 1 1   1 1 

1. Calculate: 76   −  − 30   + 
 23 53   53 23 

2. Teacher Cao and 37 students went on a field trip. During the break, Xiaoqiang asked, "Mr. Cao, how old are you
this year?" Teacher Cao replied: "Multiply my age by 2, subtract 16, divide by 2, add 8; the result just so happened
to be the total number of participants in this field trip." How old is Teacher Cao this year?

3. How many grams of water need to be added to a 100-gram 15% sugar solution to turn it into a 10% sugar solution?

4. Given that a and b are both prime numbers such that 37a + 57b = 473 , a + b = ______?

5. As shown in the figure below, the area of the rectangle ABCD is 56cm2. Point E, F and G are mid-points on the
sides of the rectangle ABCD. Find the area of the shaded region.

H D
A

E G

B F C

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6. As shown in the figure below, in the rectangle ABCD, EFGH is a square. Given that AF = 10cm and
HC = 7cm , find the perimeter of the rectangle ABCD.
E F
A B

D C
H G

7. A train is 450 meters long, and trees are planted next to the railway every 3 meters. The time between the head
of the train to reach the 1st tree and the tail of the train to reach the 101st tree is 0.5 minutes. What is the speed of
this train in m/min? (Neglect the width of the trees).

8. Find the total number of triangles in the figure shown below.

9. In the figure below, how many paths are there can form the word “APPLE”?
A
|
A—P—A
| | |
A—P—P—P—A
| | | | |
A—P—P—L—P—P—A
| | | | | | |
A—P—P—L—E—L—P—P—A

2
10. As shown in the figure, an electronic flea can jump from one circle to the adjacent circle every time it jumps.
Now, a red flea jumps 1991 steps clockwise from the circle marked with the number 0 and lands in a circle.
A black flea also jumped from the circle marked with the number 0, but it jumped 1949 steps
counterclockwise and landed in another circle. What is the product of the numbers in the two circles?
0
11 1

10 2

9 3

8 4

7 5
6

11. Given that a  b = 3a − 2b , if x  (4  1) = 7 , then x = _______ .

1
12. Jay is reading a story book. On the first day, he read 21 pages more than of the entire book. On the second
8
1
day, he read 6 pages less than of the entire book and there are still 172 pages left. How many pages are there
6
in this story book?

13. Worker A and B together can complete a project in 20 days. Worker B and C together can complete the same
project in 15 days. Worker B alone can complete this project in 30 days. If workers A, B and C work together,
how many days does it take to complete this project?

14. Chin and Wong calculated the product of the two-digit numbers A and B. Chin wrote the unit digit of A wrongly
and obtained a product of 473; Wong wrote the tens digit of A wrongly and obtained a product of 407. What is
the correct product of the numbers A and B?

3
15. As show in the figure below, find A + B + C + D + F + G

16. A cube of edge length 1cm was cut horizontally and vertically according to the figure below into 24 small
cuboids. What is the total surface area of these 24 small cuboids?

17. A, B and C are walking around a lake. They start from the same point at the same time. A and B walk in the same
direction while C walks in the opposite direction. A's speed is 5.4km/h and B's speed is 4.2km/h. If A and C meet
half an hour after their departure and 5 minutes after that, B and C meet. What is the perimeter of this lake in km?

18. In the equation below, A and B represent different numbers. If the equation is true, find the value of the 2-digit

number AB .

A0 AA = A  B  BBA

19. How many whole numbers from 629 to 2023 contain the digit “2”?

4
20. Five teams are in a tournament, with one match between each of the two teams. 3 points for the winner, 0 point
for the loser and 1 point each for both teams in a draw. After the game, the points of these five teams are exactly
five consecutive natural numbers. According to the points, the teams are placed 1st, 2nd, 3rd, 4th, and 5th, and
they each has A, B, C, D, and E draw games respectively, then the five-digit number ABCDE = ____________.

21. Jill is trying to calculate: 1 + 2 + 3 + 4 + ... using his calculator. At some point, he got the sum of 1000, and he
also found out that he had typed one of the numbers twice. What is this number?

22. Car X and car Y start travelling towards each other from place A and B respectively. The speed of car X is 50km/h.
1
The speed of Y is 40km/h. When car X reached of AB, he travelled for another 50km before meeting up with
3
car Y. How far is A and B apart in km?

23. A book sells for $3. If Mike buys this book, then the ratio of Mike’s remaining money to Tony’s money is 2:5; if
Tony buys this book, then the ratio of Mike's money to Tony’s remaining money becomes 8:13. How much
money did Mike have originally?

24. There are 3 different numbers, by using them to form 6 different three-digit numbers such that the sum of these
6 three-digit numbers is 1554, what is the sum of these 3 numbers?

5
25. As shown in the figure below, ABCD and AEFG are both squares and the area of triangle ABH is 6cm2. What is
the area of the shaded region?
D C

F E
H

G A B

26. As shown in the figure below, AB = 3 ， BC = 4 ， DC = 13 ， AD = 12 and ∠𝐴𝐵𝐶 = 90°, find the total area
of this shape.

27. Ship X and a raft travel downstream together from station A to station B. The raft only floats along the current.
At the same time, ship Y starts from station B and sails upstream to station A. 7.2 hours later, ship Y meets the
raft. Given that the distance between ship X and the raft is 31.25 kilometers after 2.5 hours and that the speeds
of ship X and ship Y in still water are equal, Find the distance between stations A and B.

28. A team of soldiers is divided into three groups A, B, and C. Given that the average ages of groups A, B, and
C are 37, 23, and 41 respectively. The average age of group A and B is 29; the average age of group B and C
is 33. What is the average age of all the soldiers?

6
29. The natural numbers 8336, 8545, and 8782 have some common features. Each number is a four-digit number
starting with 8, and there are exactly two numbers in each number that are the same. How many such
numbers are there (including the numbers 8336, 8545, and 8782)?

30. As shown in the figure below, there are 7 large and small triangles in total. Fill the nine numbers from 1 to 9
into the circles in the figure, so that the sums of the numbers at the three vertices of each triangle are all
equal. Find the maximum value of A  B  C .