Math New Drill : Level 2 Geometry(Plane figure) Problem5 KAMAKURAJOGAKUIN-2014

Point P leaves vertex A and moves straight the inside of the square of one side of 80cm according to the next rule.

< Rule >
・ When P hits each side, it rebounds.
・ When P hits each vertex, it stops.

As shown in the Fig.1 below, the angle point P hits is set to X and the angle P rebounds is set to Y.



Answer to the following questions.

(1) Y is equal to X and point P rebounds at the position of 30 cm from vertex B.
Which is the vertex that is the nearest to the position where P rebounds at the fourth time?
In addition, find the distance from the vertex.

(2) In the case of (1), how many times does P rebound before it stops?

(3) Y is half of X. The locus before P rebounds at fourth time became as shown in the Fig.2 below.
Find the angle of Z.

Math New Drill : Level 1 : Graph of Velocity Problem4 KAMAKURAJOGAKUIN-2014

In order to go from a house to school, Hanako walks from the house to the bus stop first.
She takes a bus from there and walks again after she gets off the bus.
For a while after Hanako left the house, her mother noticed s thing left behind and ran after the same way by car.
Then both of them have arrived at school at the same time.
Below is the graph which showed time and distance between Hanako and her mother after Hanako left the house.
Speed Hanako walks and speed of the bus and the car are fixed respectively.
She did not wait for a bus at a bus stop.




Answer the following questions.

(1) Find the speed per minute Hanako walks and the speed per minute of the bus respectively.

(2) Find the distance from the house to the school.

(3) Find the speed per hour of the car.

Math New Drill : Level 1 : Geometry(Plane figure) Problem3(4) KAMAKURAJOGAKUIN-2014

There is a rectangle A whose ratio between length and width is 3 : 5.
The length of this rectangle A is lengthened by 6cm and the width is shortened by 4 cm to be a rectangle B.
The ratio between length and width of the rectangle B became 9 : 8.
Find the vertical length rectangle A.
Moreover, find an area ratio of rectangle A and B with the least integer.

Math New Drill : Level 1 : Velocity Problem3(3) KAMAKURAJOGAKUIN-2014

Train A at a speed of 1,200m per minute has begun to enter a certain tunnel.
Train B of 1,500m per minute has begun to enter at the opposite side eight seconds later.
The top of train A and B came across in the middle of the tunnel.
Train B completely left the tunnel one minute 17 seconds later after train A began to enter the tunnel.
Find the length of this tunnel and the length of train B.

Math New Drill : Level 1 : Ratios and proportions Problem3(2) KAMAKURAJOGAKUIN-2014

Mother's age is 5 times of the daughter's age now.
Four years later, mother's age becomes less 4 years less than 4 times of the daughter's age.
Find the the daughter's age now.
In addition, how many years later from now does the mother's age become 4 years less than 3 times of the daughter's age?

New Drill : Level 1 : Sum and difference Problem3(1) KAMAKURAJOGAKUIN-2014

40 students played a game.
The score was either two points, four points, six points or ten points.
There were four people who had two points and eight people who had ten points.
The average score was 5.8 points.
Find the number of people who had four points and six points.

Math New Drill : Level 1 Geometry (Plane figure) Problem2(5) KAMAKURAJOGAKUIN-2014

The figure below is a figure overlapping three rectangular papers with 3cm in length and 15cm in width. 

The area of the shadow is 102 cm². 

Find the total length of bold lines.

Math New Drill : Level 1 Geometry (Plane figure) Problem2(4) KAMAKURAJOGAKUIN-2014

The figure below is a graphic that is a combination of square and sector. 

Find the difference of the area of A and B. 

Pi is assumed to be 3.14.

Math New Drill : Level 1 Number sense and theory Problem2(3) KAMAKURAJOGAKUIN-2014

When the number of tens digit of double digits integer is subtracted from the number of ones digit, it becomes five.
As for the number that replaced the number of tens digit and ones digit, it becomes bigger by seven than the double of the original integer.
Find this integer.

Math New Drill : Level 1 Ratio and Proportions Problem2(2) KAMAKURAJOGAKUIN-2014

When a consumption tax of 5% is added to the price of a certain goods, it'll be 2014 yen.
Noted that less than 1 yen of the amount of the consumption tax is cut off.
Find the price of this book.

Math New Drill : Level 1 Ratio and Proportions Problem2(1) KAMAKURAJOGAKUIN-2014

Taro began to read a certain book by 7 pages a day and Jiro began by 5 pages a day.
They started reading at the same time.
On the day when Taro finished reading, there still 114 pages were left for Jiro.
Find the pages of this book.