学英语题
-
Mathematics
Part
Ⅰ
: Questions
1 to 10, 10 marks each
1.
At the right
is shown a 4 ×
4 grid. We wish to fill
in the grid such that each row, each
column,
and
each
2
×
2
square
outlined
by
the
thick
lines
contains
the
digits
1
through 4. Some grids have already been
filled in. Find the number of ways we can
complete the rest of the grid.
Answer
：
2.
The areas of the faces of a cuboid are
84 cm
2
, 70 cm
2
and 30 cm
2
. Find
the volume of
the cuboid in
cm
3
.
Answer
：
3.
The
fraction
3
3
3
1
3
1
3
3
1
1
1
1
3
3
3<
/p>
1
3
3
1
2
3
4
can
be
wrritten
in
the
form
n
where
the
greatest
common
m
divisor
of
m
and
n
is 1, Find
m
+
n
.
Answer
：
4.
Find the sum of all the integers
N
> 1 with the properties
that the each prime factor of
N
is either 2, 3, 5 or 7,
and
N
is not divisible by any
perfect cube greater than 1.
Answer
：
5.
A
large fresh water reservoir has two types of
drainage system, small pipes and large pipes. 6
large pipes, on
their own, can drain
the reservoir in 12 hours. 3 large pipes and 9
small pipes, at the same time, can drain the
reservoir in 8 hours. How long will 5
small pipes, on their own, take to drain the
reservoir?
Answer
：
minutes
6.
At a local
village gala, the entire population turned up, 500
people. The event raised £
3,000.
Tickets were
priced as follows:
£
7.48 per man, £
7.12 per
woman and £
0.45 per child. How many
children were there?
Answer
：
P
U
R
P
L
E
C
O
M
E
T
7.
Each of the distinct letters in the
following addition problem represents a
M
E
E
T
different digit. If A=4,
f
ind the number represented by the word
“MEET”.
12
+
8
A A
A
A A A
Answer
：
8.
Let
two
8×
12
rectangles
share
a
common
corner
and
overlap.
The
distance from the bottom right corner
of one rectangle to the intersection
7
point along the right edge of that
rectangle is 7. What is the area of the
8
shaded region?
12
Answer
：