最新数学英语题

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Mathematics

PartⅠ: 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

1 digits contains the outlined by the thick lines column, and each

2 ×2 square 1

through 4. Some grids have already been filled in. Find the number of ways we can

2

complete the rest of the grid.

：Answer 3

222 . Find the volume of

, 70 cm2.The areas of the faces of a cuboid are 84 cmand 30 cm4

3the cuboid in cm. Answer：

3ncommon greatest where form

can be wrritten The 3.fraction

in the the 33m??133?1?1

33?1?1113?3?33. m+ndivisor of m and n is 1, Find Answer：

is either 2, 3, 5 or 7,

N N > 1 with the properties that the each prime factor of 4.Find the sum of all the integers

is not divisible by any perfect cube greater than 1. Nand

Answer：

A large fresh water reservoir has two types of drainage system, small pipes and large pipes. 6 large pipes, on

5.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?

minutes ：Answer

3,000. Tickets were

At a local village gala, the entire population turned up, 500 people. The event raised ￡6.0.45 per child. How many children were there? 7.48 per man, ￡7.12 per woman and ￡priced as follows: ￡Answer： E

L U R P P T E O MC Each of the distinct letters in the following addition problem represents a

7.

+

T E E M ind the number represented by the word “MEET”.different digit. If A=4, f12 8 A A A A A A Answer：

The

and overlap. share a common corner rectangles Let 8.two 8×12

distance from the bottom right corner of one rectangle to the intersection

8

7 point along the right edge of that rectangle is 7. What is the area of the

shaded region?

12 Answer：

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精品文档abcd to headquarters. For security reasons, he sent

A spy had to send the 4-digit code 9.

instead the 9 separate 4-digit codes shown. In each of the 9 codes, at least one of the

abcd , and d? occurs in its correct position. What is the value of digits a, b, c Answer：

In how many ways can one arrange the numbers 21, 31, 41, 51, 61, 71 and 81 such that

10.the sum of every four consecutive numbers is divisible by 3? Answer：

: Questions 11 to 14, 20 marks each PartⅡ

are connected by a highway, with a service station at the midpoint. Mike and Sam start BTown A and town 11.

at the same time. When Mike reaches the service station, Sam is 16 km behind. Mike reduces Bfrom A to

speed by 25% after he passes through the service station. When Sam reaches the service station, Mike is 15

?A and Bkm ahead of Sam. What's the distance between

Answer：

D

A ,

:BC=1:2, AD∥BC, AD12.Given: ABCD is a trapezoid, 1:3?S:S

DOE??AOF O F

2, Find the area of ．24cm?SAOF?BEF?E

：Answer B C

In how many different ways can the seven empty circles in the diagram on

13.

the right be filled in with the numbers 2 through 8 such that each number is used

once, and each number is either greater than both its neighbors, or less than both its

neighbors. Answer：

How many rectangles are there in the diagram on the right such that the sum of the

14.numbers within the rectangle is a multiple of 4? 1 2 3 4

：Answer 5 6 7