AZABU-2008

Time : 60 minutes

Passing mark : 70 %

Answer

Problem 1

6 - 121/13 / {39.2 - 189/4 × (2/3 - 1/5) / 0.7} × 4.9 =

Problem 2

There are three kinds of salt solutions A, B, and C weigh 60 g, 120 g, and 100g, respectively.

The salt concentration of A is 3%.

① When 20g of A and 30g of B are mixed, the salt concentration of salt solution is same as C.

② The salt concentration of salt solution D made by mixing A, B, and C altogether is to be 7.5%.

Answer the following questions.

The salt concentration of a salt solution is a ratio of the weight of salt to the weight of a salt solution.

(1) Find the weight of the salt contained in D.

(2) Find the salt concentration (%) of B.

(3) Find the salt concentration (%) of C.

Problem 3

There are A station and B station and another station C is between A and B.

Train X will leave A station at 23:10 and will arrive at intermediate C station at 2:10 on the next day.

After stopping for 20 minutes, train X will leave C station at 2:30 and it will arrive at B station at 6:10.

The speed of this train is 2.675 km per hour faster than the speed which is calculated the distance between A and B is divided by 7 hours which is actual time taken from A to B.

Find the distance of A station and B station.

Problem 4

Either the sign + of addition or the sign × of multiplication is put in the following [ ] and calculate.

Answer the following questions.

(1) When 1[ ]2[ ]3[ ]4 is calculated, Answer each calculation result to small order.

When there come out same calculation results, write only once.

(2) Answer two kinds of manner putting in + and × applicable to [ ] of the following formula.

1[ ]2[ ]3[ ]4[ ]5 = 2[ ]3[ ]4[ ]5[ ]6

Problem 5

There is a rectangular prism 3 cm in length, 4 cm in width and 5 cm in height.

As for faces of this rectangular prism, the face of the rectangle with 3cm and 4cm side is set to face A, the face with 4cm and 5cm is set to face B and the face with 5cm and 3cm is set to face C.

Answer the following questions.

(1) Make small rectangular prisms by cutting with planes which are parallel to face A, face B and face C, once, once and twice respectively.

① Find the number of small rectangular prism.

② Find the sum total of the surface area of these small rectangular prisms.

Noted that the surface area of a rectangular prism is the sum total of the area of all the faces of the rectangular prism.

(2) This rectangular prism was cut with planes which are parallel to face A, face B and face C, X times, Y times and Z times respectively.

In this case, there are 90 small rectangular prisms made and the sum total of the surface area of these rectangular prisms was 462 cm².

Find the number applicable to X, Y, and Z.

Problem 6

There is the sector OAB which is 1/4 part a circle.

Answer the following questions.

(1) Find the ratio of the area of a shadow area and the sector OAB in Fig. 1.

Noted that the straight lines OA, CD, and EF are parallel.

(2) As shown in Fig. 2, the straight line parallel to OA was drawn from each point which divided the arc AB of the sector OAB into five equally. OA is 5 cm.

Find the sum of the area of two shadow areas.

Pi is assumed to be 3.14.