Time : 50 minutes
Passing mark : 70 %
Answer : End of the problem
Problem 1
Problem 2
Problem 3
Problem 4
Problem 7
Problem 8
Problem 10
Calculation
126 / 72 + (16 - 3) / 4 =
Problem 2
Calculation
1 - (2/3 - 0.16) / 19/25 =
Problem 3
Find X.
1/6 + 7/3 / X × 5/7 = 1
Problem 4
The sales in June of a certain store decreased by 15% compared with May.
Problem 5
The sales in July of the store increased 12% compared with June.
What percentage of reduction do the sales in July become compared with May?
Problem 5
The equilateral triangle and the equilateral pentagon have overlapped, as shown in the figure.
Problem 6
Find the angle of the angle X.
Problem 6
Find the area (km2) of the paper tape when an 8 cm wide paper tape is wound around the equator of the earth one round.
Noted that the earth is to be a sphere radius 6400 km.
The answer should be rounded off the 2nd decimal place.
Noted that the earth is to be a sphere radius 6400 km.
The answer should be rounded off the 2nd decimal place.
Problem 7
A figure is trapezoid ABCD whose side AD is parallel to the side BC. BE and AC are vertical.
Find the area of this trapezoid.
Problem 8
If water is put into a certain tank only with A pipe, it will be filled to the brim with water in 15 minutes.
If water is put in only with B pipe, it will be filled to the brim with water in 10 minutes.
When water was put into this tank only with B pipe first and water was put in with both pipes after that, it was filled to the brim with water in 7 minutes.
Find the time (minute) when put in water only with B pipe.
Problem 9
Taro's father is two years older than his mother.
The age of Taro's elder brother is 1/3 of his father's age.
The age of Taro will become 1/3 of his mother's age in five years.
Find the age difference of Taro and his elder brother.
Problem 10
The character P is written to one face of a certain rectangular prism.
Problem 11
Moreover, one diagonal line is drawn on each face of three faces.
Fig. 1 and Fig. 2 shows two types of the development view of this rectangular prism.
The length of the side AB is 14 cm.
(1) Draw three diagonal lines on Fig. 2 in handwriting.
(2) It is 24 cm when the length of the circumference of rectangle ABCD is subtracted from the length of the circumference (bold line) of the developed view of Fig. 1.
Moreover, it is 10 cm when the length of the circumference of the developed view of Fig. 1 is subtracted from the length of the circumference (bold line) of the development view of Fig. 2.
Find the volume of this rectangular prism.
Problem 11
In a certain grade, there was a test of three problems A, B and C.
The percentage of the students who gave the right answer of A was 60%, who gave the right answer of B was 70% and who gave the right answer of C only was 15%.
Moreover, those who gave the right answer of A and did not give right answer of B were 18 persons.
Those who did not give right answers of all three problems were 5%.
Find the number of students of this grade.
Moreover, those who gave the right answer of A and did not give right answer of B were 18 persons.
Those who did not give right answers of all three problems were 5%.
Find the number of students of this grade.
Problem 12
The figure is a circle centering on the point O with radius of 6 cm.
Problem 13
The diameters AB and CD cross right-angled.
The point P leaves A and goes back and forth between A and O at 3 cm/s without stopping.
The point Q leaves B and goes back and forth between B and O at 2 cm/s without stopping.
P and Q leave at the same time.
(1) Find the area of the triangle CPQ 5 seconds after P and Q leave.
Moreover, find the numbers of seconds after leaving when it becomes the same area at next time.
(2) Find the area of the triangle CPQ 116 seconds after P and Q leave.
(3) There is a time when the area of the portion excluding the triangle CPQ from the circle is to be 107.04 cm2.
Find the number of seconds after P and Q leave when it becomes this area at 6th times.
Pi is assumed to be 3.14.
Moreover, find the numbers of seconds after leaving when it becomes the same area at next time.
(2) Find the area of the triangle CPQ 116 seconds after P and Q leave.
(3) There is a time when the area of the portion excluding the triangle CPQ from the circle is to be 107.04 cm2.
Find the number of seconds after P and Q leave when it becomes this area at 6th times.
Pi is assumed to be 3.14.
Problem 13
There is A town on the top of the mountain and B town at the foot of the mountain.
Hanako left A town and Taro left B town at the same time and they went back and forth one time without taking rest between A and B.
They met first at intermediate C point.
And they met again at D point where is 560 m from C point 74 minutes afterward.
Hanako and Taro go up and down the mountain with the same speed.
The ratio of the speed of going up and down is 5 : 7.
(1) Find the distance of A town and B town.
(2) Find the speed per minute of going up the mountain.
