2016 年奧海盃數學競賽
Vast Ocean Cup Mathematics Competition
Primary 4
Student Name:(Eng)
________________
E-mail:
Contestant No:
______
School Name:
Res.Address:
Tel:
Full mark:120
First Part: There are totally 8 Multiple Choices.
I. Multiple Choices (Each carries 5 marks)
Question
1
2
3
4
5
6
7
8
Marks
Answer
1. There is a quadrilateral. It is a kite and also a trapezoid. This shape should be a
A)
rhombus
B)
square
C)
rectangle
D) A parallelogram that is
not rhombus
2. Owen uses his right hand to measure objects. When he measures a 110cm object, there is a bit more
than 6 hand spans. When he measures a 175cm object, there is a bit more than 9 hand spans. When
he measures a 205cm object, at least how many hand spans long will it be?
A) 10
B) 11
C) 12
D) 13
3. Given that the greatest common factor of A and B is F. The greatest common factor of C and D is also F.
If A, B, C, D are 4 different natural numbers, which of the followings is the most accurate description
of the greatest common factor of A and C?
A) Only greater
C) Must be less than
D) Must be greater than
B) Only equal to 𝐹
than 𝐹
or equal to 𝐹
or equal to 𝐹
4. One truck can carry 18 boxes of apples. If we put 400 boxes of apples into the trucks, how many boxes
of apples will be needed to put in the last truck in order to fill it full?
A) 4
B) 14
C) 22
D) 23
5. According to the following pattern, what is the 2016th number?
123422343234423412342234323442341234223432344234……。
A) 1
B) 2
C) 3
D) 4
6. The figure is a tangram. If it is rearranged to form a rectangle,
how many more times will the height of the rectangle be longer than the width?
A) 1
1
2
times
B) 2 times
C) 3 times
D) 4 times
7. The numbers 7,8,9,10 are put into the boxes below respectively and each number can be only used
once. How many ways are there to make the equation valid? (7 + 10 = 8 + 9 and 10 + 7 = 8 + 9
can be counted as 2 combinations)
□+□−□=□
A) 2
B) 4
C) 8
D) 16
8. A robot starts from Point A in the figure and move along the line. Whenever it reaches an intersection,
it has to be turn right or left. When the robot passes several intersections and returns to point A, how
many turns could he make?
A) 97
(The turn that last time it returns to Point A doesn’t count)
B) 98
C) 99
D) 100
II. Fill in the blanks：(each carries 6 marks，total 10 questions)
9. Calculate:
(a) 32 × 9 × 7 =____________
(b) 271 × 41 =____________
(c) 9091 × 11 =____________
(d) 777 × 143 =____________
(e) 1001 ÷ 13 ÷ 11 =____________
(f) 10001 ÷ 137 =
10. Given that the product of 8 and 9 is ̅̅̅̅̅̅̅
𝑆6𝑇4 and S ≤ T, what is the largest prime number that ̅̅̅̅̅̅̅
𝑆6𝑇4 can be divided by?
____________________.
11. There are 5 people and their height is 1.41m, 1.64m, 1.57m, 1.39m and 1.48m, respectively. What is
their average height?
________________
12. Draw the reflection of the figure across the line.
13. According to the following pattern, fill in the blanks in figure 4 . (The numbers must match the
correct direction.)
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
14. There are two numbers. The sum of their product and quotient is 20 and the difference between their
product and quotient is 16. Among these two numbers, the greater number value is ______________.
15. There is a 200m road. From the start point, there is a red flag every 5m and there are 2 green flags
between every 2 red flags. How many flags are there?
______________
16. 576 boxes are formed into a square with 24 boxes per side. Owen put one coin in one of those boxes.
Yuki wants to find the coin, and she can choose one box every time, opening that box and the other 8
boxes surrounding that box. What is the minimum number of boxes she has to choose in order to find
the coin?
____________
__
17. Change a “+” to “–“ to make this equation valid. The + that has been changed is the ___________
plus from the left.
1 + 2 + 3 + 4 + ⋯ + 29 + 30 = 441
18. The figure is formed by 14 identical small squares. It is given that the perimeter of each square grid is
10cm. The perimeter of the following figure is __________cm.
III. Challenge Question：(20 marks)
19. Pick’s Theorem is a method for determining the area of a shape on a lattice. The shape has boundary
points (lattice points including vertices) and interior points within the shape.
For square lattices (Figure 1), the area is :
the number of interior points + number of boundary points ÷ 2 – 1.
For triangle lattices (Figure 2), the area is :
(the number of interior points + number of boundary points ÷ 2 – 1) × 2.
Figure 1
Figure 2
Figure 3
(a) The area of the shaded area in figure 3 is ________cm2
(b) The area of the shaded area in figure 4 is ________cm2
(c) In a square lattice, given a square with four vertices, if the number
of interior points is 100, what is the number of boundary points?
__________
(d) In a triangle lattice, given a regular hexagon, if the number of
boundary points on each side is 5, what is its area?
________cm2
Figure 4
(e) In a square lattice, given a rectangle with an area of 26 cm², if the number of interior points is 24,
draw the rectangle.
Figure 5
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