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Time : 50 minutes
Passing mark : 70%
Problem 1
Find X.
1/17 - X/2006 = (2/17 + 17/59) × 1/22
Problem 2
Three different numbers are selected and put in order from four different numbers 1, 3, X, and 9 so that the integer of triple figures is made.
The number of triple figures is 24 pieces and the average is 555.
Find X.
Problem 3
The distance between A point and B point is 10 km.
Taro walks from A point at 4 km/h to B point.
He walks for 30 minutes and take a rest for 5 minutes and he repeat this time cycle.
Jiro goes to A point from B point at 12 km/h by a bicycle without taking a rest and return to B point.
Taro and Jiro left at the same time.
Find the time (time after they left) for Jiro to pass Taro.
Moreover, find the distance from A point to the point Jiro passed.
Problem 4
The questionnaire survey was conducted on 40 sixth graders in an elementary school.
The questionnaire was as for three subjects, language, mathematics (Sansue) and science, if they like it, mark ○, if they do not like it, mark ×.
The grand total of ○ was 100 and that of × was 20.
There was no pupil who marked × to all three subjects.
There are 35 pupils who marked ○ to mathematics.
Among these, there are two pupils who marked ○ only to mathematics and four students who marked × to mathematics and ○ to science.
Answer the following questions.
(1) Find the number of the pupil who marked ○ only to language.
(2) Find the number of pupil at most who marked ○ to all three subjects.
Problem 5
There is an integer of 5 figures which is a multiple of 36.
In addition, the integer contains 2, 3 and 5 in either digit.
For example, it is 53928 etc.
Find the smallest number in such integers.
Problem 6
When 100 is divided by 35, a quotient is 2 and remainder is 30.
When 100 is divided by 40, a quotient is 2 and remainder is 20.
Find the number of three digits integer including 100 which a quotient becomes the same, when it is divided by 35 and 40.
And also find the largest integer among them.
Problem 7
As for the admission ticket of a certain theater, the advance tickets and the day tickets are available at a rate of 7 : 3.
The advance tickets are on sale three weeks before to the previous day and the day tickets are on sale 2 hours before opening of the performance.
The day ticket audience of one day began to stand in a line 3 hours before opening and joined the sequence four persons per one minute.
The day tickets were sold at a sales window of the theater to six persons per one minute.
Answer the following questions.
(1) How many day tickets audience had stood in a line 10 minutes before opening of the performance?
(2) How many minutes did the person take to enter the theater who is the day tickets visitor and was in the 120th from the beginning of the line?
(Find the time this person was in the line.)
(3) Before opening of the performance, ten percent of scheduled number of the advance tickets remained unsold and 80 percent of schedule number of of the day tickets were sold.
Find the total number of audience this day.
Problem 8
In trapezoid ABCD as shown in a figure, the point O is an intersection of a diagonal line.
The area of △ AOB is 10 cm2 and △ BOC is 25 cm2.
Find the area of trapezoid ABCD.
Problem 9
Fig. 1 and Fig. 2 are development views of the cube in which the numbers from 1 to 6 were written to each face.
It is considered that the sum of numbers written to three faces gathering in the one vertex of each cube.
As for Fig.1, the greatest sum of numbers is 15.
In the case of Fig. 2, find the greatest sum of numbers.
Problem 10
As shown in a figure, there are the right hexagon ABCDEF and a right heptagon ABGHIJK.
Find the angle of X and Y.
Problem 11
As shown in the figure, five pieces equilateral triangle of the same size are put in order without a gap.
Among quarters point of BC, point D is the point closest to the B.
The length of AE is 9 cm.
Find the length of AD.
Problem 12
Triangle ABC is a right triangle of AB = 18 cm, AC = 24 cm and BC = 30 cm.
The points P and Q are points on the bisectors of angle B and angle C, respectively.
PQ is parallel to BC. PH and AB, QK and AC are vertical respectively.
The area of pentagon AHPQK is half of the area of triangle ABC.
Find the length of PH and the length of PQ.
Problem 13
The shadow portion in the figure is made of cutting off four isosceles triangles 2cm in height from the square which is 8 cm one side.
Find the volume of the quadrangular pyramid made by assembling this development.
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