英数题练习附答案

冲南外英数题练习

1. With the same engine power, if a ferry is running for 60km with the current, it takes 5 hours fewer than when it returns. When the engine power is doubled, that means the speed of ferry in still water is doubled, it takes 1 hour fewer when the ferry is running for 60 km with the current than it is against the current. Find the speed of the current in km/h.

2. In ΔABC, lines are drawn from vertices A, B and C to their opposite sides so that the triangle is divided into 6 parts. The areas of some parts are shown in the figure. Find the area of ΔABC.

3. Equilateral triangle ABP with side AB of length 1 cm is placed outside square AXYZ with side of length 2 cm so that B is on side AX. The triangle is rotated anti-clockwise about B, then P, and so on along the sides of the square until P, A and B all return to their original positions. Find the length of the path in cm travelled by vertex P.

4. There are five positive integers. Taken four at a time, they sum to four distinct values, namely, 14, 15, 19, 20. Find the five positive integers.

5. In the figure, ABCD is a square. AP = AQ = CR = CS = 2cm. E is a point inside the square such that areas of the quadrilaterals APEQ and CRES are 7 cm2 and 9 cm2 respectively. What is the area of the square ABCD?

7. A group of workmen takes some bricks from one place to another. If each workman takes y bricks, there will be 12 bricks left. If each of them takes 8 bricks, the last workman just needs to take 7 bricks. What is the number of this group of workmen?

8. Ming went to school when it was 12:00 shown at the clock at home. On his way to school , he looked at the clock in the church and it was 12:20pm. When he reached school, he noted that the time shown at the clock in the school hall was 12:32pm. After staying for 10 minutes at school, he went back home. On his way back, he looked at the church clock again and it was 12:52pm and that the clock at home was 1:16pm when he arrived home. Ming was told that only the time shown at the clock in his home was correct, and if we assume that the speed of Ming remained constant during his journey, find the difference between both times shown at the church clock and the school hall clock and the time shown at the clock at home respectively.

9. A number A which is divisible by 9 has 2005 digits. The sum of all its digits is a, the sum of all digits of a is b and the sum of all digits of b is c. Find the value of c.

10. The diagram shows the net of a dodecahedron（十二面体）. Which of the labeled vertices (B to K) will come to A when the net is folded to make the dodecahedron?

答案：

1. 8

2. 315

4.1,2,5,6,7

5.64

6. 21,24

7. 13

8. 22,33

9. 9

10. D

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